#### totallackey

• 1212
##### Re: Problems with the Heliocentric Model
« Reply #100 on: August 10, 2019, 12:50:43 PM »
If so, why no solution announced from on high?

Why no smoke from the chimney?
Numerical solutions and analytical solutions are not the same thing.
Either you already knew this and you're just trolling around, or you didn't know this and you should really go back to basics on this.
Ok.

Please explain the difference between an analytic solution and a numerical solution and how they are differentiated when it comes to a problem involving math?

#### Tim Alphabeaver

• 143
• That's no beaver
##### Re: Problems with the Heliocentric Model
« Reply #101 on: August 10, 2019, 04:03:51 PM »
Please explain the difference between an analytic solution and a numerical solution and how they are differentiated when it comes to a problem involving math?
This post sums it up nicely:
https://www.quora.com/What-is-the-difference-between-a-numerical-and-an-analytical-solution

An analytical solution is exact.
A numerical solution is an approximation that's used when an analytical solution is unavailable or unusable.
Maybe you remember using the trapesium rule to estimate the area under a curve in maths class - that's using a numerical method instead of an analytic one. If the curve was simple enough you could have just used calculus to integrate it get an exact solution and you wouldn't need to bother with the trapesium rule.

If you're doing this for a living you'd use more complicated algorithms than the trapesium rule, and you'd generally know how accurate your numerical solution is.

This is why we can say that not having an analytical solution to the three-body problem is okay. You compute a numerical solution and know how good your solution is. This means that if I want to know the position of Jupiter in X years with an accuracy of Y meters, I can do that.

**I move away from the infinite flat plane to breathe in

#### Tom Bishop

• Zetetic Council Member
• 6458
• Flat Earth Believer
##### Re: Problems with the Heliocentric Model
« Reply #102 on: August 10, 2019, 04:46:51 PM »
Sort of like of Ptolmy used numerical computations and epicycles to predict the location of the planets?

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #103 on: August 10, 2019, 08:56:59 PM »
Tom,

As an amateur astronomer of many years experience I am used to watching and studying the night sky and would describe myself as having a better than average knowledge of how the planets 'behave' over the course of a year. Comparing what I am used to seeing in the real sky with the diagrams depicting the early Copernican heliocentric system and the Ptolemy geocentric system (both of which contain these epicycles for individual planets) I cannot say I agree with either diagram.

Some questions immediately come to mind. Firstly in relation to the epicycles why would the planets individually orbit around apparently nothing?  Why do the Moon and Sun not follow an epicycle? From a physics point of view they are just massive bodies like the planets so why should they be any different from the planets?

Finally if the planets are moving in circles (epicylces) in addition to their orbital paths then they would appear to 'wobble' w.r.t the background stars in a way which they don't. I suppose the epicycle could be some form of crude attempt to explain retrograde motion. If this is the case then it doesn't work.
RET seeks the truth as it actually is. FET seeks the truth as some would like it to be.

#### Tim Alphabeaver

• 143
• That's no beaver
##### Re: Problems with the Heliocentric Model
« Reply #104 on: August 10, 2019, 09:42:36 PM »
Sort of like of Ptolmy used numerical computations and epicycles to predict the location of the planets?
I'm not well-versed on Ptolemy's model, but it seems to me that it's simple enough model where each body moves around a fixed circle. In this case, each body's motion could be solved analytically, so no need for a numerical solution.
**I move away from the infinite flat plane to breathe in

#### Tom Bishop

• Zetetic Council Member
• 6458
• Flat Earth Believer
##### Re: Problems with the Heliocentric Model
« Reply #105 on: August 10, 2019, 11:15:57 PM »

#### Tim Alphabeaver

• 143
• That's no beaver
##### Re: Problems with the Heliocentric Model
« Reply #106 on: August 11, 2019, 11:18:07 AM »
It says here that he was using numerical computations:

https://books.google.com/books?id=JVhTtVA2zr8C&pg=PA29&source=gbs_toc_r&cad=4#v=onepage&q&f=false
Then maybe they did use numerical solutions. Like I said - not an expert. I'd need a look at the equations to provide any useful input.
**I move away from the infinite flat plane to breathe in

#### Tim Alphabeaver

• 143
• That's no beaver
##### Re: Problems with the Heliocentric Model
« Reply #107 on: August 11, 2019, 11:30:56 AM »
Another thing to think about: I grabbed this from stack exchange:

In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions.

