The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: Bobby Shafto on November 19, 2018, 11:29:32 PM
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https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns)
Predicting solar eclipses "with at least an approximation to the truth" is a low bar.
How are types of solar eclipses, duration of the eclipse and locations from whence solar eclipses will be visible predictable if it's but pattern-based?
Surely, to make accurate predictions of solar eclipses, and not merely approximations to the truth, requires much more understanding than "patterns."
There is quite a bit of detail in this description of the next solar eclipse (https://www.timeanddate.com/eclipse/solar/2019-january-6). That's not merely "pattern based." It requires an understanding of the motions of the earth and moon, relative to the sun in order to develop sufficiently accurate ephemerides to predict not just when a solar eclipse will happen but when it will begin, end, where it will be visible, partial or total (or annular).
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Go to NASA Eclispe Web Site (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Resources (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Eclipses and the Soros (https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html)
The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well.
NASA is describing that they are predicting the eclipses based on the ancient Saros Cycle as used by the Ancient Babylonians. They are not describing that they are using a Three Body Problem model of the Sun-Earth-Moon system.
Why would NASA be using ancient methods that are thousands of years old, created by a society of people who believed that the earth was flat, if there are modern methods that can predict the location of the earth, moon and sun based on Newtonian or Einsteinian laws? We should be reading about how they are solving the Three Body Problem, not about ancient methods. The word Saros and Saros Cycle appears all throughout that website, many times, and not one word about the Three Body Problem.
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Everything in astronomy is predicted on basis of patterns. Samuel Birley Rowbotham describes this in Earth Not a Globe. At the end of Chapter 11 (http://www.sacred-texts.com/earth/za/za29.htm) Rowbotham provides a complex set of equations to find the time, magnitude, and duration of a Lunar Eclipse and explains that these equations add nothing to our knowledge of the eclipses, but is merely a mathematical instrument based on repeating occurrences to predict a future event.
Those who are unacquainted with the methods of calculating eclipses and other phenomena, are prone to look upon the correctness of such calculations as powerful arguments in favour of the doctrine of the earth's rotundity and the Newtonian philosophy, generally. One of the most pitiful manifestations of ignorance of the true nature of theoretical astronomy is the ardent inquiry so often made, "How is it possible for that system to be false, which enables its professors to calculate to a second of time both solar and lunar eclipses for hundreds of years to come?" The supposition that such calculations are an essential part of the Newtonian or any other theory is entirely gratuitous, and exceedingly fallacious and misleading. Whatever theory is adopted, or if all theories are discarded, the same calculations can be made. The tables of the moon's relative positions for any fraction of time are purely practical--the result of long-continued observations, and may or may not be connected with hypothesis. The necessary data being tabulated, may be mixed up with any, even the most opposite doctrines, or kept distinct from every theory or system, just as the operator may determine.
...The simplest method of ascertaining any future eclipse is to take the tables which have been formed during hundreds of years of careful observation; or each observer may form his own tables by collecting a number of old almanacks one for each of the last forty years: separate the times of the eclipses in each year, and arrange them in a tabular form. On looking over the various items he will soon discover parallel cases, or "cycles" of eclipses; that is, taking the eclipses in the first year of his table, and examining those of each succeeding year, he will notice peculiarities in each year's phenomena; but on arriving to the items of the nineteenth and twentieth years, he will perceive that some of the eclipses in the earlier part of the table will have been now repeated--that is to say, the times and characters will be alike. If the time which has elapsed between these two parallel or similar eclipses be carefully noted, and called a "cycle," it will then be a very simple and easy matter to predict any future similar eclipse, because, at the end of the "cycle," such similar eclipse will be certain to occur; or, at least, because such repetitions of similar phenomena have occurred in every cycle of between eighteen and nineteen years during the last several thousand years, it may be reasonably expected that if the natural world continues to have the same general structure and character, such repetitions may be predicted for all future time. The whole process is neither more nor less--except a little more complicated--than that because an express train had been observed for many years to pass a given point at a given second--say of every eighteenth day, so at a similar moment of every cycle or eighteenth day, for a hundred or more years to. come, the same might be predicted and expected. To tell the actual day and second, it is only necessary to ascertain on what day of the week the eighteenth or "cycle day" falls.
Tables of the places of the sun and moon, of eclipses, and of kindred phenomena, have existed for thousands of years, and were formed independently of each other, by the Chaldean, Babylonian, Egyptian, Hindoo, Chinese, and other ancient astronomers. Modern science has had nothing to do with these; farther than rendering them a little more exact, by averaging and reducing the fractional errors which a longer period of observation has detected.
As an instance of the complicated process into which modern theorists have allowed themselves to "drift," the following formula is here introduced:--
<equations to find the time, magnitude, and duration of a lunar eclipse>
The formulæ above quoted are entirely superfluous, because they add nothing to our knowledge of the causes of eclipses, and would not enable us to predict anything which has not hundreds of times already occurred. Hence all the labour of calculation is truly effort thrown away, and may be altogether dispensed with by adopting the simple process referred to at page 153, and calling that which eclipses the moon the "lunar eclipsor," or the moon's satellite, instead of the "earth's shadow," just as the moon is the sun's eclipsor.
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Cyclic patterns of periodicity tell you when, not where.
So, how can you predict where the moon's shadow (or, if not the moon, then some other celestial body's shadow) will be cast on the face of the earth based on past patterns?
As far as I can tell, the "ancients" never had enough data to predict where a solar eclipse would be seen. Even today, that wouldn't be possible based simply on patterns of the timing of past eclipses, including the Saros cycle. That's could only be possible by understanding the motion of the bodies; and not to the precision necessary to solve an n-body problem. But pattern periodicity is not sufficient nor accurate to anymore more than prediction windows. Now, it's much more precise than that because we understand the motion of the bodies much more than did "the ancients."
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How do they predict the Solar Eclipse? Lets go to their Solar Eclipse website (https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html):
1.4 Saros
The Saros arises from a harmonic between three of the Moon's orbital cycles. All three periods are subject to slow variations over long time scales, but their current values (2000 CE) are:
Synodic Month (New Moon to New Moon) = 29.530589 days = 29d 12h 44m 03s
Anomalistic Month (perigee to perigee) = 27.554550 days = 27d 13h 18m 33s
Draconic Month (node to node) = 27.212221 days = 27d 05h 05m 36s
One Saros is equal to 223 synodic months, however, 239 anomalistic months and 242 draconic months are also equal (within a few hours) to this same period:
223 Synodic Months = 6585.3223 days = 6585d 07h 43m
239 Anomalistic Months = 6585.5375 days = 6585d 12h 54m
242 Draconic Months = 6585.3575 days = 6585d 08h 35m
With a period of approximately 6,585.32 days (~18 years 11 days 8 hours), the Saros is valuable tool in investigating the periodicity and recurrence of eclipses. It was first known to the Chaldeans as an interval when lunar eclipses repeat, but the Saros is applicable to solar eclipses as well.
(https://eclipse.gsfc.nasa.gov/SEsaros/image/Fig1a.GIF)
Figure 1 Eclipses from Saros 136: 1901 to 2045
(click for larger figure)
Any two eclipses separated by one Saros cycle share similar characteristics. They occur at the same node with the Moon at nearly the same distance from Earth and at the same time of year. Because the Saros period is not equal to a whole number of days, its biggest drawback as an eclipse predictor is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120° with each cycle. For solar eclipses, this results in a shift of each succeeding eclipse path by ~120° west. Thus, a Saros series returns to approximately the same geographic region every three Saros periods (~54 years and 34 days). This triple Saros cycle is known as the Exeligmos. Figure 1 shows the path of totality for nine eclipses belonging to Saros 136. This series is of particular interest because it is currently producing the longest total eclipses of the 20th and 21st centuries. The westward migration of each eclipse path from 1901 through 2045 illustrates the consequences of the extra 1/3 day in the Saros period. The northward shift of each path is due to the progressive increase in gamma from -0.3626 (in 1901) to 0.2116 (in 2045). The color figure Recent Eclipses of Saros 136 shows nine eclipse paths from the series (1937 through 2081).
Saros series do not last indefinitely because the synodic, draconic, and anomalistic months are not perfectly commensurate with one another. In particular, the Moon's node shifts eastward by about 0.48° with each eclipse in a series. The following narrative describes the life cycle of a typical Saros series at the Moon's descending node. The series begins when the New Moon occurs ~17° east of the node. The Moon's umbral/antumbral shadow passes about 3500 km south of Earth and a small partial eclipse will be visible from high southern latitudes. One Saros period later, the umbra/antumbra passes ~250 km closer to Earth's geocenter (gamma increases) and a partial eclipse of slightly larger magnitude will result. After about 10 Saros cycles (~200 years), the first umbral/antumbral eclipse occurs near the South Pole of Earth. Over the course of the next 7 to 10 centuries, a central eclipse occurs every 18.031 years (= Saros), but will be displaced northward by about 250 km with respect to Earth's center. Halfway through this period, eclipses of long duration occur near the equator (mid-series eclipses may be of short duration if hybrid or nearly so). The last central eclipse of the series takes place at high northern latitudes. Approximately 10 more eclipses will be partial with successively smaller magnitudes. Finally, the Saros series ends 12 to 15 centuries after it began at the opposite pole.
(https://eclipse.gsfc.nasa.gov/SEsaros/image/Fig2a.GIF)
Figure 2 Eclipses from Saros 136: 2117 to 2261
(click for larger figure)
Based on the above description, the path of each umbral/antumbral eclipse should shift uniformly north in latitude after every Saros period. As Fig. 2 shows, this is not always the case. Nine members from Saros 136 are plotted for the years 2117 through 2261. Although the paths of previous eclipses in this series were shifting progressively northward (Figure 1), the trend here is reversed and the paths shift south. This temporary effect is due to the tilt of Earth's axis combined with the passage of Saros 136 eclipses from the Northern Hemisphere's autumnal equinox through winter solstice. Note that the season for this group of eclipses runs from September through December. With each successive eclipse, Earth's Northern Hemisphere tips further and further away from the Sun. This motion shifts geographic features and circles of latitude northward with respect to the Sun-Earth line at a rate that is faster than the change in gamma. Consequently, the eclipse paths appear to shift south in latitude until the winter solstice when they again resume a northward trend.
The scenario for a Saros series at the ascending node is similar except that gamma decreases as each successive eclipse shifts south of the previous one. The southern latitude trend in eclipse paths reverses to the north near the Northern Hemisphere summer solstice.
Because of the ellipticity of the orbits of Earth and the Moon, the exact duration and number of eclipses in a complete Saros series is not constant. A series may last 1,226 to 1,551 years and is composed of 69 to 87 eclipses, of which 39 to 59 are umbral/antumbral (i.e., annular, total, or hybrid). At present (2008), there are 39 active Saros series numbered 117 to 155. The number of eclipses in each of these series ranges from 70 to 82, however, the majority of the series (84.6%) are composed of 70 to 73 eclipses.
Historically speaking, the word Saros derives from the Babylonian term "sar" which is an interval of 3600 years. It was never used as an eclipse period until English astronomer Edmund Halley adopted it in 1691. According to R. H. van Gent, Halley "...extracted it from the lexicon of the 11th-century Byzantine scholar Suidas who in turn erroneously linked it to an (unnamed) 223-month Babylonian eclipse period mentioned by Pliny the Elder (Naturalis Historia II.10[56])."
The page talks egregiously about the Saros Cycle, which is the ancient method of predicting the eclipses.
The Solar Eclipse appears as a little line on the earth, since it is only seen on a narrow path between the sun and moon, and not to everyone. There is also a dynamic component. It moves over time, and can be computed based on the Saros Cycle: "Based on the above description, the path of each umbral/antumbral eclipse should shift uniformly north in latitude after every Saros period." Comments are made of 'because of the tilt of the earth', but the Flat Earth model has an analogue to that as well. We can see that the entirety of this is based on pattern of occurrences, movement, etc. It is not a dynamic Sun-Earth-Moon Round Earth system.
The ancients may not have had enough data to predict world-wide occurrences, but as Rowbotham says, "modern astronomers" have merely improved on the ancient pattern-finding methods.
Surely, if there were a modern way of predicting the eclipse through the computation of a heliocentric or round earth system, it would be used. The fact that we are reading about the ancient flat earth Saros Cycle on NASA's own website, speaks volumes. It vindicates Rowbotham and entirely discredits modern astronomy.
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003
Maybe someone better do a little more homework before making statements. There are folks that can use Newtonian mechanics to predict what the tables do. Again, you could go back to Rowbotham and try to apply his statement at the end of Chapter 11. However I feel that something has been learned this time. Equations are just nothing more than relationships between things. With modern computers you could use the Newtonian equations to describe the relationships between all the bodies. If these equations accurately predict some observable event then it will give some credence to the relationships described in the equations. Is there anyone who wants to bet that NASA already has either this set of equations or more likely something that they have independently developed themselves? It is never wise for an amateur to bet against a professional.
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003
Maybe someone better do a little more homework before making statements. There are folks that can use Newtonian mechanics to predict what the tables do. Again, you could go back to Rowbotham and try to apply his statement at the end of Chapter 11. However I feel that something has been learned this time. Equations are just nothing more than relationships between things. With modern computers you could use the Newtonian equations to describe the relationships between all the bodies. If these equations accurately predict some observable event then it will give some credence to the relationships described in the equations. Is there anyone who wants to bet that NASA already has either this set of equations or more likely something that they have independently developed themselves? It is never wise for an amateur to bet against a professional.
Please find anything like those equations in NASA's very detailed descriptions on how they compute the eclipses. Newton's equations are not used. Newton's equations are just a cartoon, and cannot simulate the Sun-Earth-Moon system. It falls apart very quickly.
The author of that paper appears to be reverse engineering an example of the Saros Cycle with a load of his own personal math designed to declare that he solved it and came up with a value that was close. At the end he admits to using something similar to dimensional analysis to find his desired result; it is not a dynamical result. Its utility is likely nill.
He even claims in his introduction that he is the first ever to use Newton's equations for the eclipse! Wow. Show where this work has been used in any application. You have presented me a paper with equations, by someone claiming to have found a match to a number in the Saros Cycle. I have presented an organization that is actually predicting the eclipses. Nothing like those equations are used.
If anyone really has solved the Three Body Problem, it is a guaranteed Nobel Prize. The Three Body Problem and the failure to simulate even the simplest heliocentric system with Newton's laws has eluded the greatest minds for hundreds of years.
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003
Maybe someone better do a little more homework before making statements. There are folks that can use Newtonian mechanics to predict what the tables do. Again, you could go back to Rowbotham and try to apply his statement at the end of Chapter 11. However I feel that something has been learned this time. Equations are just nothing more than relationships between things. With modern computers you could use the Newtonian equations to describe the relationships between all the bodies. If these equations accurately predict some observable event then it will give some credence to the relationships described in the equations. Is there anyone who wants to bet that NASA already has either this set of equations or more likely something that they have independently developed themselves? It is never wise for an amateur to bet against a professional.
Please find anything like those equations in NASA's very detailed descriptions on how they compute the eclipses. Newton's equations are not used. Newton's equations are just a cartoon, and cannot simulate the Sun-Earth-Moon system. It falls apart very quickly.
The author of that paper appears to be reverse engineering an example of the Saros Cycle with a load of his own pointless math designed to declare that he solved it and came up with a value that was close. If it wasn't close, he just added more equations where it became close to a desired value. That's how it works in that world. Its utility is likely nill.
He even claims in his introduction that he is the first ever to use Newton's equations for the eclipse! Wow. Show where this work has been used in any application.
If anyone really has solved the Three Body Problem, it is a guaranteed Nobel Prize. The Three Body Problem and the failure to simulate even the simplest heliocentric system with Newton's laws has eluded the greatest minds for hundreds of years.
