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No, it doesn't make sense at all. Gravity also affects photons, which have zero mass.I know that you understand Relativity quite well, so why do you make statements like this just to bait people when you clearly know the answer?
[...]
...but it isn't worth $3 to find out what Logan the Overwatch player from Michigan had for breakfast.Oh you silly. It's not about hearing what Logan had for breakfast, it's about Logan saying "thanks Baby Thork for the sub" in front of all those other people! You're special now! Your name was said on stage!
I need to cite 6 credible sourcesGood luck.
Did you just post a quote from j*** bl*** on this forum?Jack Black? He's a legend mate, back off
I'm under the impression that there are only a few experiments which are actually put forward as evidence for the universal attraction of mass.I think this is kind of true, but the few experiments that do exist are all pretty consistent so there's no incentive to provide further evidence. Add on to that the fact that there's really no viable alternative and you end up with where we are now: who's going to be interested in doing this experiment?
[...]
You're not paying for a service, you're paying to support a streamer.Read the OP. You are not making a donation, you are subbing ... ie giving half to Twitch. No one is 'supporting' Twitch. It doesn't need support. It has Amazon bankrolling it.
/thread
Within this 300 year time interval, we again have the huge problem of the sensitive dependence on initial conditions.I think you've taken a very roundabout route to reach the same conclusion that I did in my first few posts in this thread: the universe is chaotic.
Here is the earth trailing orbit of the exoplanet discovering Kepler satellite - 66,600 mph . How ?https://www.airspacemag.com/daily-planet/keplers-unusual-orbit-54411507/If you launch any satellite out of Earth's sphere of influence, it will go into basically this orbit. What do you expect that a satellite would do?
in order to accelerate constantly in a direction we would need not only a constant energy source but an INCREASING energy source as required energy in order to keep accelerating would eventually tend towards infinity.Someone needs to take another look at their 'Introduction to Relativity' notes
[...]Well after some to-and-froing it seems like we actually agree on this one!
Stokes' theorem applied to an interferometer whose center of rotation coincides with its geometrical center:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2023979#msg2023979
Formula:
Stokes' theorem applied to an interferometer whose center of rotation no longer coincides with its geometrical center (MGX, RLGs):
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2208660#msg2208660
Formula:
I don't understand. Who was talking about analytical solutions? Those are numerical solutions that I linked you to:Quotehttps://web.archive.org/save/https://academic.oup.com/pasj/article/70/4/64/4999993
Over a thousand new periodic orbits of a planar three-body system with unequal masses -- “ 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. ”
Further down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a "clean numerical simulation"
Now, where can we find examples of numerical three body problem solutions with bodies of different masses?
Sandokhan, do you know where we can find them?You could try looking up the thing I told you to look up, NASA's Horizons catalogue.
https://ssd.jpl.nasa.gov/?horizons_doc
Searching this document for "integrate":
"comets and asteroids numerically integrated by Horizons."
"Comets and asteroids are numerically integrated on demand over a maximum interval of A.D. 1600 to A.D. 2500"
"To construct an SPK file for a comet or asteroid, Horizons retrieves the latest orbit solution and numerically integrates the object's trajectory over a user-specified time span less than 200 years."
"and are then numerically integrated on-demand by Horizons to other times of interest"
Need I go on?
From your link:QuoteComet and asteroid ephemerides are integrated from initial conditions called "osculating elements". These describe the 3-dimensional position and velocity of the body at a specific time. The integrator starts with this state and takes small time steps, summing the perturbing forces at each step before taking another step. A variable order, variable step-size integrator is used to control error growth. In this way, the gravitational attraction of other major solar system bodies on the target body trajectory is taken into account.
Summing of perturbing forces?
This sounds like what Dr. Gopi Krishna Vijaya is explaining in his Replacing the Foundations of Astronomy paper:
https://reciprocalsystem.org/PDFa/Replacing%20the%20Foundations%20of%20Astronomy%20(Vijaya,%20Gopi%20Krishna).pdfQuoteEpicycles Once More
Following the Newtonian era, in the 18th century there were a series of mathematicians – Bernoulli, Clairaut, Euler, D’Alembert, Lagrange, Laplace, Leverrier – who basically picked up where Newton left off and ran with it. There were no descendants to the wholistic viewpoints of Tycho and Kepler, but only those who made several improvements of a mathematical nature to Newtonian theory. Calculus became a powerful tool in calculating the effects of gravitation of all the planets upon each other, due to their assumed masses. The motion of the nearest neighbor – the Moon – was a surprisingly hard nut to crack even for Newton, and several new mathematical techniques had to be invented just to tackle that.