From what I've read analytic solutions and closed-form solutions are the same thing.
I could imagine a case like y=x^2, which is definitely closed-form, to not be closed-form to someone like Ptolemy. How do you calculate a square (or sqrt(x), or sin(x)) in 100AD? The answer seems to be that you get a table that someone else wrote and look it up.
**I move away from the infinite flat plane to breathe in

#### AllAroundTheWorld

• 2358
##### Re: Problems with the Heliocentric Model
« Reply #108 on: August 12, 2019, 10:17:33 AM »
Sort of like of Ptolmy used numerical computations and epicycles to predict the location of the planets?
Actually yes, exactly like that.
But that model was later replaced with a better, heliocentric one. That's how science works.
You seem to struggle with this concept.
And Ptolmy wasn't a flat earther...
If you are making your claim without evidence then we can discard it without evidence.

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #109 on: August 12, 2019, 09:52:42 PM »
I have always enjoyed the Khan Academy.  Here is a good link that show some simulated demonstrations of solar system events.  A number of links to the left side to check out.

https://www.khanacademy.org/partner-content/nasa/measuringuniverse/spacemath1/a/the-geocentric-universe
RET seeks the truth as it actually is. FET seeks the truth as some would like it to be.

#### robinofloxley

• 79
##### Re: Problems with the Heliocentric Model
« Reply #110 on: August 13, 2019, 09:13:24 AM »
Sort of like of Ptolmy used numerical computations and epicycles to predict the location of the planets?
Actually yes, exactly like that.
But that model was later replaced with a better, heliocentric one. That's how science works.
You seem to struggle with this concept.
And Ptolmy wasn't a flat earther...

I've noticed Tom and others bring up epicycles more than once, but I don't really see the significance. I don't think Tom actually believes planetary orbits are physically epicycles, just that epicycles are a mathematical tool to predict orbits. OK, so epicycles of sufficient complexity could be used to predict orbits. So what. We have other tools now and we use them instead, so presumably these new tools are either more accurate or easier to use or produce results faster.

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #111 on: August 15, 2019, 09:51:09 PM »
Regarding the 'problem' with the heliocentric model, doesn't the existence of stellar parallax kind of demonstrate that the Earth is orbiting the Sun?  After all if it wasn't then the stars would show no parallax would they.
RET seeks the truth as it actually is. FET seeks the truth as some would like it to be.

#### Tom Bishop

• Zetetic Council Member
• 6458
• Flat Earth Believer
##### Re: Problems with the Heliocentric Model
« Reply #112 on: August 18, 2019, 02:28:47 PM »
Regarding the 'problem' with the heliocentric model, doesn't the existence of stellar parallax kind of demonstrate that the Earth is orbiting the Sun?  After all if it wasn't then the stars would show no parallax would they.

Some stars exhibit zero parallax, while other stars exhibit positive or negative parallax of about equal distribution. Stars which exhibit ''negative parallax'' travel in a direction contradictory to heliocentrism, and are usually dismissed as "errors".

http://web.archive.org/web/20100826022827/http://www.realityreviewed.com/Negative%20parallax.htm

Quote
A careful examination of photographic plates that have been exposed to the same region of sky, but at times that are a few months apart, will reveal the fact that some stars have shifted their position with respect to the 'background' stars. Such stars are assumed to be closer to us than the (effectively) infinitely far away 'background' stars, and the effect is naturally given the name of stellar parallax.

~

'''Negative Parallax'''

There are 1,058,332 objects in the Tycho Main Catalogue, and these have a median astrometric precision of 7 mas for visual magnitude 9 and below, increasing through 25 mas for visual magnitude 10-11.

Using the ESA's parameter entry table [5], we selected field three (parallax) and specified a range of -919 (min) to -20 (max) mas, over the entire dataset. This produced 262,100 records of negative parallax objects, or 25% of the total.

Next we selected the positive parallax objects via a minimum value of 20 mas and a maximum of 701.5 mas. This resulted in 310,758 records, or 29% of the total.

The remaining 46% of the Tycho Main Catalogue entries can be assumed to possess zero parallax, within the precision of (0 ± 20) mas.

Section 2.2 Contents of the Tycho Catalogue [6] makes the following statement regarding Field T11, "The trigonometric parallax, π, is expressed in units of milliarcsec. The estimated parallax is given for every star, even if it appears to be insignificant or negative (which may arise when the true parallax is smaller than its error)."

A further test was conducted, to see if the stars moving across the astrometric instrument slit were directionally different in the northern celestial hemisphere to what they were in the southern celestial hemisphere. In this case, as well as the parallax field, the declination field was also selected. Of the non-zero-parallax stars in the northern celestial hemisphere (0°N ≤ δ ≤ 90°N), 45% of them had a negative parallax, and in the southern celestial hemisphere (0°S ≤ δ ≤ 90°S), 46% of non-zero objects had a negative parallax. So here again is a very symmetrical distribution that would be typical of a naturally occurring phenomenon.