You have presented me a paper with equations, by someone claiming to have found a match to a number in the Saros Cycle. I have presented an organization that is actually predicting the eclipses. Nothing like those equations are used.
Physicists Discover a Whopping 13 New Solutions to Three-Body Problem
By Jon CartwrightMar. 8, 2013 , 4:30 PM
https://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem
Home News Physics Space
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Daily news
20 September 2017
Infamous three-body problem has over a thousand new solutions
https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/
I'd also like to point out that your dates and comment about Babylon and the Saros familyof Cycles is inaccurate.
History books claim that Babylon threw out FET in favor of RET before they could apply the Saros Cycles to anything accurate.
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Here are some selected quoted from that New Scientist article you posted: "Infamous three-body problem has over a thousand new solutions" (https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/)
The new solutions were found when researchers at Shanghai Jiaotong University in China tested 16 million different orbits using a supercomputer.
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Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane.
Knot-like paths
In addition, the researchers did not test the orbits’ stability. It’s possible that the tiniest disturbance in space or rounding error in the equations could rip the objects away from one another.
“These orbits have nothing to do with astronomy, but you’re solving these equations and you’re getting something beautiful,” says Vanderbei.
...
Aside from giving us a thousand pretty pictures of knot-like orbital paths, the new three-body solutions also mark a starting point for finding even more possible orbits, and eventually figuring out the whole range of winding paths that three objects can follow around one another.
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“This is kind of the zeroth step. Then the question becomes, how is the space of all possible positions and velocities filled up by solutions?” says Richard Montgomery at the University of California, Santa Cruz. “These simple orbits are kind of like a skeleton to build the whole system up from.”
As plainly stated, the stable orbits that can be found have nothing that looks like heliocentric astronomy. The system, at its very basic level, is unable to be created.
The "thousands of stable solutions" are scenarios where the bodies have the same mass or where one of the bodies is mass-less. All of these scenarios are incredibly sensitive, and none represent anything that looks like a heliocentric system. They are crazy loopy orbits, based on situations that would not happen in nature, and which fall apart with the slightest touch.
As admitted, astronomy is still in the stone age. They are on the zeroth step.
Do you want to know why they are on the zeroth step? It is simply because the heliocentric system and the laws of newton do not actually work. Would New Scientist be trumpeting a triumphant victory of coming up with crazy three-body orbits that would not exist in nature if this science were truly mature? The triumphant victory is that they were able to come up with these unrealistic orbits. This research will be used to search for hints for getting the basic system of Copernicus and Newton working at all...
The state of modern astronomy is actually quite sad.
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Well, again, it looks like you are consulting with people who don't know how to solve a problem. It's time you look at the people who actually can. My link was to a person who had all the equations that described the motions of the Sun, Moon, and Earth. These equations are able to predict when an eclipse will occur. That should be a pretty good confirmation that everything is correct. Of course everything is based upon the Earth orbiting the Sun and the Moon orbiting the Earth. That totally anathema to the beliefs on this site. There's really nothing I can do about that. The best you can do is show that the results are invalid or the math is incorrect. Denial really isn't a river in Egypt.
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Read above Ron, an astronomer just admitted that the state of astronomy is in the stone age. The belief that modern astronomy is sophisticated or advanced in any manner is false. It is a farce.
Poliastro, an astrodynamics software developer, shared an image of the most state of the art methods in the field of Celestial Mechanics for simulating the Sun-Earth-Moon System on basis of the restricted three body problem (where one of the bodies is massless).
https://twitter.com/poliastro_py/status/993418078036873216?lang=en
Look at this beautiful plot of several numerical methods for the restricted three body problem taken from Harier et al. "Solving Ordinary Differential Equations I". The use of high order Runge-Kutta methods is pervasive in Celestial Mechanics. Happy Monday!
(https://pbs.twimg.com/media/DclUYMPXcAEOCUF.jpg)
Does this look like the heliocentric system you were taught in school?
Do you think that, if there were a "real" way to run this model, that this image would even exist and we would be simulating such things?
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The diagram was probably one of the unsuccessful attempts of an astronomer made to describe a 3 body problem. Maybe he had better luck after a few more adjustments to the parameters. It's a similar argument you made last week with an amateur radio operator not being able to bounce a signal off the moon. Of course others can and do on a regular basis. There are mathematicians who have solved the 3 body problem 100 years ago and I gave links to those names. Just about all of them are known to me and I studied their works years ago in my engineering math classes. I would like to give some of them a 'swift kick' because their equations are hard to understand, but when they are, they work as advertised. It has been said that everyone is useful for something. Some are useful as a bad example. It's always best to pay attention to the ones who are good examples.
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I will never understand (unless it's a willful attempt to deceive) why Tom always wants to start at the Saros cycles. The page you guys want is this one: https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html
The information you want is located under the header 'predictions' which is thus:
The coordinates of the Sun used in these predictions are based on the VSOP87 theory [Bretagnon and Francou, 1988]. The Moon's coordinates are based on the ELP-2000/82 theory [Chapront-Touze and Chapront, 1983]. For more information, see: Solar and Lunar Ephemerides (https://eclipse.gsfc.nasa.gov/SEcat5/ephemeris.html). The revised value used for the Moon's secular acceleration (https://eclipse.gsfc.nasa.gov/SEcat5/secular.html) is n-dot = -25.858 arc-sec/cy*cy, as deduced from the Apollo lunar laser ranging experiment (Chapront, Chapront-Touze, and Francou, 2002).
The largest uncertainty in the eclipse predictions is caused by fluctuations in Earth's rotation (https://eclipse.gsfc.nasa.gov/SEhelp/rotation.html) due primarily to tidal friction of the Moon. The resultant drift in apparent clock time is expressed as ΔT (https://eclipse.gsfc.nasa.gov/SEcat5/deltat.html) and is determined as follows:
pre-1950's: ΔT calculated from empirical fits to historical records derived by Morrison and Stephenson (2004)
1955-present: ΔT obtained from published observations
future: ΔT is extrapolated from current values weighted by the long term trend from tidal effects
A series of polynomial expressions (https://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html) have been derived to simplify the evaluation of ΔT for any time from -1999 to +3000. The uncertainty in ΔT (https://eclipse.gsfc.nasa.gov/SEcat5/uncertainty.html) over this period can be estimated from scatter in the measurements.
I've never been able to locate the source(s) reference by that work and others, but I've also never dug particularly hard into it. Feel free, maybe you'll dig up more.
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I took a quick look at the link you gave. It's interesting to note some of the sources for the data used in the equations. One was the laser reflector placed upon the moon. Of course this device is used by the astronomers use precisely measure this distance between the Moon and Earth. This distance, of course, changes just a bit all the time because the Earth-Moon system is not static, it's dynamic with all the small changes that happen continuously with the Moon and Earth. Of course with the equipment used the distance to the moon is known to the centimeter. Again this is totally anathema to the premises of this site, but I am not responsible for the information. It's just the best information available. Probably everything is reduced to a computer program where all the numbers are 'crunched' on a continuous basis as new data comes in.
As the saying goes: "Never start a knife-fight with a man holding a gun"
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How do they predict the Solar Eclipse? Lets go to their Solar Eclipse website (https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html)
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You linked to a page about periodicity of solar eclipses. Even so, that page concedes that the Saros cycle is but a useful tool and "modern digital computers using high precision solar and lunar ephemerides can directly predict the dates and circumstances of eclipses." (emphasis mine).
The predictive methods including location, duration, type and not just when is here (https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html).
(Curious Squirrel beat me to it.)
Excerpt:
(http://oi67.tinypic.com/wmk185.jpg)
What's the analog in a flat earth model for sun and moon coordinates?
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Here are some selected quoted from that New Scientist article you posted: "Infamous three-body problem has over a thousand new solutions" (https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/)
The new solutions were found when researchers at Shanghai Jiaotong University in China tested 16 million different orbits using a supercomputer.
...
Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane.
Knot-like paths
In addition, the researchers did not test the orbits’ stability. It’s possible that the tiniest disturbance in space or rounding error in the equations could rip the objects away from one another.
“These orbits have nothing to do with astronomy, but you’re solving these equations and you’re getting something beautiful,” says Vanderbei.
...
Aside from giving us a thousand pretty pictures of knot-like orbital paths, the new three-body solutions also mark a starting point for finding even more possible orbits, and eventually figuring out the whole range of winding paths that three objects can follow around one another.
...
“This is kind of the zeroth step. Then the question becomes, how is the space of all possible positions and velocities filled up by solutions?” says Richard Montgomery at the University of California, Santa Cruz. “These simple orbits are kind of like a skeleton to build the whole system up from.”
As plainly stated, the stable orbits that can be found have nothing that looks like heliocentric astronomy. The system, at its very basic level, is unable to be created.
The "thousands of stable solutions" are scenarios where the bodies have the same mass or where one of the bodies is mass-less. All of these scenarios are incredibly sensitive, and none represent anything that looks like a heliocentric system. They are crazy loopy orbits, based on situations that would not happen in nature, and which fall apart with the slightest touch.
As admitted, astronomy is still in the stone age. They are on the zeroth step.
Do you want to know why they are on the zeroth step? It is simply because the heliocentric system and the laws of newton do not actually work. Would New Scientist be trumpeting a triumphant victory of coming up with crazy three-body orbits that would not exist in nature if this science were truly mature? The triumphant victory is that they were able to come up with these unrealistic orbits. This research will be used to search for hints for getting the basic system of Copernicus and Newton working at all...
The state of modern astronomy is actually quite sad.
I reread those articles and couldn't find anything in them that remotely matched your interpretation of them
It appears you cherry pick sentences and take the entirety of the articles out of context, add your own assumptions to in an attempt to discredit them or make them fit your own views.
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I will never understand (unless it's a willful attempt to deceive) why Tom always wants to start at the Saros cycles. The page you guys want is this one: https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html
The information you want is located under the header 'predictions' which is thus:
The coordinates of the Sun used in these predictions are based on the VSOP87 theory [Bretagnon and Francou, 1988]. The Moon's coordinates are based on the ELP-2000/82 theory [Chapront-Touze and Chapront, 1983]. For more information, see: Solar and Lunar Ephemerides (https://eclipse.gsfc.nasa.gov/SEcat5/ephemeris.html). The revised value used for the Moon's secular acceleration (https://eclipse.gsfc.nasa.gov/SEcat5/secular.html) is n-dot = -25.858 arc-sec/cy*cy, as deduced from the Apollo lunar laser ranging experiment (Chapront, Chapront-Touze, and Francou, 2002).
The largest uncertainty in the eclipse predictions is caused by fluctuations in Earth's rotation (https://eclipse.gsfc.nasa.gov/SEhelp/rotation.html) due primarily to tidal friction of the Moon. The resultant drift in apparent clock time is expressed as ΔT (https://eclipse.gsfc.nasa.gov/SEcat5/deltat.html) and is determined as follows:
pre-1950's: ΔT calculated from empirical fits to historical records derived by Morrison and Stephenson (2004)
1955-present: ΔT obtained from published observations
future: ΔT is extrapolated from current values weighted by the long term trend from tidal effects
A series of polynomial expressions (https://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html) have been derived to simplify the evaluation of ΔT for any time from -1999 to +3000. The uncertainty in ΔT (https://eclipse.gsfc.nasa.gov/SEcat5/uncertainty.html) over this period can be estimated from scatter in the measurements.
I've never been able to locate the source(s) reference by that work and others, but I've also never dug particularly hard into it. Feel free, maybe you'll dig up more.
What are you pointing me to look at? It says that the coordinates from the sun and the moon come from other models. Are you just posting the names of models and blindly expecting us to assume that it is all based on a Round Earth Heliocentric System? That certainly appears to be your tactic. Deceptive.
It absolutely is not based on a Round Earth model or a Heliocentric System.
The first model for the sun comes from VSOP, which is addressed in our wiki link Bobby provided in the OP:
VSOP
VSOP (French: Variations Séculaires des Orbites Planétaires) is a popular software package used to generate planetary ephemeris, the position of astronomical objects in the sky. It is used in astronomy software such as Stellarium and Celestia. It has been alleged that VSOP uses a geometric RET model to make its predictions, and so VSOP and the astronomy software which use it is therefore validation of the theory. We find, however, that VSOP is based on the ancient pattern methods of epicycles and perturbations:
Comparing VSOP to the Ptolemaic System
The following is left by an editor on VSOP's Wikipedia Talk Page (Archive):
“ Modelling VSOP on a ubiquitous PC computer program, starting with only one element for each of the three parameters (L, B R) and then slowly incrementing the number of elements, gives a sense of irony that it is in fact nothing more than a more complex development of the ancient deferent / epicycle system used by Ptolemy. A system that despite being totally dismissed out of hand for being intellectually "wrong", was able to provide a prediction service accurate enough to match the observational resolution available (naked eye, with no reliable mechanical timekeeping). A system that, astoundingly to this author, was able to detect and measure, accurately, the lunar evection, one of the still-used perturbations of the Earth-Moon system. Summing powers of sines and cosines is certainly tantamount to circles upon (or perhaps within) circles; recursing, or perhaps simply nesting, almost endlessly. Whilst of course this is totally irrelevant to the mathematics, it perhaps behooves Wikipedia's wider terms of reference to include this as a philosophical point. ”
Comments from Celstia Developers
Celestia Developers comment on the large number of planet-specific terms used in computing positions:
https://celestia.space/forum/viewtopic.php?f=2&t=8285 (Archive)
“ VSOP87 is a set of polynomials describing the orbits of the major planets. There are over 1000 terms in each series. ”
https://celestia.space/forum/viewtopic.php?f=3&t=2592 (Archive)
“ I could add more terms to the VSOP-87 series, but there are already over 1000 per major planet ”
The model is bases on the ancient system of epicycles, not the Heliocentric or Round Earth system. The system of the perturbations and the epicycles are mathematical tools to find patterns. See: https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations
The only person here being deceptive here is you, by blindly quoting the names of models without showing us that it is based on a Heliocentric or Round Earth model.
In the Wiki we also look at the NOAA Solar Calculator (https://wiki.tfes.org/NOAA_Solar_Calculator), which is again, another pattern based sun model.
It is your responsibility to demonstrate your nonsensical assumptions for these models.
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All of the arguments above seem to be a divergence from the original answer I gave about the equation to predict eclipses. I have to admit that I was somewhat complicit myself when answering some of the posts. In an scientific investigation it's best to focus very tightly on a single issue at a time and either solve it, try something else, or abandon the attempt altogether and go back to 'square one'. The original proposition, I believe, was that there wasn't any equation that could just apply Newtonian mechanics to predict an eclipse. I supplied such information, and I believe that there is more out there. If the equations don't actually work then it will be easy to show that the eclipse doesn't happen as calculated. If the equations do work then you will have to examine the implications of what the equations say. It looks like the discussion has diverged to answering the general case of the 3 body problem and all the examples that don't work. Is it possible to get back to answering the question about the eclipse prediction equations that do seem to work?
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Go to NASA Eclispe Web Site (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Resources (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Eclipses and the Soros (https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html)
The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well.
NASA is describing that they are predicting the eclipses based on the ancient Saros Cycle as used by the Ancient Babylonians.
Tom, what evidence do you have that the Ancient Babylonians used the Saros Cycle to predict solar eclipses? The relatively large size of the earth's shadow on the moon makes observing and predicting lunar eclipses fairly easy. However, the relatively tiny size of the moon's shadow on the earth makes solar eclipses much, much harder to observe, let alone predict.