In the process, a new form of theory became popular: Perturbation theory. In this approach, a small approximate deviation from Newton's law is assumed, based on empirical data, and then a rigorous calculation of differential equation is used to nail down the actual value of the deviation. It does not take much to recognize that this was simply the approach taken before Kepler by Copernicus and others for over a thousand years – adding epicycles to make the observations fit. It is the same concept, but now dressed up in gravitational disguise:
In other words, the entire thought process took several steps backwards, to redo the same process as the Ptolemaic - Copernican epicycle theory, only with different variables. The more logical way of approach would have been to redirect the focus of the improved mathematical techniques to the assumptions in Newton’s theory, but instead the same equations were re-derived with calculus, without examining the assumptions. Hence any modern day textbook gives the same derivation for circular and elliptical motion that Newton first derived in his Principia. The equivalence of the epicycle theory and gravitational theory has not been realized, and any new discovery that fits in with the mathematical framework of Newtonian gravity is lauded as a “triumph of the theory of gravitation.” In reality, it is simply the triumph of fitting curves to the data or minor linear extrapolations – something that had already been done at least since 2nd century AD. Yet the situation is conceptually identical.
~
The Dead End
In the late 19th century, one of the French mathematicians – Henri Poincaré – had already discovered that many of the terms being used in the “perturbation” series by mathematicians like Laplace and Lagrange were becoming infinite for long periods of time, making the system unstable. In simple words, the solutions ‘blow up’ fairly quickly. He also showed that the general problem of 3 mutually gravitating bodies was insoluble through any mathematical analysis! Many physicists and mathematicians built up modern “Chaos theory” based on these ideas, to show simply that one cannot calculate the movements of the planets accurately. Thus began the field of non-linear dynamics.
In the middle of the 20th century, with computers entering the field, the mathematicians pretty much gave up on calculating the orbits by themselves and programmed the computer to do it, even though it was mathematically shown that these orbits were incalculable. They had to be satisfied with approximations or numerical methods (or “brute force” methods.) The result of it all was that after 300 years, Newtonian/Einsteinian thought lands in the same spot that Kepler ended: the orbits point to a living or chaotic system. Only now, there is the additional baggage of all the wrong concepts introduced with regard to “inverse-square law”, “gravitational attraction”, “gravitational mass” and “curved space-time” along with uncountable number of minor assumptions. In this process, an enormous amount of human effort was put to derive thousands of terms in equations over centuries. The entire enterprise has been a wild goose chase
You are witnessing the damage done by Albert Michelson when he claimed that the formula published in 1925 was actually describing the Sagnac effect.
To this very day, the best physicists have been unable to realize that the formula which features the area is the Coriolis effect formula.
However, in the past twenty years, for the first time, the topological considerations of the Sagnac interferometer have been taken into account.
According to Stokes' rule can an integration of angular velocity Ω over an area A be substituted by an integration of tangential component of translational velocity v along the closed line of length L limiting the given area.
Thus, there will always be two formulas for any Sagnac interferometer.
Imagine this: the physicists at Cambridge University are confusing the Coriolis effect with the Sagnac effect, even though they describe very different physical situations.
The Sagnac effect is distributed along a line and not over an area.
Yet, Michelson, most likely intentionally, took advantage of the state of affairs in light interferometry at the beginning of the 20th century, and infused into mainstream science a huge misrepresentation.
Those are numerical simulations that I quoted.Your opening line was "The availiable solutions for the Three Body Problem are very limited..." and then you go on to say "Where are the solutions with bodies of different masses?"
Those are numerical simulations that I quoted.You could try looking up the thing I told you to look up, NASA's Horizons catalogue.QuoteFurther down, in the section "Numerical searching for periodic orbits" we verify that these are numerical simulations: -- “ As mentioned by Li and Liao (2017), many periodic orbits might be lost by means of traditional algorithms in double precision. Thus, we further integrate the equations of motion by means of a “clean numerical simulation" ”
Again, where can we find numerical simulations with different masses other than your statement that they exist?
Your reference to the NASA models are questionable, as they are using perturbation methods.
[...]This paper just says they are the same thing? So is this 'Coriolis force' on a RLG just the same as the Sagnac effec? That's what this paper says #confused
The Coriolis effect would be negligible if, and only if, the interferometer also registers the Sagnac effect upon the velocity of the light beams.I thought RLGs register the Sagnac effect as their main method of calculating rotation.
Otherwise, you need the Coriolis effect to correctly calculate the fringe shifts, which in turn leads to the computation of the angular velocity.