~

In Fig. 3, 46% of all stars are located between the limits indicated by the two dotted lines on either side of the mean (the centre point of the stellatum thickness), and from Fig. 2 we see that this would imply 27% of stellatum stars would be closer to us (and thus display positive parallax) and 27% would be further away than the majority (and thus display negative parallax). I.e., 46% are middle stars (as termed in Fig. 2), 27% are inner stars (c.f. 29% from the Tycho Main Catalogue), and 27% are outer stars (c.f. 25% from the Tycho Main Catalogue).

~

'''Conclusion'''

It is an indisputable fact that stellar parallax, like the phases of Venus, has been widely cited as 'proof' that the World orbits the Sun. This is unfortunate, since the phenomenon proves no such thing. The only thing it does prove is that either the World is moving with respect to the stars, or that the stars are moving with respect to the World.

At this the geocentrists usually rest their case, claiming that the adoption of a heliocentric philosophy is just as much a matter of faith as the adoption of a geocentric philosophy. However, this invocation of faith is unnecessary and unjustified, for if it were such a simple choice between the World going around the Sun, or some stars moving slightly in order to conveniently give the appearance of the World going around the Sun, then the heliocentrists would have a point of strong probability (as opposed to a point of proof) in their favour, and geocentrism would indeed become more faith than science. Contrariwise it is worthwhile noting that credibility as regards the sizes of the Sun and Moon discs producing the observed solar eclipse effect that we marvel at sits more comfortably with the intelligent design position that geocentrism tends to imply, rather than with the heliocentrists and their claim of coincidence.

The phenomenon of stellar parallax is not what we have been generally led to believe, because in exactly the same way that Eddington 'proved' Einstein's General Theory of Relativity in 1919 by rejecting, omitting or deleting 60% of his measurement data on the bending of starlight, so modern astrophysics maintains the misconception that parallax 'proves' the Kopernikan philosophy of the World hurtling around the Sun, by ignoring and dismissing the entire dataset of negative parallax measurements.

The ESA, unlike Eddington before them, have kept and filed data values which do not fit in with the ruling model of the universe, and should be commended for so doing, but nevertheless they do seem to dismiss a significant proportion of their measurements rather glibly. Of course, they do say that these may arise due to measurement error, but the number and symmetrical distribution of these values would tend to deny this as being anything other than an exception to the rule.

Furthermore, although angular parallax measurements are small (the largest positive value gives an angle ACB, in Fig. 1, on the order of only 0.7 of an arcsecond), the effect is known to be genuine by way of photographic plates taken at various times over a period of twelve months which clearly show the same slight movement of some stars with respect to the background star field. In other words, stellar parallax is an observable phenomenon that is repeatable, rather than being experimental or statistical errors in measurement.

When the full picture is revealed and considered, therefore, it is clearly geocentrism that has the potential to fully and adequately account for the hundreds of thousands of negative parallax observations that have now been recorded, although it is acknowledged that a detailed explanation is not currently available.

Author information: https://web.archive.org/web/20031113155858/http://www.erionline.co.uk/Profile%20Dr%20Neville%20Jones.htm

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #113 on: August 18, 2019, 02:43:24 PM »
« Last Edit: August 18, 2019, 03:00:51 PM by newhorizons »
RET seeks the truth as it actually is. FET seeks the truth as some would like it to be.

#### Tom Bishop

• Zetetic Council Member
• 6458
• Flat Earth Believer
##### Re: Problems with the Heliocentric Model
« Reply #114 on: August 18, 2019, 03:04:30 PM »
https://physics.stackexchange.com/questions/244645/negative-parallax

https://astronomy.stackexchange.com/questions/26250/what-is-the-proper-interpretation-of-a-negative-parallax

http://adsabs.harvard.edu/full/1943AnDea...4....1L

http://www.mpia.de/~calj/parallax.pdf

Negative parallax can be more of a statistical result rather than an actual measurement. And therefore not evidence against heliocentricism.