For example:
From the 'Canon of Eclipses' from 1207 BC to 1600 AD, you can follow a series of total solar eclipses that were visible over Egypt between 1157 and 115 BC spanning over 1000 years of potential observations. There is no simple, or discernible, pattern. Sometimes 8 months separates two total solar eclipses, sometimes as many as 400 months separate the two! This means that, knowing that an eclipse happened during a particular month and year, there is no simple additive period that lets you anticipate when the next total solar eclipse will happen, even in the same geographical location. This doesn't even allow for the possibility of bad weather which would further reduce the number of observable eclipses.
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Go to NASA Eclispe Web Site (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Resources (https://eclipse.gsfc.nasa.gov/eclipse.html) -> Eclipses and the Soros (https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html)
The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well.
NASA is describing that they are predicting the eclipses based on the ancient Saros Cycle as used by the Ancient Babylonians.
Tom, what evidence do you have that the Ancient Babylonians used the Saros Cycle to predict solar eclipses? The relatively large size of the earth's shadow on the moon makes observing and predicting lunar eclipses fairly easy. However, the relatively tiny size of the moon's shadow on the earth makes solar eclipses much, much harder to observe, let alone predict.
For example:
From the 'Canon of Eclipses' from 1207 BC to 1600 AD, you can follow a series of total solar eclipses that were visible over Egypt between 1157 and 115 BC spanning over 1000 years of potential observations. There is no simple, or discernible, pattern. Sometimes 8 months separates two total solar eclipses, sometimes as many as 400 months separate the two! This means that, knowing that an eclipse happened during a particular month and year, there is no simple additive period that lets you anticipate when the next total solar eclipse will happen, even in the same geographical location. This doesn't even allow for the possibility of bad weather which would further reduce the number of observable eclipses.
The Babylonians started using the Saros Cycles about 3rd or 4th century BC but I believe it was named 2 or 3 different names. The term Saros came into use several centuries later. But it was the same process. Again I'd like to point out that the Babylonians dropped the FE belief in favor of RE belief several centuries prior them using the Saros Cycles. Tom also claimed claimed that the Saros Cycles are primarily a FET concept in his comment or question as to why would NASA use a primarily FE concept to predict eclipses.
History. The earliest discovered historical record of what is known as the saros is by Chaldean (neo-Babylonian) astronomers in the last several centuries BC. ... The name "saros" (Greek: σάρος) was applied to the eclipse cycle by Edmond Halley in 1691, who took it from the Suda, a Byzantine lexicon of the 11th century.
https://en.wikipedia.org/wiki/Saros_(astronomy)
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According to a legend firmly established, Thales of Milet (VIth century before J.-C.) would be released very early from the belief in the divine causality of eclipses. In fact, according to the Greek historian Herodotus (about 484-425 BC), Thales had predicted to the Ionians an obscuration of the the Sun "for the year in which it occurred" (Survey I 74). Few authors, both ancient and modern, have questioned that which was held for one of the seven sages, has been able to predict a solar eclipse. According to Pseudo Plutarch (Opinion of philosophers, II 24), Thales understood the nature of the phenomenon ("the solar eclipse occurs when the Moon, whose nature is terrestrial, is placed just under him".) But this would obviously be not enough to move to the infinitely more complex step of the prediction of an eclipse occurring on a specific date and visible in a specified region of the globe. Some historians determined as sure that May 28, 585 BC was the date of the solar eclipse announced by Thales and the American historian O. Neugebauer said that there is no cycle to predict a solar eclipse in a given place, and that around 600 BC, and that the ephemerides compiled by the Babylonians and used by Thales did not contain any theory for predicting eclipses of the Sun. This legend of Thales is as unreliable as the one of Anaxagoras (500-428 BC) who "thanks to his knowledge of astronomical science" (Pliny the Elder, Natural History, II, 149), would have predicted a meteorite fall!
Point out "Thales" $ "Saros" are name for the same things.
https://promenade.imcce.fr/en/pages4/468.html
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This page (https://eclipse.gsfc.nasa.gov/SEhelp/rotation.html) explains how Halley (who financed Newton’s principia) rediscovered the Saros cycle
The eclipse paths he predicted were shifted with respect to the historical records. Halley identified the increasing length of the day as the reason for this, but it took 300 years to explain why the day was increasing in length.
The ocean tides are casued by the gravitational pull of the Moon and, to a lesser extent, the Sun. But as the tides are attracted to the Moon, the oceans appear to rise and fall while Earth rotates beneath them. This tidal friction gradually transfers angular momentum from Earth to the Moon. Earth loses energy and slows down while the Moon gains the energy and consequently its orbital period and distance from Earth increase.
The key point is how Halley was able to predict eclipse paths that differed from the tables. It follows he cannot have been using the tables themselves, or there would have been no difference.
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NASA is describing that they are predicting the eclipses based on the ancient Saros Cycle as used by the Ancient Babylonians.
No, they are not claiming to use the Saros Cycle to predict eclipses. They talk about how the geometry of the earth-moon-sun system creates the cycle, but not how to use the cycle to predict eclipses. For example, they say that a cycle moves from partial eclipses to total eclipses "after ten or eleven Saros cycles..." Well, which is it this Saros, ten or eleven? How would you know? In fact, if you look on another of their pages (https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html#section106) you find the situation is more unpredictable than that: "the number of partial eclipses in the initial phase ranges from 6 to 25" with no guidance on how to know from past cycles how many might be in future cycles. The futility of using the Saros cycle for prediction is made fully evident when they sum it all up: "...the exact duration and number of eclipses in a complete Saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central" That's no kind of basis for prediction!
Everything in astronomy is predicted on basis of patterns.
No, it is not. Patterns are a starting point. Understanding the reason for the patterns and (just as important) the deviations from those patterns yields better tools for prediction. For example, each Saros cycle has a different number of eclipses in it, and a different number of partial, annular, hybrid (sometimes zero), and total (sometimes zero) eclipses. How can that form the basis for prediction? The interval between eclipses in the same Saros is eight years, eleven days, and approximately eight hours. APPROXIMATELY. How can THAT form the basis for prediction? The answer is that it cannot, and it does not. The Saros Cycle is a way to categorize eclipses. To predict them you need to know the underlying physical movements, not just look up dates in a chart and project forward from them.
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To resolve this I wrote to Fred (https://en.wikipedia.org/wiki/Fred_Espenak) Espenak (https://www.nasa.gov/topics/solarsystem/features/eclipse/espenak.html) (website (https://www.eclipsewise.com)).
I asked
I occasionally contribute to a Flat Earth website with the aim of correcting scientific misconceptions and misrepresentations. One of the claims made by Flatearthers is that space science, eclipses etc is entirely based on patterns and tables such as Saros, and Newton’s theory of gravitation does not enter into it at all. The 3 body problem is frequently cited as a reason why science and gravitation cannot predict eclipses. Is this true?
Of course he used to work for NASA, which will disqualify his opinion for some, but here is what he wrote, together with permission to publish here in his name.
Ed -
In a word “rubbish!”
Modern eclipse predictions do NOT use the Saros.
Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation.
More specifically, I use the Jet Propulsion Laboratory Developmental Ephemeris 430 (i.e., JPL DE430) to calculate the positions of the Moon, and Sun with respect to Earth. This is the raw material from which the Besselian elements used in eclipse predictions are derived from (https://en.wikipedia.org/wiki/Besselian_elements). It involves a lot of spherical geometry to calculate every conceivable aspect of any solar eclipse.
Using this method, I can calculate the time of the start and end of any solar eclipse to a fraction of a second for any location on Earth. I challenge any flat Earther to match that precision and accuracy using flat Earth geometry.
Best regards,
Fred Espenak
PS - By the way, the JPL DE is also used to help navigate all the interplanetary spacecraft into orbits or flybys of the planets (e.g., New Horizons and Pluto).
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Of course he used to work for NASA, which will disqualify his opinion for some
Probably, although that would be an odd response from Tom when he is the one claiming NASA do use these cycles and linking to various NASA pages and willfully misunderstanding them to pretend they say what he claims they say.
This should really be the end of the matter, but I doubt it will be from past experience.
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Tell Fred that response is nonsense. Read up on the Jet Propulsion Laboratory Development Ephemeris here: https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris
Read that page. Note that it is based on perturbations.
Recall that Celestial Mechanics professor Charles Lane Poor told us that perterbations = epicycles (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations), and that epicycles = a way to find patterns from the ideal state.
The fact that it is based on perturbations shows that claims that it is based on a model founded on modern theories to be nonsense. It simply doesn't matter if some are calling the perterbations "relativistic corrections" or a "solution to the n-body problem". Perturbations are epicycles -- they provide corrections from the ideal state. They correct the wild and erratic movemnts of the planets to something ideal and predictable. These systems are using the same type of methods that were used to predict patterns in the sky developed hundreds of years ago!
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Tell Fred that response is nonsense. Read up on the Jet Propulsion Laboratory Development Ephemeris here: https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris
Read that page. Note that it is based on perturbations.
Recall that Charles Lane Poor told us that perterbations = epicycles (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations), and that epicycles = a way to find patterns from the ideal state.
The fact that it is based on perturbations shows that claims that it is based on a model founded on modern theories to be nonsense. It simply doesn't matter if some are calling the perterbations "relativistic corrections" or a "solution to the n-body problem". Perterbations are epicycles -- they provide corrections from the ideal state. They correct the wild and erratic movemnts of the planets to something ideal and predictable. These systems are using the same pattern-based methods that were used hundreds of years ago!
Where do you get your definition of perturbation from Tom? It doesn't appear to match the definition given by the link in the wikipedia article at all. In fact cycles/epicycles aren't mentioned at all in the article. You appear to be slapping definitions on, and otherwise sticking your fingers in your ears (figuratively) and claim what's written in the articles is a lie. So where are you getting your definitions and information from? As I was unaware you were an expert in the field of Astronomy to be crying false at the statements of said experts. You've now point blank called Fred Espenak a liar. So I'm curious where you get your information from to say that.
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Read up on the Jet Propulsion Laboratory Development Ephemeris here: https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris
Read that page. Note that it is based on perturbations.
I can't find that in the page you linked.
I did find: "Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions." And perturbations are applied.
But not "based on perturbations." Rather, based on equations of motion.
Nowhere does it say its based on "ancient" cycles.
Bet the "ancients" could never have predicted the 2003 solar eclipse (Saros 152) that was visible over Antarctica.
(http://oi63.tinypic.com/311qj9f.jpg)
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Where do you get your definition of perturbation from Tom? It doesn't appear to match the definition given by the link in the wikipedia article at all. In fact cycles/epicycles aren't mentioned at all in the article. You appear to be slapping definitions on, and otherwise sticking your fingers in your ears (figuratively) and claim what's written in the articles is a lie. So where are you getting your definitions and information from? As I was unaware you were an expert in the field of Astronomy to be crying false at the statements of said experts. You've now point blank called Fred Espenak a liar. So I'm curious where you get your information from to say that.
I've posted this wiki link numerous times already, and Bobby has as well: https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations
Perturbations
Description and Function
Gravitation Vs. Relativity
by Charles Lane Poor, PhD
Full Text Link
Motion of the Planets p.132
“ The deviations from the “ideal” in the elements of a planet’s orbit are called “perturbations” or “variations”.... In calculating the perturbations, the mathematician is forced to adopt the old device of Hipparchus, the discredited and discarded epicycle. It is true that the name, epicycle, is no longer used, and that one may hunt in vain through astronomical text-books for the slightest hint of the present day use of this device, which in the popular mind is connected with absurd and fantastic theories. The physicist and the mathematician now speak of harmonic motion, of Fourier’s series, of the development of a function into a series of sines and cosines. The name has been changed, but the essentials of the device remain. And the essential, the fundamental point of the device, under whatever name it may be concealed, is the representation of an irregular motion as the combination of a number of simple, uniform circular motions. ”
Motion of the Planets p.138
“ The Tide Predicting Machine of the Coast and Geodetic Survey at Washington is a note-worthy example of the application of the mechanical method [of prediction via epicycles]. The rise and fall of the tide at any port is a periodic phenomenon, and it may, therefore, be analyzed, or separated into a number of simple harmonic, or circular components. Each component tide will be simple, will have a definite period and a constant amplitude; and each such component may be represented mechanically by the arm of a crank, the length of which represents the amplitude; each crank arm being, in fact, the radius of one of the circles in our diagram.
Such a machine was invented by Sir William Thomson and was put in operation many years ago. The machine at present in use at Washington was designed by William Ferrel. It provides for nineteen components and directly gives the times and heights of high and low waters. In order to predict the tides for a given place and year, it is necessary to adjust the lengths of the crank arms, so that each shall be the same proportion of the known height of the corresponding partial tide, and to adjust the periods of their revolutions proportionally to the actual periods. Each arm must also be set at the proper angle to represent the phase of the component at the beginning of the year. When all these adjustments have been made, the machine is started and it takes only a few hours to run off the tides for a year, or for several years. This machine probably represents the highest possible development of the graphical or mechanical method. It is a concrete, definite mechanical adaptation of the epicyclic theory of Hipparchus.
But, because the Coast Survey represents and predicts the movements of tidal waters by a complicated mass of revolving cranks and moving chains, does any one imagine for a moment that the actual waters are made up of such a system of cranks? No more did Hipparchus believe that the bodies of the solar system were actually attached to the radial arms of his epicycles; his was a mere mathematical, or graphical device for representing irregular, complicated motions.
While the graphical, or mechanical method is limited to a few terms, the trigonometrical, or analytical method is unlimited. It is possible to pile epicycle upon epicycle, the number being limited only by the patience of the mathematician and computer. ”
Celestial Mechanics professor Charles Lane Poor lays out perturbations quite clearly. Perturbations = Epicycles, and Epicycles = a mathematical way to derive patterns from an ideal state, as exemplified by the tide predicting machine which predicts the tides.
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Read up on the Jet Propulsion Laboratory Development Ephemeris here: https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris
Read that page. Note that it is based on perturbations.
I can't find that in the page you linked.
I did find: "Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions." And perturbations are applied.
But not "based on perturbations." Rather, based on equations of motion.
Do a search on that page, Bobby. Perturbations are mentioned numerous times. It simply doesn't matter if anyone calls them as something which "accounts for the equations of motion" or that they are "corrections for gravity/relativity/etc," or that they "provide a solution to the n-body problem."
The method of perturbations is a pattern-predicting method, as explained by Celestial Mechanics professor Charles Lane Poor.
Nowhere does it say its based on "ancient" cycles.
Charles Lane Poor tells us that they are epicycles, and there are other mentions of epicycles used in the VSOP section of the "Astronomy is Based on Patterns" page you linked in the OP.
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Celestial Mechanics professor Charles Lane Poor lays out perturbations quite clearly. Perturbations = Epicycles, and Epicycles = a mathematical way to derive patterns from an ideal state, as exemplified by the tide predicting machine which predicts the tides.
Thus spake Dr. Poor. Understandable that you've latched onto his 1922 work because it endorses a conclusion for which you are arguing. But if you're arguing from authority, as if citing a "celestial mechanics professor" is supposed to shut down criticism of your wiki page, you must know his was a cynical, critical and minority view.
He also contested General Relativity, which has since survived many challenges.
Just because you found one person who said (in 1922) what you want to believe is true, doesn't make it true. What do others say? You can't close your mind off once you find a passage that supports your preferred view.
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Do a search on that page, Bobby. Perturbations are mentioned numerous times.
Mentioned, yes. "Based on..." no.
Charles Lane Poor tells us...
Others tell us otherwise.
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Consider as well: It's also possible for Dr Lane to be using a differing definition for his own work, just as TFES uses a different definition of 'perspective' than is mainstream. The article on JPL specifically hyperlinks to another article on perturbations, that explains what they are. Why would you look to use an older definition from someone else? The one you are constantly attempting to use doesn't appear to agree with current definitions, and I would argue you only wish to force it forward because it supports your PoV.
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https://en.wikipedia.org/wiki/Charles_Lane_Poor
Charles Lane Poor (January 18, 1866 – September 27, 1951) was an American astronomy professor, noted for his opposition to Einstein's theory of relativity.
Essentially a Victorian scientist. Do you have any more recent sources?
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It looks like there is confusion in the word 'perturbations'. Charles Lane Poor seemed to use that word in one context and the modern-day scientists seem to be using the same word to describe something altogether different. In any event, the modern-day folks take the bodies and put them into an initial condition. Then all the Newtonian laws are applied with a computer program. Perturbations are then the difference between what the first approximation to the predicted motion and the actual observed motion happens to be. The first approximation is the result of the classic 3 body problem based upon the nominal condition of all the bodies. After the results of the first approximation are in then the program is amended to adjust the orbits for the perturbations (differences) due to all smaller effects on the orbital bodies. In each case the model is adjusted using the standard Newtonian laws of motion to calculate the ever-smaller adjustments needed. The whole process is a mixture of the old and the new. Newtonian laws of motion are the underlying theme to everything and the modern computers are just a means to accomplish all the calculations. At heart of everything is the mathematics that was needed to fine tune the Newtonian laws to choreograph everything.
At no time are any historical data used in any of these calculations. All the orbital data is newly calculated with the computer program.
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More modern sources aren't really needed, just more accurate ones. Look at the works of Nathaniel Bowditch and Issac Newton for a better idea of how things actually work in the real world. Observe and compare those observations to what the theory says. If there's a difference adjust accordingly. When one theory had a plethora of problems it usually is better to consider something else. Apply Occam's razor, that usually is best.
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https://en.wikipedia.org/wiki/Perturbation_(astronomy)
Most systems that involve multiple gravitational attractions present one primary body which is dominant in its effects (for example, a star, in the case of the star and its planet, or a planet, in the case of the planet and its satellite). The gravitational effects of the other bodies can be treated as perturbations of the hypothetical unperturbed motion of the planet or satellite around its primary body.
They state that the 'gravitational effects' are being treated on basis of "perturbations".
Further down, we read about Special Perturbations:
In methods of special perturbations, numerical datasets, representing values for the positions, velocities and accelerative forces on the bodies of interest, are made the basis of numerical integration of the differential equations of motion.[6] In effect, the positions and velocities are perturbed directly, and no attempt is made to calculate the curves of the orbits or the orbital elements.[2] Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small.[4] Once applied only to comets and minor planets, special perturbation methods are now the basis of the most accurate machine-generated planetary ephemerides of the great astronomical almanacs.[2][7]
From Perturbations in Complex Molecular Systems (https://www.ingentaconnect.com/content/ben/ctmc/2013/00000013/00000014/art00011) we read the following:
“ In general perturbation methods starts with a known exact solution of a problem and add “small” variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or “butterfly effect” in complex systems are examples of perturbation theories. ”
It's just a way to find patterns from the ideal state. It is a method that is used in many areas of science. Perturbation methods have nothing to do with any modern theory of astronomy.
Recall that Charles Lane Poor said that planetary perturbations are calculated on basis of Fourier series.
In the below paper by the Smithsonian Astrophysical Observatory we see that planetary perturbations are being calculated on basis of Fourier series:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690030023.pdf
The analytical procedure for computing second-order perturbations in
rectangular coordinates, according to Brouwer's theory of planetary motion,
is given. Single- and double-harmonic analyses and the multiplication of
Fourier series with numerical coefficients are used in the computations. In
the series multiplication, a variable tolerance is considered, enabling us to
avoid the difficulties arising from a small divisor.
Looks like Charles Lane Poor was, and still is, correct.
Fourier Series = Data Analysis/Fourier Analysis = Finding Patterns
https://esajournals.onlinelibrary.wiley.com/doi/full/10.1002/ecs2.1944
Further, Fourier series have been used to quantify a variety of complex periodic patterns in ecology
https://www.tandfonline.com/doi/abs/10.1080/713819066?journalCode=tmop19
When two or more patterns, each exhibiting some form of periodicity, overlap there usually result distinct moiré fringes. If the periodicities in the original patterns are represented by Fourier series, the shape and harmonic structure of the moiré fringes can be predicted
All of it is just data and pattern analysis.
"The terms and definitions changed! Now it means that the planets are calculated entirely based on Newton and Einstein's laws..." Sure sure...
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of the planets it totally nullifies the underlying theory.
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
That's just fluff. As soon as they start using perturbation methods, Fourier series, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.
Huh?
Perturbations are deviations. They aren't stand-alone.
Deviations from what?
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.
Why on earth would it 'totally nullify the underlying theory'??
Give me a reason.
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Probably you continue to be confused (maybe intentionally) about what is happening. Patterns tend to emerge from the data but those patterns are the result NOT the cause of any prediction. The cause of the predictions are the application of the basic laws of motion of bodies containing mass NOT the application of patterns that were noticed in the past. It's like saying that there is a pattern for how you put a nut on a bolt. 'Righty Tighty / Lefty Loosie' is definitely a pattern that applies to a mechanical device but doesn't have much to do with how it actually operates. The Fourier series is the application of the Sine Wave pattern (like a nut / bolt) that is useful for describing a lot of things that can happen in a cycle, like an orbital cycle. It's just a tool that can be used to describe the overall motion of a body. You can use a wrench to fix your car, but that doesn't have much to do with the laws of motion that are in force when you go around a curve. It looks like there is a pattern in your ideas and replies and I'm thinking I may be able to base a prediction on your response.
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.
Why on earth would it 'totally nullify the underlying theory'??
Give me a reason.
Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.
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If you look further down, Tom, you will clearly see how these equations mathematically solve for Newtonian forces.
It's not 'just patterns'.
That's just fluff. As soon as they start using perturbation methods, Fourier series, harmonic motion, data and statistical analysis to compute the position of planet it totally nullifies the underlying theory.
Why on earth would it 'totally nullify the underlying theory'??
Give me a reason.
Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.
What are these 'gravitational effects' they are talking about, whose theoretical existence is apparently nullified, according to you.
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Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.
The starting point for "perturbations" are the idealized motions themselves. They don't "nullify" them.
Neptune was discovered by the perturbation of the orbit of Uranus by an unseen object. Uranus had an expected motion. It was the observed deviations from that expected motion that led to the prediction of another unseen body that ultimately turned out to be Neptune.
Perturbations are not an end unto themselves. They don't "nullify" laws of motion. They are modifiers.
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Simply because they are not predicting the position of the planets based on netwon's laws, but on pattern analysis of the "numerous gravitational effects caused by the other bodies of the solar system" which are said to be behind the very complex motion of the planets.
The starting point for "perturbations" are the idealized motions themselves. They don't "nullify" them.
Neptune was discovered by the perturbation of the orbit of Uranus by an unseen object. Uranus had an expected motion. It was the observed deviations from that expected motion that led to the prediction of another unseen body that ultimately turned out to be Neptune.
Perturbations are not an end unto themselves. They don't "nullify" laws of motion. They are modifiers.
About time for Tom to link to this, http://www.sacred-texts.com/earth/za/za60.htm I think.
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What I see here is the implementation of the successive approximation model. The first step is to gather all the information you have about something you need to investigate. Next is the formulate a theory about what needs to be done. After that you take some actions based upon your theory and see what happens. You expect to make errors. Very few do something new perfectly the first time. After you analyze the errors maybe it will point you to some new information you didn't have previously. Using that new information you can modify your theory and again take some actions. You keep repeating this process until you are successful. In the link provided I did read the story about Le Verrier. This was an application of the successive approximation model. Le Verrier probably did apply the principles of Newtonian mechanics and did locate the planet but made some errors in the paths. These errors probably were not a problem with the theory, but more likely a problem with the initial assumptions made. Maybe Le Verrier used some data from another source that wasn't quite accurate. Maybe he didn't quite understand something about Newtonian mechanics correctly, or maybe he made a stupid error in calculation. I think it wasn't a problem with the theory, it more likely was a problem with best guess data. Sometimes a theory just doesn't work at all no matter what you try. At that point nothing at all will make sense. All I can say about that is some theories are from Mars, and other are from Uranus.
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Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.
https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/
Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.
The biggest problem in astronomy is getting it to work!
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Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.
https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/
Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.
The biggest problem in astronomy is getting it to work!
I *might* be reading this wrong but it sounds to me that what they are creating/finding here are equations that they can use that will simulate a stable orbit for an extended period without modification. However that's NOT how they calculate the movements for the eclipse tables. I'll try and dig it up when I have more time, but it might also be in one of the quotes already and I'm missing it. But the movements of the Earth/Moon/Sun system (and the solar system in general) aren't done via a specific solution to the three body problem. They're done by an iterative solving of all the effects on a body repeatedly.
You take a snapshot of where all the bodies appear at T=0. You calculate all the acting effects on every body and apply them to your next snapshot at T=1. You then do this again for every interval of T. There's no need to have a solution for a 3-body problem (which the Earth/Moon/Sun very likely isn't anyway) as you aren't attempting to solve it via a singular equation. This is likely how such software as the 'Universe Sandbox' works, or at least similarly.
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003#tab1
Well the discussion subroutine has come full circle back to near the start again. The OP Bobby was hypothesizing that you would need more than just pattern based descriptions to accurately predict eclipses. My link points to a researcher that has all the equations using strictly Newtonian mechanics that accomplishes that objective. The three body diversion was tried. It didn't fly far. Now it's time to 'square yourself in the hatch' and illustrate just what the problems are with the equations proffered in the paper pointed to in the link. They sure look OK to me. Can I expect another diversionary tactic or a useful criticism that can be objectively discussed?
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Nonsense. We need only look at the Three Body Problem to see that the theories of Newton do not work. Let us go back to the New Scientist article at the beginning of this thread which triumphs the finding of crazy loopy sensitive orbits that only exist under special conditions.
https://www.newscientist.com/article/2148074-infamous-three-body-problem-has-over-a-thousand-new-solutions/
Perhaps the most important application of the three-body problem is in astronomy, for helping researchers figure out how three stars, a star with a planet that has a moon, or any other set of three celestial objects can maintain a stable orbit.
The implication is that the objects cannot maintain a stable orbit. They cannot simulate it at all. This is the end-all be-all to any and all questions on the matter, really. The Heliocentric system that is proposed is not possible.
The biggest problem in astronomy is getting it to work!
I *might* be reading this wrong but it sounds to me that what they are creating/finding here are equations that they can use that will simulate a stable orbit for an extended period without modification. However that's NOT how they calculate the movements for the eclipse tables. I'll try and dig it up when I have more time, but it might also be in one of the quotes already and I'm missing it. But the movements of the Earth/Moon/Sun system (and the solar system in general) aren't done via a specific solution to the three body problem. They're done by an iterative solving of all the effects on a body repeatedly.
You take a snapshot of where all the bodies appear at T=0. You calculate all the acting effects on every body and apply them to your next snapshot at T=1. You then do this again for every interval of T. There's no need to have a solution for a 3-body problem (which the Earth/Moon/Sun very likely isn't anyway) as you aren't attempting to solve it via a singular equation. This is likely how such software as the 'Universe Sandbox' works, or at least similarly.
It sounds pretty clear to me:
“This is kind of the zeroth step. Then the question becomes, how is the space of all possible positions and velocities filled up by solutions?” says Richard Montgomery at the University of California, Santa Cruz. “These simple orbits are kind of like a skeleton to build the whole system up from.”
They are at the zeroth step: The Stone Age.
They are going to use these orbits like a skeleton to "build the whole system up from."
The following quote says it all:
But these new orbits rely on conditions that are somewhere between unlikely and impossible for a real system to satisfy. In all of them, for example, two of the three bodies have exactly the same mass and they all remain in the same plane.
Why didn't the supercomputer find possible orbits for bodies of slightly different masses? Because they can't exist.
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The above is in line with my post a few days ago on the subject:
I assume you're referring to FET when saying, " General application of the Three Body Problem are, in fact, impossible". Because in this day and age it's very simple.
"They could predict the eclipses thousands of years into the future". This statement is contradiction of the former. ???
Prediction of three or more orbiting bodies under the Newtonian System is impossible. Literally impossible. It is one of the greatest problems of astronomy, mathematics, and classical mechanics. They can't get the heliocentric system to work.
Take a look at the existing Three Body Problem solutions. The bodies are either all of the same mass, or some of them are mass-less. The applications are very limited.
The famous physicist Henri Poincare studied the Three Body Problem. Here is a quote from 'Mathematics Applied to Deterministic Problems in Natural Sciences' about Poincare's discoveries:
As Poincare experimented, he was relieved to discover that in most of the situations, the possible orbits varied only slightly from the initial 2-body orbit, and were still stable, but what occurred during further experimentation was a shock. Poincare discovered that even in some of the smallest approximations some orbits behaved in an erratic unstable manner. His calculations showed that even a minute gravitational pull from a third body might cause a planet to wobble and fly out of orbit all together.
The available solutions to the Three Body Problem, beyond looking unlike anything seen in Heliocentric Theory, are so sensitive that the slightest change or imperfection will tear the entire system apart. As a very illustrative demonstration, take a look at this online Three Body Problem simulator that uses the simplest possible figure eight pattern, which requires three identical bodies of equal mass that move at very specific momentum and distance in relation to each other.
Demo: Figure-Eight Three Body Problem
(https://wiki.tfes.org/images/thumb/6/6c/Three_body_sim.png/350px-Three_body_sim.png) (https://cloud.anylogic.com/model/f1999d97-8de2-4804-9940-5ae261d7ad86?mode=SETTINGS&tab=GENERAL)
Adjust the slider values in the upper left to something very slight to find what happens. What you will see is a demonstration of Chaos Theory. Any slight modification to the system creates a chain reaction of random chaos.
This is precisely the issue of modeling the Heliocentric System, and why the fundamental systems as depicted in popular astronomy cannot exist. Only very specific and very sensitive configurations may exist. The slightest deviation, such as with a system with unequal masses, or the minute influence from a gravitating body external to the system will, as Poincare found, cause the entire system to fly apart!
Play the demo. Adjust the sliders to something very slight. We can see that that only very specific configurations could exist.
Again, I ask, why did the supercomputer not find orbits with different masses?
Why do the bodies need to be of exactly the same mass, or one of the bodies mass-less?
These questions will ignored, in favor of ignorance, because of a refusal to accept that Copernicus was wrong.
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They cannot simulate it at all.
lol that's nonsense.
A three million year integration of the earth's orbit (http://adsabs.harvard.edu/abs/1991AJ....101.2287Q)
describes a numerical simulation of all nine planets carried out by integrating newton's equations of motion. it says that explicitly in the paper and describes the method of integration.
La2010: A new orbital solution for the long term motion of the Earth (https://arxiv.org/pdf/1103.1084.pdf)
some book-nerd frenchman named jacques laskar loves making long-term models of the solar system. here's his most recent one.
also you evidently don't understand that "chaotic" motion does not imply that everything flies apart. that's not even what your article says. the motion of the objects in the solar system can be (and is) chaotic without ejecting all the planets in it.
https://www.nature.com/articles/338237a0
The solution is chaotic, with a maximum Lyapunov exponent that reaches the surprisingly large value of ∼ 1/5 Myr–1. The motion of the Solar System is thus shown to be chaotic, not quasiperiodic. In particular, predictability of the orbits of the inner planets, including the Earth, is lost within a few tens of millions of years. This does not mean that after such a short timespan we will see catastrophic events such as a crossing of the orbits of Venus and Earth; but the traditional tools of quantitative celestial mechanics (numerical integrations or analytical theories), which aim at unique solutions from given initial conditions, will fail to predict such events.
again i'd like to point out that you should follow your own advice and demonstrate an accurate understanding of the subject you are criticizing. otherwise it's just vapid.