According to the author that I quoted the star catalog shows that there were about as many stars in negative parallax as there are positive parallax. Positive = 29% of the total. Negative = 25% of total. Remainder had zero parallax. If true, then there are thousands of stars exhibiting negative parallax. The ones which support your model are correct, and the ones which contradict your model are wrong and errors? Very interesting.
« Last Edit: August 18, 2019, 03:12:35 PM by Tom Bishop »

#### AllAroundTheWorld

• 2358
##### Re: Problems with the Heliocentric Model
« Reply #115 on: August 18, 2019, 03:22:34 PM »
The ones which support your model are correct, and the ones which contradict your model are wrong and errors? Very interesting.
Wow. I mean, you’re right that one shouldn’t cherry pick but that is literally all you do so it’s a bit rich you raising your eyebrow at it.

From what I understand (admittedly I’m no expert in this field) the parallax for distant stars should be so close to zero that the error inherent in taking these measurements means you’ll sometimes get a negative and sometimes get a positive. Actually neither are right. For closer objects the amount of parallax is big enough compared with the error that the measurements can be used to estimate the distance to them
If you are making your claim without evidence then we can discard it without evidence.

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #116 on: August 18, 2019, 03:39:38 PM »
Quote
If true, then there are thousands of stars exhibiting negative parallax

Only thousands Tom..  do you know how many stars we estimate there are in the Milky Way Galaxy alone?  I know single star clusters alone which contain a million stars or more so 'thousands' is a very small fraction indeed and given the very small angles involved then it is hardly surprising.  I would have thought the number would be more like tens of thousands. Even that would be a very small fraction.

Parallax though is just one of numerous points of evidence that support the heliocentric model.  Remind me again... what is meant by Occams Razor?

« Last Edit: August 18, 2019, 03:44:20 PM by newhorizons »
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#### Tom Bishop

• Zetetic Council Member
• 6458
• Flat Earth Believer
##### Re: Problems with the Heliocentric Model
« Reply #117 on: August 18, 2019, 04:07:58 PM »
Well, it said hundreds of thousands:

Quote
There are 1,058,332 objects in the Tycho Main Catalogue, and these have a median astrometric precision of 7 mas for visual magnitude 9 and below, increasing through 25 mas for visual magnitude 10-11.

Using the ESA's parameter entry table [5], we selected field three (parallax) and specified a range of -919 (min) to -20 (max) mas, over the entire dataset. This produced 262,100 records of negative parallax objects, or 25% of the total.

Next we selected the positive parallax objects via a minimum value of 20 mas and a maximum of 701.5 mas. This resulted in 310,758 records, or 29% of the total.

The remaining 46% of the Tycho Main Catalogue entries can be assumed to possess zero parallax, within the precision of (0 ± 20) mas.

The history of this is interesting...

https://books.google.com/books?id=b2l8cO4wpL4C&pg=PA63&dq=%22a+large+negative+parallax+of%22&hl=en&sa=X&ved=0ahUKEwjzguuE49LfAhUQQq0KHTO_CCYQ6AEIKjAA#v=onepage&q&f=true

The above astronomer says that astronomers tend to jump to subjective instrumental errors at the drop of hat. He points out and declares that y Draconis has a large negative parallax and aberration that is impossible to accept, and that this was found and verified by others, by "however and whomever treated the outcome".
« Last Edit: August 18, 2019, 04:11:10 PM by Tom Bishop »

#### newhorizons

• 95
##### Re: Problems with the Heliocentric Model
« Reply #118 on: August 18, 2019, 04:46:12 PM »
Hundreds of thousands is still a very small number when it comes to stellar populations.

The GAIA satellite is set to measure around a billion stars and that is still less than 1% of the estimated population of the Milky Way.
RET seeks the truth as it actually is. FET seeks the truth as some would like it to be.

#### garygreen

• 2036
##### Re: Problems with the Heliocentric Model
« Reply #119 on: August 18, 2019, 07:05:34 PM »
noisy data can easily produce negative parallax values:

it's relatively simple to demonstrate that negative parallax values are the result of measurement error.  you simulate a set of known parallax values, and you recover them with mock measurements.  even if you give your mock measurements only gaussian noise (no systematics), you will still recover negative parallax values.

Luri+2018 demonstrates this here: https://github.com/agabrown/astrometry-inference-tutorials/blob/master/luminosity-calibration/DemoNegativeParallax.ipynb

for an in-depth treatment of the these measurement uncertainties as they pertain to gaia, see:

https://arxiv.org/pdf/1804.09376.pdf
https://arxiv.org/pdf/1507.02105.pdf
https://arxiv.org/pdf/1804.10121.pdf
https://github.com/agabrown/astrometry-inference-tutorials/

the punchline is that parallax catalogs are dominated by faint, distant sources (this is true of all astronomical surveys).  faint, distant sources will have small parallaxes (they are distant), and large positional measurement uncertainties (they are faint).
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