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Why didn't the supercomputer find possible orbits for bodies of slightly different masses? Because they can't exist.
"And yet we see the bumblebee CAN fly."
Position + Motion + Perturbations => Ephemerides
Ephemerides + Spherical Geometry => Besselian Elements
Not patterns.
Thinking that proving a globe earth model isn't possible somehow proves the flat earth model correct is poor critical reasoning.
Thinking that the N-body problem somehow means ephemerides are "pattern-based" is poor critical reasoning.
Predictions of when, where, how long, type, swath are not only NOT pattern-based, they also only work within the spherical geometry of a globe earth. Unless, that is, you have a comparable model that can make similarly accurate predictions. I don't know how that can be possible when there isn't even a flat earth map.
Erroneously claiming predictions are pattern-based and that an expert in calculating the Besselian Elements of future (and past) solar eclipses is speaking nonsense and is not really applying spherical geometry in producing his outputs is not a logical way to defend a flat earth model. The first step ought to be to develop a flat earth model that can show some alternative success.
I grow so weary watching flat earth advocates taking the approach that "globebusting" somehow bolsters a flat earth argument, as if the flat earth stands in default if the globe is refuted. Adding misunderstanding and erroneous claims to the mix only makes it worse. I've stated my criticism of the wiki article. I'll bow out.
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No, Gary. Answer the question. You did just as I stated. The question was ignored.
Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?
Your links are clearly talking about something else, such as an analysis of the perturbations and statistical analysis that constitutes current planetary prediction methods, not n-body solutions and simulations.
Answer the question:
Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?
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The question was ignored.
nice goalposts. i wasn't replying to a question. i replied to your statement that there do not exist any numerical simulations of the solar system based on its geometry and newton's equations of motion. you described it as "not possible." i provided you with two important ones.
Your links are clearly talking about something else, such as an analysis of the perturbations and statistical analysis that constitutes current planetary prediction methods, not n-body solutions and simulations.
lol so in other words you didn't bother to even attempt to read or understand any of it. nice. why do i even bother.
Why can only bodies of equal masses, or with one of the bodies being mass-less, exist in these three body problem solutions?
this is something like me asking "UA is dumb because how can the earth go faster than the speed of light???" and you correctly answering "your question is based on a false premise. you fundamentally misunderstand the position you are criticizing."
me shouting just answer the question!!! at you would be pretty disingenuous.
it is not the case that those are the only solutions to the three-body problem. your own source says that there are lots of periodic solutions to the three-body problem, even for unequal masses.
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Lets see these orbits with unequal masses, Gary. Here is a recent paper on unequal masses and the Three Body Problem by the people with the supercomputer:
Over a thousand new periodic orbits of a planar three-body system with unequal masses (https://academic.oup.com/pasj/article/70/4/64/4999993)
Abstract
The three-body problem is common in astronomy, examples of which are the solar
system, exoplanets, and stellar systems. Due to its chaotic characteristic, discovered by
Poincare, only three families of periodic three-body orbits were found in 300 years, until ´
2013 when Suvakov and Dmitra ˇ sinovi ˇ c ( ´ 2013, Phys. Rev. Lett., 110, 114301) found 13 new
periodic orbits of a Newtonian planar three-body problem with equal mass. Recently,
more than 600 new families of periodic orbits of triple systems with equal mass were
found by Li and Liao (2017, Sci. China-Phys. Mech. Astron., 60, 129511). Here, we report
1349 new families of planar periodic orbits of the triple system where two bodies have
the same mass and the other has a different mass. None of the families have ever been
reported, except the famous “figure-eight” family. In particular, 1223 among these 1349
families are entirely new, i.e., with newly found “free group elements” that have been
never reported, even for three-body systems with equal mass. It has been traditionally
believed that triple systems are often unstable if they are non-hierarchical. However,
all of our new periodic orbits are in non-hierarchical configurations, but many of them
are either linearly or marginally stable. This might inspire the long-term astronomical
observation of stable non-hierarchical triple systems in practice. In addition, using these
new periodic orbits as initial guesses, new periodic orbits of triple systems with three
unequal masses can be found by means of the continuation method, which is more
general and thus should have practical meaning from an astronomical viewpoint.
Their supercomputer found three body problem solutions where two of the bodies had exactly the same mass and one of the masses was different.
Hence, we see that our position is entirely vindicated. The possibilities of these orbits are very limited. None of this is anything like the imaginary astronomy proposed by Copernicus.
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I did some research on statistics and chaos theory a while back. Just because there’s chaos doesn’t mean a solution can’t be found. Scientists studying planetary motion have already figured this out. Last year I was able to calculate Pi to about 4 figures to the right of the decimal place just using about 100 million random numbers generated by my Python program. Talk about chaos! My program did require about 8 hours of run time to complete.
The research papers I read had a program that could calculate planetary motions of the entire known solar system including the moon and accounting for 5 different asteroids. It took over a year of processing time on a desk top computer, but the results modeled everything back for millions of years. Yes, they did say that the accuracy of the data started to decline the further out they went. My other readings did indicate that the Lyapunov time for a solar system was about 50 million years so the results I read about were not too surprising.
Now maybe you have come across an example of what doesn’t work, but there are examples of what does work out there. Yes, the Newtonian equations do work. Yes, multi-body solutions can be accurately calculated. Eclipses can be predicted accurately using just Newtonian equations. All the information is at your disposal if you choose to access it. Of course, you can also access all the failures as well and use them to your advantage. I fully understand that you have the flat earth ball & chain firmly wrapped around your neck and that limits your options. At least this response will put another mark on the wall for you, and that’s the good news.
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Tell Fred that response is nonsense.
Tell him yourself. I would love to read the correspondence between the two of you.
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Lets see these orbits with unequal masses, Gary.
i posted two already. the first two links describe two independent n-body simulations of the solar system (here, n=9 and all the masses are different). these models numerically integrate newton's laws of motion for all 8 planets plus pluto.
Hence, we see that our position is entirely vindicated. The possibilities of these orbits is very limited.
your authors don't say anything like that.
tbh you obviously don't understand what your authors are even talking about. they're looking for analytic solutions. they're looking for sets of initial conditions that create periodic orbits. these cases are special because if you know the initial conditions at t=0, then you have a single expression to tell you the positions of the objects at t=whenever.
but that doesn't have anything to do with numerical integration. literally no one but you is claiming that anyone has an analytic model of the solar system.
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[to Tom] tbh you obviously don't understand what your authors are even talking about. they're looking for analytic solutions. they're looking for sets of initial conditions that create periodic orbits. these cases are special because if you know the initial conditions are t=0, then you have a single expression to tell you the positions of the objects at t=whenever.
but that doesn't have anything to do with numerical integration. literally no one but you is claiming that anyone has an analytic model of the solar system.
Yup this seems merely like the distinction you find all over the place in engineering i.e. between closed form or analytic solutions, and numerical solutions. From Wikipedia:
A complete solution for a particular three-body problem would provide the positions for all three particles for all time, given three initial positions and initial velocities. In general, no closed-form solution for such a problem exists, and the time evolution of the system is believed to be chaotic. The use of computers, however, makes solutions of arbitrarily high accuracy over a finite time span possible using numerical methods for integration of the trajectories. https://en.wikipedia.org/wiki/Three-body_problem#Gravitational_systems
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Tell Fred that response is nonsense.
Tell him yourself. I would love to read the correspondence between the two of you.
I did call it...
Interesting that Tom follows up his assertion that the response is nonsense with a link to a Wiki page which says:
Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem
There's more, but it's clear they're not just using patterns but using numerical solutions.
Tom's attempts to derail the thread and troll should be ignored.
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I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits. The moon is retreating from the earth at the rate of about 1 inch per year. Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time. It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system. Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.
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tbh you obviously don't understand what your authors are even talking about. they're looking for analytic solutions. they're looking for sets of initial conditions that create periodic orbits. these cases are special because if you know the initial conditions at t=0, then you have a single expression to tell you the positions of the objects at t=whenever.
but that doesn't have anything to do with numerical integration. literally no one but you is claiming that anyone has an analytic model of the solar system.
Gary, it has been pointed out to you on the numerous times we have had these conversations. All of these models are numeric solutions.
From my last link about the supercomputer: https://academic.oup.com/pasj/article/70/4/64/4999993
Look at the sections:
1 Introduction
2 Numerical searching for periodic orbits
3 Results
Where do you see that they are searching for analytic solutions? It clearly says that they are numerically searching. This 'objection' is incorrect. It is widely accepted that there is no possible general purpose analytical solution, and it is rarely attempted. These numeric models are hoped to one day help create a general purpose analytic solution.
edby and Bobby, I see that you are making the same argument.
Recall this post:
https://twitter.com/poliastro_py/status/993418078036873216?lang=en
Look at this beautiful plot of several numerical methods for the restricted three body problem taken from Harier et al. "Solving Ordinary Differential Equations I". The use of high order Runge-Kutta methods is pervasive in Celestial Mechanics. Happy Monday!
(https://i.imgur.com/Zkqthvb.jpg)
Again, we see that these are numerical methods, and not based on an analytical solution. This argument is clearly and fantastically wrong.
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Interesting that Tom follows up his assertion that the response is nonsense with a link to a Wiki page which says:
Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem
There's more, but it's clear they're not just using patterns but using numerical solutions.
Tom's attempts to derail the thread and troll should be ignored.
This was addressed with a definition and explanation of the perturbational methods provided earlier. That someone is claiming on Wikipedia that they provide "relitavistic corrections" or that they "account for the gravity of the many bodies of the solar system" or that they essentially "solved the n-body problem" does not matter. They did not solve the n-body problem, obviously.
Issac Newton, the authority who brought the laws of physics to the solar system, used the influence of God to explain why his solar system doesn't fall apart:
https://books.google.com/books?id=hy48DQAAQBAJ&lpg=PP1&pg=PA34#v=onepage&q&f=false
At the beginning of the 18th century, Newton famously wrote that the solar system needed occasional divine intervention (presumably a nudge here and there from the hand of God) in order to remain stable.11 This was interpreted to mean that Newton believed his mathematical model of the solar system—the n body problem—did not have stable solutions. Thus was the gauntlet laid down, and a proof of the stability of the n body problem became one of the great mathematical challenges of the age.
11Newton's remarks about divine intervention appear in Query 23 of the 1706 (Latin) edition of Opticks, which became Query 31 of the 1717 (2nd Edition) edition see Quote Q[New] in Appendix E). Similar 'theological' remarks are found in scholia of the 2nd and 3rd editions of Principia, and in at least one of Newton's letters. In a 1715 letter to Caroline, Princess of Wales, Leibniz observed sarcastically that Newton had not only cast the Creator as a clock-maker, and a faulty one, but now as a clock-repairman (see [Klo73], Part XXXIV, pp. 54-55).
Please tell us, if you are a true believer, who solved the n-body issues and got the solar system to work? Surely, there must be a name for this famous figure.
Tell us the name of this person to put this issue to bed.
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I am thinking that the whole universe is just an example of Brownian motion on a galactic scale. The earth is just a minute part of that universe and we are all just moving thru time tying to make sense out of the limited observations we can make. It has been observed that certain laws of motion do apply and can predict where an object will go if all the variables can be measured in advance and don’t change along the way. I would agree that there probably isn’t an explicit equation of motion for the entire known solar system. If there was that equation would have to have an infinite number of terms to fully describe every little thing. I don’t think that you need to know everything about everything to calculate something useful. Newtonian equations of motion can calculate the positions of the known bodies in the solar system with enough accuracy to be useful. There will always be some previously unknown factor that can change things, but then the equation can be adjusted. Brownian motion only accounts for the statistical, not the absolute. I can fully agree that the solar system must contend with a certain amount of chaos. That chaos so far only requires small changes in the overall scheme of things. It’s like driving to work in the morning. You know exactly where you will end up, but there may be some small delays or detours along the way that you didn’t know about when you left the house. Eventually the sun will supernova, it has been said, and the earth, flat or round, will be consumed. When that happens, it will just be another example of the chaotic nature of the galaxy and ashes to ashes and dust to dust for us all.
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I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits. The moon is retreating from the earth at the rate of about 1 inch per year. Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time. It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system. Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.
This is illogical, markjo. A supercomputer tested millions and millions of combinations and could only find solutions where at least two of the masses were exactly the same. If the masses were not exactly the same, or if the velocities or positions of the bodies of the system were slightly changed from their perfect configuration, the system quickly fell apart, as was studied by Poincare, and as was demonstrated in the demo provided to you earlier. These are highly sensitive configurations.
Mainstream Astronomy generally states that it is possible for a star to have a planet, and for that planet to have a moon. Why don't we see that in any of these orbits?
Making a slight adjustment to the masses of the bodies in the demo we saw earlier did not create a different "chaotic" system that somehow stayed together. It always created a chaotic system that tore itself apart. Such is the basis of Chaos Theory. One small chaotic element creates a very large chaotic result.
I request and demand that you demonstrate your argument.
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000100003#tab1
Well, there's been another loop in the discussion. The OP Bobby was hypothesizing that you would need more than just pattern based descriptions to accurately predict eclipses. My link points to a researcher that has all the equations using strictly Newtonian mechanics that accomplishes that objective. Is this an infinite loop? Where is the exit?
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Reply #63 was interesting. The curves showed how an Arenstorf Orbit goes awry after a limited number of iterations. What was interesting was the use of the work of Arenstorf to illustrate a point. The Apollo program used the Arenstorf Orbits to successfully get men to the moon. Of course, if you do a little research the orbits needed depended upon the recognized figures for the earths and moons gravity. Also, the recognized distances were used. In FET the earth’s gravity is greatly reduced and the Arenstorf Orbit wouldn’t even be possible in the given circumstances. It is totally illogical to use an example based upon something that is unrecognized by FET. It would a better idea to show why the 3-body problem won’t work using an example based upon the Flat Earth paradigm with a ‘greatly diminished’ force of gravity postulated by FET.
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I can't help but to wonder if Tom is under the impression that the various bodies our solar system are in stable orbits. The moon is retreating from the earth at the rate of about 1 inch per year. Gravitational perturbations cause asteroids and comets get kicked out the the oort cloud, asteroid and kuiper belts all the time. It's even believed that the orbits of several planets have moved closer to or further away from the sun during the early development of the solar system. Looking to the 3-body problem for stable periodic systems is purely academic because it just doesn't reflect the reality of the solar system that we live in.
This is illogical, markjo. A supercomputer tested millions and millions of combinations and could only find solutions where at least two of the masses were exactly the same. If the masses were not exactly the same, or if the velocities or positions of the bodies of the system were slightly changed from their perfect configuration, the system quickly fell apart, as was studied by Poincare, and as was demonstrated in the demo provided to you earlier. These are highly sensitive configurations.
Mainstream Astronomy generally states that it is possible for a star to have a planet, and for that planet to have a moon. Why don't we see that in any of these orbits?
Making a slight adjustment to the masses of the bodies in the demo we saw earlier did not create a different "chaotic" system that somehow stayed together. It always created a chaotic system that tore itself apart. Such is the basis of Chaos Theory. One small chaotic element creates a very large chaotic result.
I request and demand that you demonstrate your argument.
I'm not completely sure that I understand what you want. Do you want me to demonstrate that the solar system is not stable?
I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under. Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc
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I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under. Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc
Nice!
Learned a new term: Lyapunov Time (https://en.wikipedia.org/wiki/Lyapunov_time)
Which led to a Wikipedia article I didn't know existed: Stability of the Solar System (https://en.wikipedia.org/wiki/Stability_of_the_Solar_System)
This is why I love this board.
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I think that this article may help clarify some misconceptions about 3-body systems that you seem to be operating under. Yes, it's written for financial investors, but it has some good information that is relevant.
https://medium.com/@mikeharrisNY/misconceptions-about-the-three-body-problem-and-its-relation-to-forecasting-c0c0a2bf44cc
Nice!
Learned a new term: Lyapunov Time (https://en.wikipedia.org/wiki/Lyapunov_time)
Which led to a Wikipedia article I didn't know existed: Stability of the Solar System (https://en.wikipedia.org/wiki/Stability_of_the_Solar_System)
This is why I love this board.
If you Google 'stability of the solar system' you will find a lot more :)
I am puzzled as to what Tom's argument is. I think it's something like:
1. If classical mechanics is true, then the solar system is highly unstable
2. The solar system is not highly unstable
3. Ergo classical mechanics is not true
The argument is valid (premises imply conclusion), the question is whether the premises are true. Also, whether that is what Tom is arguing. A lot of sidewinds in this discussion.
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Do a search for "Laskar" in that Stability of The Solar System (https://en.wikipedia.org/wiki/Stability_of_the_Solar_System) link. You will find that the analysis and derivatives are based on his work.
Sandokan addressed Laskar here earlier this year:
This explains it well.
It does not, on the contrary.
Scott Tremaine's arguments rest totally on Jacques Laskar's numerical simulations.
(https://image.ibb.co/e2EYGJ/gil00_zpslwerxjhx.jpg)
(https://image.ibb.co/d4EawJ/gil01_zpsbzfkgbpu.jpg)
(https://image.ibb.co/mtf4qd/gil02_zpsodpyookj.jpg)
(https://image.ibb.co/gDuxAd/gil03_zpsibabxpcg.jpg)
(https://image.ibb.co/b8Giiy/gil04_zps4wcpajjf.jpg)
(https://image.ibb.co/nPa9Oy/gil05_zpsmmpvvhcu.jpg)
(https://image.ibb.co/dx9VVd/gil06_zpsljjqeiia.jpg)
(https://image.ibb.co/bys63y/gil07_zpsalpm8lqo.jpg)
In summary:
(https://i.imgur.com/GtNbE1K.png)
Rama, look at the quotes Sandokan gave in response to edby about the millions of years stability stuff.
(https://i.imgur.com/tZdVR23.png)
Where did he get his data on "eccentricity" and "orbital shape," one may ask? From the place all astronomers get it from under in their fantasy conjecture: The sky!
Smooth out over "long term trends." This clearly indicates a statistical analysis.
(https://i.imgur.com/wqCEEKy.png)
Newtons laws and equations are not used. It is based on something else entirely.
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Yes continue to ignore modern eclipse predictors directly refuting you and the recent models of the solar system that are presented and cherry pick text from a while ago. It’s incredibly convincing.
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Oh I remember this is the Velikovsky stuff. We discussed that before.
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Oh I remember this is the Velikovsky stuff. We discussed that before.
What is the rebuttal? I fail to see where one was provided.
I see that the sources are cited in the text:
(https://i.imgur.com/V3vTwss.png)
(https://i.imgur.com/iJoabM8.png)
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Charles Ginenthal is the author of Carl Sagan and Immanuel Velikovsky and co-author of Stephen J. Gould and Immanuel Velikovsky. He has published papers in the journals Aeon, Meta Research, and The Velikovskian (of which he is Publisher).
Aeon is a ‘digital magazine of ideas’
Meta Research does not seem to be a physics journal
What is the rebuttal? I fail to see where one was provided.
Velikovsky
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The sources cited are not Velikovsky.
I see that the sources are cited in the text:
(https://i.imgur.com/V3vTwss.png)
(https://i.imgur.com/iJoabM8.png)
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Some of the arguments are interesting. I see that sources like Jacques Laskar are used to make a point that the solar system is in chaos. Actually, my research seemed to yield that Laskar did claim that stability was possible up to around 10 million years. After that things may get shaky. What little I saw of a book of his certainly had an illustration of the solar system with the sun at the center and all the traditional planets orbiting them. Maybe Laskar was making all the wrong assumptions in the first place and should have had the Sun orbiting above the flat Earth. I see that the scientists so far that have worked on the 3-body problem have all been working under the assumption that the earth is a sphere and the center of the solar system is the sun. I want to see some authoritarian works (with lots of equations of motion) showing that the 3-body problem can’t be solved using the FET paradigm. That way, at least, I can get a handle on what the masses, orbits, and diameters of all the bodies happen to be. You can’t seem to get any of that from the Wiki on this site.
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Tom. I don't think that anyone is saying that Saros isn't important for understanding why and more or less when eclipses happen. Astronomers wouldn't keep bringing it up if it wasn't.
However, Saros simply isn't as useful for predicting exactly where and when eclipses occur (especially total solar eclipses) as you might want to us think. That is unless you can show us the procedure for using Saros alone to predict exactly when the next total solar eclipse will be visible in any given location.
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Gary, it has been pointed out to you on the numerous times we have had these conversations. All of these models are numeric solutions.
of course they're numerical integrations. there is no general analytic solution, so it has to be a numerical method. lol i didn't say that they aren't using a numerical method, you're just too confused to know the difference. i'm saying that they're using a numerical method to simulate lots and lots of different initial conditions, and they're searching for initial conditions that lead to stable, periodic configurations.
tbh i don't even get what your argument is anymore. you started with numerical simulations of the solar system are impossible, and you've now arrived at these are numerical simulations you ifiot!!!
(https://i.imgur.com/Zkqthvb.jpg)
Again, we see that these are numerical methods, and not based on an analytical solution. This argument is clearly and fantastically wrong.
lol. you don't have a clue what this is an image of, do you? that's awesome. please find more arenstorf orbits and post them. once again, literally no one but you is saying that there is an analytic solution to n-body problems. they're always solved with numerical methods.
Sandokan addressed Laskar here earlier this year: <pdfs>
unsurprisingly, sandy's author very selectively quotes Newton's Clock to make it seem like Ivars Peterson actually agrees with him. he doesn't. i'm also not surprised that you haven't bothered to read any of this material yourself.
(https://i.imgur.com/8HmRza0.png)
(https://i.imgur.com/W7k0ohY.png)
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Gary, it has been pointed out to you on the numerous times we have had these conversations. All of these models are numeric solutions.
of course they're numerical integrations. there is no general analytic solution, so it has to be a numerical method. lol i didn't say that they aren't using a numerical method, you're just too confused to know the difference. i'm saying that they're using a numerical method to simulate lots and lots of different initial conditions, and they're searching for initial conditions that lead to stable, periodic configurations.
tbh i don't even get what your argument is anymore. you started with numerical simulations of the solar system are impossible, and you've now arrived at these are numerical simulations you ifiot!!!
There are numerical simulations. They are the very sensitive ones that fall apart at the slightest touch, make odd orbits that look nothing like what is theorized in astronomy, and require at least two bodies of equal mass.
If you believe this to be something else entirely, then where are the three body simulations with bodies of different masses? Why do these simulations need to have at least two bodies of equal masses? You have explained nothing, and continuously ignore this question.
unsurprisingly, sandy's author very selectively quotes Newton's Clock to make it seem like Ivars Peterson actually agrees with him. he doesn't. i'm also not surprised that you haven't bothered to read any of this material yourself.
https://i.imgur.com/8HmRza0.png
https://i.imgur.com/W7k0ohY.png
Peterson was not misquoted. From Newton's Clock (https://books.google.com/books?id=-xwv6L733aoC&lpg=PA249&ots=y1AQeR4UZJ&dq=instead%20of%20using%20ful%20equations%20of%20motion%20newtons%20clock&pg=PA252#v=onepage&q&f=false):
(https://i.imgur.com/QJjG4f3.png)
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Peterson was not misquoted.
Gary said Peterson was 'selectively quoted', not that he was misquoted.
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Another find on Laskar's methods:
https://www.sciencedirect.com/science/article/pii/001910359290196E
Using a different approach based on perturbation techniques and
huge dedicated algebraic manipulations, Laskar (1985, 1988) managed to
transform the equations of motion of the eight main planets of the Solar
System in order to obtain a new system where only the slowly precessing
motions of the orbits where present, and not the orbital frequencies
From the Wikipedia article on perturbations (https://en.wikipedia.org/wiki/Perturbation_theory):
This general procedure is a widely used mathematical tool in advanced sciences and engineering: start with a simplified problem and gradually add corrections that make the formula that the corrected problem becomes a closer and closer match to the original formula.
History
Perturbation theory was first devised to solve otherwise intractable problems in the calculation of the motions of planets in the solar system.
...Since astronomic data came to be known with much greater accuracy, it became necessary to consider how the motion of a planet around the Sun is affected by other planets. This was the origin of the three-body problem; thus, in studying the system Moon–Earth–Sun the mass ratio between the Moon and the Earth was chosen as the small parameter. Lagrange and Laplace were the first to advance the view that the constants which describe the motion of a planet around the Sun are "perturbed", as it were, by the motion of other planets and vary as a function of time; hence the name "perturbation theory"
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I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.
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I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.
I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.
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http://adsbit.harvard.edu//full/1991CeMDA..50...73W/0000073.000.html
Here's a good place to start. Of course it may be completely fake as NASA is involved. All you would have to do is prove all the equations are fake.
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http://adsbit.harvard.edu//full/1991CeMDA..50...73W/0000073.000.html
Here's a good place to start. Of course it may be completely fake as NASA is involved. All you would have to do is prove all the equations are fake.
It's talking about a limited possibility for a generalized solution for the Three Body Problem. From the conclusion:
(https://i.imgur.com/akqvJoq.png)
Essentially, it is not easy to model chaos:
Chaos and the Solar System (http://ptrow.com/articles/ChaosandSolarSystem5.htm)
by Paul Trow
What exactly is chaos? We can give an example by a rigid pendulum, such as in a grandfather clock. If the pendulum swings freely, its motion will be perfectly regular and periodic, and if there were no friction, it would continue this way forever. The system is perfectly predictable – it is the opposite of chaos. But now suppose that we place an electric magnet at the base of the pendulum, and arrange for the magnet turn on momentarily at regular intervals – say once every second – at which time it exerts a magnetic force on the pendulum. This device is rather like a parent pushing a child on a swing, but unlike the parent who pushes in time with the swing, the magnet’s forces are out of phase with the pendulum. If the magnet exerts its force during the pendulum’s downward swing, it speeds the pendulum up – but if it does so during the upward swing, it slows the pendulum down. The question is simply this: what will happen to the pendulum? Will it swing regularly or irregularly? Can we predict its motion at all?
Since the device is such a simple deterministic system, and the magnet’s push occurs at regular intervals, we might guess that the pendulum’s motion would be periodic. In other words, after a while the motion would begin to repeat itself. Surprisingly, what actually happens is that the pendulum begins to swing irregularly, sometimes higher and sometimes lower, without any discernible pattern. We are no more able to predict how high the pendulum will go after a few swings than we are to predict the outcome of a roll of the dice. What this device shows is that a simple deterministic mechanism can generate what appears to be random motion – in other words, it is chaotic.
There is a historical irony in the fact that this simple device is chaotic. Galileo studied the motion of freely swinging pendulums, and discovered that their period is independent of the length of the pendulum. Indeed, this discovery, along with his famous analysis of falling bodies and projectiles, were some of the first quantitative descriptions of terrestrial motion. Galileo’s work was one of the two most significant influences on Newton’s thinking. The irony is that something so simple as a pendulum – the very symbol of the deterministic universe – can be altered so slightly as to produce chaos. And the historical question this raises is why it took almost three hundred for someone to recognize the possibility of chaotic motion. I think it is safe to say that because Galileo and the other great genius of the scientific revolution were searching for order in the universe, they were blind to the existence of chaos all around them.
The author goes on, describing that the motion of planetary systems has been an issue for a long time.
Describing the motion of any planetary system (including purely imaginary ones that exist only on paper) is the subject of a branch of mathematics called celestial mechanics. Its problems are extremely difficult and have eluded the greatest mathematicians in history.
The mathematician and theoretical physicist Henri Poincaré was instrumental in showcasing the challenges of Celestial Mechanics:
As other mathematicians had done before, Poincaré considered a special case in which there are just three planetary bodies (the so-called three-body problem). Poincaré, however, tried a novel approach to the problem: rather than trying to explicitly solve the equations of motion, as mathematicians had always done previously, he looked at the qualitative behavior of planetary orbits - for example, whether they were periodic or followed more irregular paths. This approach had a liberating effect, enabling him to see possibilities that others had overlooked. What he discovered was quite unexpected: the motion of a planet in a three-body system can be very wild and unpredictable indeed. Its orbit can follow an apparently random curve, winding back around itself over and over again, like a long and tangled string. As he described such curves:
When one tries to depict the figure formed by these two curves and their infinity of intersections, each of which corresponds to a doubly asymptotic solution, these intersections form a kind of net, web, or infinitely tight mesh; neither of the two curves can ever cross itself, but must fold back on itself in a very complex way … Nothing can give us a better idea of the complexity of the three-body problem.
The article continues:
Poincaré’s discovery was surprising because it contradicted age-old assumptions about the motion of the planets. Beginning with the early Greeks, who thought that the planets moved in circles, astronomers had long believed that planetary motion was built up from simple motion. The theories of Kepler and Newton reinforced this belief. Before Poincaré, no one had imagined that such complicated, unpredictable motion could occur in the solar system. It must have come as a shock to him to realize that the motion of a planet could appear to be as random as that in a pinball machine.
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I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.
I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.
I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask. Gary linked two simulations of the solar system (https://forum.tfes.org/index.php?topic=11374.msg174008#msg174008). You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do. You really can't make this up.
Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.
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I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.
I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.
I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask. Gary linked two simulations of the solar system (https://forum.tfes.org/index.php?topic=11374.msg174008#msg174008). You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do. You really can't make this up.
Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.
Do a search for the terms we have been talking about in this thread in those links. They are based on perturbation and pattern-based methods. No one can model chaos. Don't be ridiculous.
Read Frank's comment again. He agrees that NASA is using the Saros Cycle, but is pointing out that he is getting his data for the sun and the moon in his work from the JPL DE model, which he thinks is a n-body simulation of the solar system. In reality it uses predictions based on perturbations... just like everything else... and which we have been egregiously defining in this thread.
Will Saros-mister Frank come here and tell us that all authors, celestial mechanics professors, and articles are wrong about perturbation methods?
Will Frank come here and tell us that what we are reading amounts to a coincidental series of typos, that the three body problem is a trivial thing that was solved by mathematicians hundreds of years ago, or, perhaps that JPL has a secret n-body simulation of the solar system?
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https://arxiv.org/pdf/1508.02312.pdf
Here's another paper on the 3 body problem. Just what kind of specification are you looking for in the 3 body problem? What exactly would it prove to you if a solution was available?
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...he is getting his data for the sun and the moon in his work from the JPL DE model,
which he thinks is a n-body simulation of the solar system.
Where does he say he thinks that? (http://Where does he say he thinks that?)
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https://arxiv.org/pdf/1508.02312.pdf
Here's another paper on the 3 body problem. Just what kind of specification are you looking for in the 3 body problem? What exactly would it prove to you if a solution was available?
The solutions are limited Ron. Lets ask this mathematician at askamathematician.com:
https://www.askamathematician.com/2011/10/q-what-is-the-three-body-problem/
Q: What is the three body problem?
Physicist: The three body problem is to exactly solve for the motions of three (or more) bodies interacting through an inverse square force (which includes gravitational and electrical attraction).
The problem with the 3-body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).
My point is that the Three Body Problem can't create a sun with a planet that has a moon, like Copernicus told us. Astronomy is in the Stone Age. Prediction in astronomy is through other means that involve pattern-finding of the observed movements of the planets.
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I don’t understand how Tom can continually be presented with multiple different simulations of the solar system and the continue on to say there are no n-body problem solutions that have bodies of differing mass.
I didn't write these sources that I am quoting. Lets see the three body simulations of three bodies with unequal masses. Feel free to provide evidence for your argument rather than submitting a content-less post.
I wasn't talking about your sources.Please try and understand what is written, and if you have questions ask. Gary linked two simulations of the solar system (https://forum.tfes.org/index.php?topic=11374.msg174008#msg174008). You also decided that a member of NASA's eclipse prediction team doesn't understand how NASA predicts eclipses, but you do. You really can't make this up.
Hopefully someone coming to the site will see exactly how out of touch your arguments are with the evidence at hand.
Do a search for the terms we have been talking about in this thread in those links. They are based on perturbation and pattern-based methods. No one can model chaos. Don't be ridiculous.
Those are numerical solution driven models of the solar system. It’s exactly what you said was impossible.
Read Frank's comment again. He agrees that NASA is using the Saros Cycle, but is pointing out that he is getting his data for the sun and the moon in his work from the JPL DE model, which he thinks is a n-body simulation of the solar system. In reality it uses predictions based on perturbations... just like everything else... and which we have been egregiously defining in this thread.
Will Saros-mister Frank come here and tell us that all authors, celestial mechanics professors, and articles are wrong about perturbation methods?
Will Frank come here and tell us that what we are reading amounts to a coincidental series of typos, that the three body problem is a trivial thing that was solved by mathematicians hundreds of years ago, or, perhaps that JPL has a secret n-body simulation of the solar system?
Frank said explicitly that “Modern eclipse predictions do NOT use the Saros.” The opposite of what you are saying. Furthermore he says, “Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation.”
This is in exact opposition of what you are saying. It could not be clearer.
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Ed -
In a word “rubbish!”
Modern eclipse predictions do NOT use the Saros.
Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation. [Fred thinks that there is an n-body solar system out there based on Newton's Laws ]
More specifically, I use the Jet Propulsion Laboratory Developmental Ephemeris 430 (i.e., JPL DE430) to calculate the positions of the Moon, and Sun with respect to Earth. [Fred gives JPL DE as his evidence, because he mentions using them on his website for computing the positions of the sun or moon over the earth. JPL DE admits to be based on perturbation theory] This is the raw material from which the Besselian elements used in eclipse predictions are derived from (https://en.wikipedia.org/wiki/Besselian_elements). [See below] It involves a lot of spherical geometry to calculate every conceivable aspect of any solar eclipse.
Using this method, I can calculate the time of the start and end of any solar eclipse to a fraction of a second for any location on Earth. I challenge any flat Earther to match that precision and accuracy using flat Earth geometry.
Best regards,
Fred Espenak
PS - By the way, the JPL DE is also used to help navigate all the interplanetary spacecraft into orbits or flybys of the planets (e.g., New Horizons and Pluto).
Basselian elements
http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/predictions.htm
Intro:
Bessel developed the method used to calculate and describe precisely any eclipse, based on using a coordinate system oriented to the shadow’s axis. The basic steps are: elements are calculated in the Besselian system to describe geometrical quantities; the observer’s position is transformed to Bessel’s coordinate system; equations of condition are formed; circumstances are derived that describe the time and the place of observable events or conditions in the Besselian system; the circumstances are transformed back to topocentric or geocentric coordinates. Many people have actually used the Besselian elements in calculating the eclipses.
Article continues:
Whether an eclipse will occur depends mostly on the coming together of two periodical phenomena, in this case the reaching of the proper lunar phase and the passing through a node. For more generality, we'll investigate the coming together of two arbitrary phenomena A and B. We assume that phenomenon A has a period PA, that phenomenon B has period PB, and that the lengths of those periods are constant.
...
Approximation With a Ratio of Whole Numbers
To base predictions of Z on periods, we must approximate γ with a ratio a⁄b of positive whole numbers. If we can find such a and b, then we can say that a periods PB are almost equal to b periods PA, and that hence that much time after a previous Z another Z will occur.
...
The first couple of very good approximations that we find for eclipses are listed in the following table. The very good approximations are a⁄b. The corresponding period of prediction and great period (to be explained later) are y (in years) en c (in years). The number of successful predictions in a row to be expected is between n1 and n2. The fraction of successful predictions of further eclipses based on earlier eclipses and the prediction period is equal to P. Very good approximation number 12 has the unusably large prediction period of 12393.4 years.
...
The Great Period
Eventually we use some approximation
(Eq. 10) γ' = a⁄b
for γ with whole numbers a and b. These numbers do not have to be determined using the method described above, and don't even need to give a particularly good approximation to γ. We assume (without loss of generality) that a and b have no divisors in common.
This approximation corresponds to the assumption that b periods PA are equal to a periods PB and that that much time after a previous Z there will be a next Z. We'll refer to this period of time as the period of prediction and will indicate it as y.
Plenty of other references of "periods" as the article continues.
We are reminded of the following quote of T.G. Ferguson in the Earth Review for September 1894, as appears in our literature:
No Doubt some will say, 'Well, how do the astronomers foretell the eclipses so accurately.' This is done by cycles. The Chinese for thousands of years have been able to predict the various solar and lunar eclipses, and do so now in spite of their disbelief in the theories of Newton and Copernicus. Keith says 'The cycle of the moon is said to have been discovered by Meton, an Athenian in B.C. 433,' then, of course, the globular theory was not dreamt of.
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From Fred's website on Besselian elements:
http://www.eclipsewise.com/solar/SEhelp/SEbeselm.html
The eight Besselian elements needed to characterize a solar eclipse can be summarized as follows:
x, y - Cartesian coordinates of the lunar shadow axis in the (in units or Earth's equatorial radius)
L1, L2 - Radii of the Moon's penumbral and umbral/antumbral shadows in the (in units or Earth's equatorial radius)
d - Declination of the Moon's shadow axis on the celestial sphere
µ - Hour angle of the Moon's shadow axis on the celestial sphere
f1, f2 - Angles of the penumbral and umbral/antumbral shadow cones with respect to the axis of the lunar shadow
The details for actual eclipse calculations using the Besselian elements can be found in the references listed below.
Hardly a round earth model. A Round Earth Solar System can't be simulated with this information. Where is the Round Earth Element? Is it the mention of the Earth's "equatorial radius"? A Round Earth is proven, and is entirely simulated, because an equation is using something called the earth's "equatorial radius"? Patently ridiculous. The Flat Earth Radius has an analogue to the Round Earth Radius (https://wiki.tfes.org/Erathostenes_on_Diameter). That something with that name is used shows nothing.
The fact that "celestial sphere" is mentioned makes it obvious. The celestial sphere is a regular astronomy term for the local celestial sphere to where we find bodies in the sky above us.
This does not look like a simulation of the Sun-Earth-Moon system at all.
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Ed -
In a word “rubbish!”
Modern eclipse predictions do NOT use the Saros.
Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation. [Fred thinks that there is an n-body solar system out there based on Newton's Laws ]
More specifically, I use the Jet Propulsion Laboratory Developmental Ephemeris 430 (i.e., JPL DE430) to calculate the positions of the Moon, and Sun with respect to Earth. [Fred gives JPE DE as his evidence, because he mentions using them on his website for computing the positions of the sun or moon. JPE DE admits to be based on perturbation theory] This is the raw material from which the Besselian elements used in eclipse predictions are derived from (https://en.wikipedia.org/wiki/Besselian_elements). [See below] It involves a lot of spherical geometry to calculate every conceivable aspect of any solar eclipse.
Using this method, I can calculate the time of the start and end of any solar eclipse to a fraction of a second for any location on Earth. I challenge any flat Earther to match that precision and accuracy using flat Earth geometry.
Best regards,
Fred Espenak
PS - By the way, the JPL DE is also used to help navigate all the interplanetary spacecraft into orbits or flybys of the planets (e.g., New Horizons and Pluto).
Basselian elements
http://www.math.nus.edu.sg/aslaksen/gem-projects/hm/0304-1-08-eclipse/predictions.htm
Intro:
Bessel developed the method used to calculate and describe precisely any eclipse, based on using a coordinate system oriented to the shadow’s axis. The basic steps are: elements are calculated in the Besselian system to describe geometrical quantities; the observer’s position is transformed to Bessel’s coordinate system; equations of condition are formed; circumstances are derived that describe the time and the place of observable events or conditions in the Besselian system; the circumstances are transformed back to topocentric or geocentric coordinates. Many people have actually used the Besselian elements in calculating the eclipses.
Whether an eclipse will occur depends mostly on the coming together of two periodical phenomena, in this case the reaching of the proper lunar phase and the passing through a node. For more generality, we'll investigate the coming together of two arbitrary phenomena A and B. We assume that phenomenon A has a period PA, that phenomenon B has period PB, and that the lengths of those periods are constant.
...
Approximation With a Ratio of Whole Numbers
To base predictions of Z on periods, we must approximate γ with a ratio a⁄b of positive whole numbers. If we can find such a and b, then we can say that a periods PB are almost equal to b periods PA, and that hence that much time after a previous Z another Z will occur.
...
The first couple of very good approximations that we find for eclipses are listed in the following table. The very good approximations are a⁄b. The corresponding period of prediction and great period (to be explained later) are y (in years) en c (in years). The number of successful predictions in a row to be expected is between n1 and n2. The fraction of successful predictions of further eclipses based on earlier eclipses and the prediction period is equal to P. Very good approximation number 12 has the unusably large prediction period of 12393.4 years.
...
The Great Period
Eventually we use some approximation
(Eq. 10) γ' = a⁄b
for γ with whole numbers a and b. These numbers do not have to be determined using the method described above, and don't even need to give a particularly good approximation to γ. We assume (without loss of generality) that a and b have no divisors in common.
This approximation corresponds to the assumption that b periods PA are equal to a periods PB and that that much time after a previous Z there will be a next Z. We'll refer to this period of time as the period of prediction and will indicate it as y.
Etc.
We are reminded of the following quote of T.G. Ferguson in the Earth Review for September 1894, as appears in our literature:
No Doubt some will say, 'Well, how do the astronomers foretell the eclipses so accurately.' This is done by cycles. The Chinese for thousands of years have been able to predict the various solar and lunar eclipses, and do so now in spite of their disbelief in the theories of Newton and Copernicus. Keith says 'The cycle of the moon is said to have been discovered by Meton, an Athenian in B.C. 433,' then, of course, the globular theory was not dreamt of.
I am not sure why you keep highlighting the word period. Is this supposed to be some sort of gotcha moment?
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I am not sure why you keep highlighting the word period. Is this supposed to be some sort of gotcha moment?
It's pattern-based prediction. The fact that "periods" and the ancient Saros Cycle is needed at all, and is plastered all over NASA's website, rather than a purely mathematical model of the earth-moon-sun system, says it all.
Astronomy is still in the Stone Age.
Astronomers must appeal to "perturbations" and "periods" rather than actual models of the solar system.
Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns. If Fred wants an argument from a Flat Earther he need only look in the mirror.
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Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns.
Tom, what evidence do you have that Flat Earth civilizations were able to use just patterns like Saros cycles to accurately predict solar eclipses?
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I am not sure why you keep highlighting the word period. Is this supposed to be some sort of gotcha moment?
It's pattern-based prediction. The fact that "periods" and the ancient Saros Cycle is needed at all, and is plastered all over NASA's website, rather than a purely mathematical model of the earth-moon-sun system, says it all.
lol, you dont even know what the word period means in this context. A period is simply an amount of time it takes to complete one cycle of a repeating event. Of course orbits have a period in this context.
Astronomy is still in the Stone Age.
Incorrect.
Astronomers must appeal to "perturbations" and "periods" rather than actual models of the solar system.
Flat Earth Civilizations came up with the idea to predict astronomical phenomena with patterns. If Fred wants an argument from a Flat Earther he need only look in the mirror.
You dont know what a period means, something I learned in high school in probably grade 9 or 10. The odds of you understanding any of this subject becomes even less likely. To borrow your turn of phrase, you should feel ashamed and embarrassed to so badly misrepresent the topic you are disputing.
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You are providing zero evidence, Rama Set. Go and ask a mathematician about the three body problems you say simulate the Sun-Earth-Moon system. Can't be done.
Astronomy cannot simulate the Sun-Earth-Moon system.
We are witnessing the continued failure of Team Ball to defend their position that the solar system can be simulated, which is repeatedly professed to be true. Year after year, this conversation repeats itself. The fantasy cannot exist under Newton's laws. The Three Body Problem shows that. It is not an merely academic exercise. It was Newton's own personal failing to model his theory, and which required an appeal to divine intervention to solve. Farcical failure.
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I don’t understand where your failure to understand comes from. You have been provided multiple simulations of the solar system in this thread. All this is ignoring, of course, that we have successfully navigated proves in to the orbits of other planets, which is sportingly not brought up. But really, the denial is pathological, and the misunderstandings are disastrous. Literally a member of the NASA eclipse team directly refuting your position is in this thread and you deny it. So whatever argument you believe you are making is utterly unconvincing.
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There is zero evidence that the n-body issues have been solved. Provide evidence that the n-body problems have been solved and that the solar system, or the sun-earth-moon system, can be simulated.
Why do the existing solutions and simulations of the three body problem require at least two bodies of the exact same mass? This has yet to be addressed.
I thought we were told that it was possible for a sun to have a planet, and for that planet to have a moon? That's not possible in astronomy? Then none of it is possible. It is a farce.
It is difficult for you guys to show that it is possible because you are wrong.
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You are providing zero evidence, Rama Set. Go and ask a mathematician about the three body problems you say simulate the Sun-Earth-Moon system. Can't be done.
Astronomy cannot simulate the Sun-Earth-Moon system.
Perhaps not, but it can provide an accurate approximation.
https://www.youtube.com/watch?v=eR3aylKwPyY
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...Rather, they are based on the orbital mechanics of the Earth, Moon, and Sun as laid out by Newton’s theory of gravitation.
[Fred thinks that there is an n-body solar system out there based on Newton's Laws ]
That is not what Fred can be said to think based on the statement her wrote. This is the crux of the divergence from my opening post. Espenak is not saying that there is an N-Body solution. It's irrelevant to what Fred is saying.
You're conflating issues. I don't think it's intentional. I think you are just mistaken and you've erected a false dichotomy based on the N-body issue.
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https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Dissertations/1998_Wilson.pdf
Here is a 3 body problem plus spacecraft. The 3 main bodies are Earth, Moon, and Sun. All the motions and gravitational field vectors are calculated so the spacecraft can successfully navigate it's mission. The spacecraft did complete the mission and verified all the calculations of the 3 body problem. Now you have a calculation and an actual verification of the accuracy. The problem is no longer theory, it's fact.
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As far as I am aware, it is not possible to even approximate the Sun-Earth-Moon system. The video you posted implies masses of different sizes; when this is not the case with the Three Body Problem.
Take a look at the Three Body Problem family gallery: http://three-body.ipb.ac.rs/
Here is an N-Body Orbit Gallery, which showcases the limited orbits that can be made, and which must assume that bodies are of equal mass or mass-less: http://rectangleworld.com/demos/nBody/
The ones that look like a heliocentric system don't exist. I am unable to find that family anywhere in the list of families.
https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Dissertations/1998_Wilson.pdf
Here is a 3 body problem plus spacecraft. The 3 main bodies are Earth, Moon, and Sun. All the motions and gravitational field vectors are calculated so the spacecraft can successfully navigate it's mission. The spacecraft did complete the mission and verified all the calculations of the 3 body problem. Now you have a calculation and an actual verification of the accuracy. The problem is no longer theory, it's fact.
That's a student's dissertation about navigating around a hypothetical system with existing three body problem solutions. The name of the chapters tell that it is using the restricted three body problem, where two of the masses are massive and one is of a negligible mass.
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That is completely true, however the model outlined in the dissertation was actually employed to send the GENESIS satellite to collect solar wind samples and return it to the earth. That project was completed. You have to do more research to realize that fact.
Do more research on what 'restricted' means. Your definition is incorrect. A 3 body restricted mission was completed a long time ago. What that means is Earth, Moon, spacecraft. The restricted part means that one of the bodies doesn't affect the other two. Anytime you have gravitational force between two bodies each body will affect the other. The earth rotates around the sun, but it could also be said that the sun rotates around the earth. The sun is a lot more massive so the orbit is quite small in relation to the orbit of the earth. The same goes for the Earth Moon relationship. If you send a spacecraft into the gravitational field of the earth, moon, or sun those bodies will also move, but it's like pissing in the ocean, you won't be able to measure it. The effect on the spacecraft is completely different because of the ratio of the masses. The masses of any of the objects involved don't have to be the same. Each can be different.
In the case of the GENESIS mission the problem solved and demonstrated to work was the restricted 4 body problem. Earth, Moon, Sun, and spacecraft. Each with a completely different mass. Example shown and demonstrated to work. I don't think a caveman could have completed the project.
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Peterson was not misquoted. From Newton's Clock (https://books.google.com/books?id=-xwv6L733aoC&lpg=PA249&ots=y1AQeR4UZJ&dq=instead%20of%20using%20ful%20equations%20of%20motion%20newtons%20clock&pg=PA252#v=onepage&q&f=false):
(https://i.imgur.com/QJjG4f3.png)
do you really not understand what quote mining is? it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making. yes, the author makes that remark about laskar's work in 1983. but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results. he describes the nature and results of some of those simulations.
the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly. read the quotes i posted. he's quite clear.
Lets see the three body simulations of three bodies with unequal masses.
i already provided you with a nine-body simulation. this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve.
A three million year integration of the earth's orbit (http://adsabs.harvard.edu/abs/1991AJ....101.2287Q)
(https://i.imgur.com/AY2HS7B.png)
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Sounds like 3 million year predictions is not accurate enough for Mr. Bishop. Is the bar for RE math a billion years? Infinity with zero inaccuracy? As for patterns, those Saros cycles are from 2000 up to 12000 year patterns... How is any human being without today’s computing power supposed to make predictions on a cycle that takes thousands of years and they can’t see most of them in any one region of the planet. This is assuming there aren’t clouds covering up a partial eclipse. It is impossible for anyone on the planet to make accurate solar eclipse predictions without modern calculations. We are still waiting how the ancients could predict the exact locations on the planet where solar eclipses will be visible. Not when somewhere on the planet, but where, width, distance, direction of those solar eclipses? Lunar eclipses are easy compared to pinpointing the shadow of the moon onto the Earth exactly.
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Peterson was not misquoted. From Newton's Clock (https://books.google.com/books?id=-xwv6L733aoC&lpg=PA249&ots=y1AQeR4UZJ&dq=instead%20of%20using%20ful%20equations%20of%20motion%20newtons%20clock&pg=PA252#v=onepage&q&f=false):
(https://i.imgur.com/QJjG4f3.png)
do you really not understand what quote mining is? it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making. yes, the author makes that remark about laskar's work in 1983. but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results. he describes the nature and results of some of those simulations.
the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly. read the quotes i posted. he's quite clear.
Lets see the three body simulations of three bodies with unequal masses.
i already provided you with a nine-body simulation. this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve.
A three million year integration of the earth's orbit (http://adsabs.harvard.edu/abs/1991AJ....101.2287Q)
(https://i.imgur.com/AY2HS7B.png)
From the abstract of that Harvard paper: " The initial conditions are taken from the JPL DE 102 ephemeris."
Wikipedia says about the JPL DE 102 ephemeris: "Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. "
Tom's point stands.
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Sounds like 3 million year predictions is not accurate enough for Mr. Bishop.
A quotation from gary's paper: "'Accurate' can only be loosely defined in this context."
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Peterson was not misquoted. From Newton's Clock (https://books.google.com/books?id=-xwv6L733aoC&lpg=PA249&ots=y1AQeR4UZJ&dq=instead%20of%20using%20ful%20equations%20of%20motion%20newtons%20clock&pg=PA252#v=onepage&q&f=false):
(https://i.imgur.com/QJjG4f3.png)
do you really not understand what quote mining is? it's dishonest to selectively quote a text to make it seem as if the author is making a different point than he or she is actually making. yes, the author makes that remark about laskar's work in 1983. but then immediately after that he explains that other simulations absolutely did model the solar system directly and confirmed laskar's results. he describes the nature and results of some of those simulations.
the source that you presented as a credible authority explicitly disagrees with everything you are claiming, and he says so directly. read the quotes i posted. he's quite clear.
Lets see the three body simulations of three bodies with unequal masses.
i already provided you with a nine-body simulation. this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve.
A three million year integration of the earth's orbit (http://adsabs.harvard.edu/abs/1991AJ....101.2287Q)
(https://i.imgur.com/AY2HS7B.png)
From the abstract of that Harvard paper: " The initial conditions are taken from the JPL DE 102 ephemeris."
Wikipedia says about the JPL DE 102 ephemeris: "Each ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. "
Tom's point stands.
No it doesn’t. It is a simulation of multiple objects of varying mass. Tom claimed this was impossible.
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Did you read the paper? You are suggesting that 1 radian of error to Earths location after 3 million years of calculations proves Toms point? 1 radian! It’s not 100% perfect over millions of years so the Earh is flat, that’s what you are saying.
Tom's point stands.
Your bar for RE math is impossible to meet, yet FE requires magic to make the most critical parts of it work (even with magic, it still doesn’t work). Not just magic like UA, but selective magic UA, a cartwheeling universe around the accelerating Earth, accelerating and decelerating magically held aloft Sun and Moon without visibly changing in speed, magic bendy light in specific ways up down curving whichever way is needed at that moment in time, ice wall no one has ever seen... I can go on for a while here I haven’t even listed the most obvious issues...
Literally, nothing in FEH matches reality and that’s ok.
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i already provided you with a nine-body simulation. this is literally a simulation of the solar system carried out by directly calculating newton's laws and letting the system evolve.
A three million year integration of the earth's orbit (http://adsabs.harvard.edu/abs/1991AJ....101.2287Q)
https://i.imgur.com/AY2HS7B.png
Read the first two sentences of that abstract:
Abstract
We have integrated the equations of motion of the nine planets and the Earth's spin axis for 3.05 million years into the past. The equations include the dominant relativistic corrections and the corrections for the quadropole movement of the Earth-Moon system
Why would we need "relativistic corrections" if this is, as you assert, a full simulation of gravity?
The Wikipedia article on Perturbation Theory (https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns#Perturbations) says:
“ This general procedure is a widely used mathematical tool in advanced sciences and engineering: start with a simplified problem and gradually add corrections that make the formula that the corrected problem becomes a closer and closer match to the original formula. ”
If your formula doesn't work, just keep adding corrections until it does. Science!
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It’s a simulation, not an implementation of the scientific method. The question of why you would add relativistic corrections to a model using GR seems pretty self-evident.
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Did you read the paper? You are suggesting that 1 radian of error to Earths location after 3 million years of calculations proves Toms point? 1 radian! It’s not 100% perfect over millions of years so the Earh is flat, that’s what you are saying.
Actually the paper says "At the end of integration, the fractional error in the earth's position is shown to be less than 0.03 radian, and larger errors of up to several radians are shown for other planets." This is only theoretical however because you cannot verify the positions of the planets 3 million years ago. To quote the paper: "We believe that the physical model, the initial conditions and the integration procedure are accurate enough that the fractional error in Earth's position is less than 0.03 radian."
The off topic grandstanding rhetorical stuff in your post will ignored.
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Please shut off your trolling motor, drop anchor, and put out a hook and a line for some facts that you can keep.
If your formula doesn't work, just keep adding corrections until it does. Science!
Newtonian equations work fine. You can get any desired level of accuracy you want. When you need more accuracy all you do is provide the necessary accuracy to the variables in the formula. Of course that's the crux of the problem. There are always measurement errors. In some cases there are variables out there that are unknown. Anytime you have a measurement error it usually tells you something. Sometimes small errors are completely expected and have a known cause. Other times you can have an error that's unexpected and you can use that information for further investigation. Everything is probabilistic. If I make a measurement 10000 times and all the numbers are within say 1 in a million and I then get a number that is way out of that range, what would be the expected result? Probably I wouldn't expect that the formula is defective. I would look for an obvious problem with the equipment or some anomalous event nearby that had an unwanted effect on your measurement. In most cases you will end up finding out why there was a problem with the reading. If you made another 10000 readings that were completely different and weren't expected by your equations, only then, would I suspect my equations.
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This has gone way off the rails.
The N-body problem is a red herring.
The issue I raised in the opening post of this topic is the TFES Wiki's (Tom's) claim that eclipse predictions are based on patterns. That's wrong, and whether or not the N-Body problem eludes solution doesn't matter. Cycles are time-based. There is nothing about a Saros cycle that can provide the parameters needed to calculate Besselian elements of a solar eclipse.
You can't get this from a cycle:
(http://oi67.tinypic.com/27y8k08.jpg)
You can't produce this based on a mere cycle:
(http://oi65.tinypic.com/317cj6u.jpg)
This is the predicted solar eclipse for July 2, 2019. It's part of Saros cycle 127. But that's not the basis for predicting the detailed characteristics of the eclipse: the where, the how much, the duration, etc. For that, you need the Besselian elements, which are based on the relative position and motion of the earth/moon/sun and spherical geometry of the earth. It doesn't matter if the ephemeris providing earth/moon/sun location and motion are divinely granted or calculated based on a perfect solution to the 3-body problem of these 3 bodies, with or without perturbation by other solar system or galactic bodies. It doesn't matter. That's a distraction. Either intentional or misguided.
The ability to calculate where on earth the eclipse will be seen, the degree of totality, the coverage of the umbra and penumbra, precisely when it will begin and end, etc. doesn't hinge on solving the n-body problem. There is no flat earth model analog for how Fred Espenak performs his calculations by using an ephemeris of a rotating globe earth, orbited by a globe moon, orbiting a spherical sun. It's based on spherical geometry and absolutely requires input of position and motion of the 3-bodies. It's not "patterns" at all.
Tom has managed to derail this and get everyone debating aspects how the ephemerides are produced, under the illogical reasoning that if a million-year stable n-body solution can't be calculated using Newtonian mechanics, that the entire edifice collapses and all that remains is "patterns."
When eclipse #58 in Saros Cycle 127 begins, it will occur and have the characteristics predicted. That prediction won't be just a table look up of a pattern. It will be calculated based on the shape of the earth, the shape of the moon's shadow on the convex surface of the globe earth, based on position and motion of the 3-body earth-moon-sun system taken from an ephemeris, the utility or accuracy of which doesn't require a solution to the n-body problem.
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This has gone way off the rails.
The N-body problem is a red herring.
The issue I raised in the opening post of this topic is the TFES Wiki's (Tom's) claim that eclipse predictions are based on patterns. That's wrong, and whether or not the N-Body problem eludes solution doesn't matter. Cycles are time-based. There is nothing about a Saros cycle that can provide the parameters needed to calculate Besselian elements of a solar eclipse.
You can't get this from a cycle:
(http://oi67.tinypic.com/27y8k08.jpg)
You can't produce this based on a mere cycle:
(http://oi65.tinypic.com/317cj6u.jpg)
This is the predicted solar eclipse for July 2, 2019. It's part of Saros cycle 127. But that's not the basis for predicting the detailed characteristics of the eclipse: the where, the how much, the duration, etc. For that, you need the Besselian elements, which are based on the relative position and motion of the earth/moon/sun and spherical geometry of the earth. It doesn't matter if the ephemeris providing earth/moon/sun location and motion are divinely granted or calculated based on a perfect solution to the 3-body problem of these 3 bodies, with or without perturbation by other solar system or galactic bodies. It doesn't matter. That's a distraction. Either intentional or misguided.
The ability to calculate where on earth the eclipse will be seen, the degree of totality, the coverage of the umbra and penumbra, precisely when it will begin and end, etc. doesn't hinge on solving the n-body problem. There is no flat earth model analog for how Fred Espenak performs his calculations by using an ephemeris of a rotating globe earth, orbited by a globe moon, orbiting a spherical sun. It's based on spherical geometry and absolutely requires input of position and motion of the 3-bodies. It's not "patterns" at all.
Tom has managed to derail this and get everyone debating aspects how the ephemerides are produced, under the illogical reasoning that if a million-year stable n-body solution can't be calculated using Newtonian mechanics, that the entire edifice collapses and all that remains is "patterns."
When eclipse #58 in Saros Cycle 127 begins, it will occur and have the characteristics predicted. That prediction won't be just a table look up of a pattern. It will be calculated based on the shape of the earth, the shape of the moon's shadow on the convex surface of the globe earth, based on position and motion of the 3-body earth-moon-sun system taken from an ephemeris, the utility or accuracy of which doesn't require a solution to the n-body problem.
Another interesting aspect of these modern computations is they show detailed models of the exact size and shape of the moon and compensate for the eart's terrain as the shadow passes over it. You can actually see in the shadow structures such as crater rims etc on the moon. I'll see if I can find the article I read that had a motion model that showed this. Quite fascinating.
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I like that prediction map. The last total solar ellipse I've personally witnessed was over 60 years ago. I've seen a couple lunar eclipses in the last 10 years. This discussion did go off the rails many posts ago as I tried to say myself. Unfortunately I was also complicit (sadly) in the continuation of the n-body argument myself. You see diversionary tactics on here all the time. The whole point isn't to propagate any new information but to simply generate posts. The more posts the better. Probably there is a logic ladder that someone has that says something like this: If the discussion is on subject A then throw out a question on subject B, or say subject C has got to be false. You see subjects of a similar nature on here with the same kinds of diversions evoked. For me the whole thing is interesting.
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Please shut off your trolling motor, drop anchor, and put out a hook and a line for some facts that you can keep.
Do me a favor and don’t do that. Warned.
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You can't produce this based on a mere cycle:
(http://oi65.tinypic.com/317cj6u.jpg)
I do not see why not. You just posted a cycle. That very gif animation is a cycle that repeats itself. The eclipses repeat themselves. And if they have trends that differ, that can be accounted for.
Prediction in astronomy is merely the use of equations to predict the cycles.
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I do not see why not. You just posted a cycle. That very gif animation is a cycle that repeats itself.
Not sure if serious. Should I report this as low-content trolling? Or are you sincere in equating a looping animated graphic of a specific eclipse as being an example of the cyclic nature of eclipses?
Here's a challenge. The coming eclipse depicted in this animation has specific characteristics:
- where and when it begins
- where and when it ends
- where and when it will be at maximum
- duration of the eclipse at that maximum
- where on the earth's surface totality can be observed
- where on the earth's surface partial eclipse can be observed
- the magnitude (how much larger the angular diameter of the moon -- or shadow object -- is than the sun)
When were the previous solar eclipses to have the same characteristics as this one such that you can claim this one is predictable simply by a cyclical pattern? Go ahead and peruse Saros 127 (of which this eclipse is a part) and find the pattern for me that allows for prediction of the above details.
The eclipses repeat themselves. And if they have trends that differ, that can be accounted for.
Prediction in astronomy is merely the use of equations to predict the cycles.
Show me.