Is Motion Relative?: A Look at Helio/Geo Centric Fundamentals

[Swapnil]

It is often said that the ancient greeks were wrong because they thought that the Sun revolves around the Earth whereas Copernicus was right because he thought that the Earth revolved around the Sun. My question is weren't they both right since motion is relative?

 

[russ_watters]

Not really. You can, of course, construct equations to model the motion of a system from any reference point you wish, but selection of the reference frame makes a big difference in the complexity of the system. Ie, if you choose to make the solar system geocentric, the orbits of all the planets become pretty bizarre. Planets like Mars would orbit backwards sometimes. Obviously the equations for gravity and motion won't work for an orbit like that, so all you'd really be able to do is construct an ad hoc model for each planet and never be able to be able to predict the behavior of newly found objects.

 

[Swapnil]

OK, so its harder to work with a Geo-centric model than a Helio-centric model. But that doesn't change the fact that they were both right, right?

 

[neutrino]

OK, so its harder to work with a Geo-centric model than a Helio-centric model. But that doesn't change the fact that they were both right, right?

Someone correct me if I'm wrong, but I think the Aristotleans considered the Earth the to be the absolute centre of the the universe. I think till Hubble came along, something or the other was the absolute centre of the universe. First it was the Earth, then the Sun (Copenicus), and then the Milkyway(Herschel).

 

[russ_watters]

OK, so its harder to work with a Geo-centric model than a Helio-centric model. But that doesn't change the fact that they were both right, right?

No. AFAIK, no one was ever able to construct a geocentric model that actually worked to the point where it was difficult to distinguish the results from what Newton's theories (much less Einstein's) predicted. Ie, the basic reason for needing to move beyond Ptolmey is that his model didn't work very well. They just kept adding epicycles, but were never able to make the model work very well.

There are still crackpots running around who have wacky ideas about Geocentrism, and you'll find some on BadAstronomy.com, but I remember some discussions where people put it to them to actually try to build some woking models and no one could. It isn't something to be taken seriously.

 

[russ_watters]

Someone correct me if I'm wrong, but I think the Aristotleans considered the Earth the to be the absolute centre of the the universe. I think till Hubble came along, something or the other was the absolute centre of the universe. First it was the Earth, then the Sun (Copenicus), and then the Milkyway(Herschel).

That's a different issue (several, really). Until decent telescopes were invented, no one had a very good idea of the definition of "universe" anyway.

 

[selfAdjoint]

No. AFAIK, no one was ever able to construct a geocentric model that actually worked to the point where it was difficult to distinguish the results from what Newton's theories (much less Einstein's) predicted. Ie, the basic reason for needing to move beyond Ptolmey is that his model didn't work very well. They just kept adding epicycles, but were never able to make the model work very well.

There are still crackpots running around who have wacky ideas about Geocentrism, and you'll find some on BadAstronomy.com, but I remember some discussions where people put it to them to actually try to build some woking models and no one could. It isn't something to be taken seriously.

Their basic problem was not the epicycles per se. As has been noted elsewhere, a rigorous epicycle formalism is just Fourier analysis in disguise, and it should be able to reproduce any reasonable physics. The problem that hung up the ancient Greeks, and Copernicus too! was uniform motion. They insisted that the bodies have uniform angular "circular" motion and broke the pattern of epicycles to make this happen by other means, using points called equants which were displaced from the centers of their deferents (the big circles the epicycles turned on) about which the total motion was supposed to be uniform. This fallacy was only broken by Kepler, and it cost him a lot of work, using Tycho's excellent data, to do it.

 

[DaveC426913]

OK, so its harder to work with a Geo-centric model than a Helio-centric model. But that doesn't change the fact that they were both right, right?

Geocentrism may be able to simulate motions planets (and roughly at that) I don't know if that counts as a model. They were never able to explain what caused the planets to follow those paths.

Heliocentrism does explain (using Kepler's Law and gravity) what causes the planets to follow the paths they do. It is a model.

 

[russ_watters]

Their basic problem was not the epicycles per se. As has been noted elsewhere, a rigorous epicycle formalism is just Fourier analysis in disguise, and it should be able to reproduce any reasonable physics.

You're pushing my math, but doesn't that just yield a potentially endless series of bandaid terms who'se overall length depends on how precise you want the model to be?

 

[Quaoar]

You guys are assuming the OP is arguing for a geocentric model over a heliocentric model. I think he is just saying that from a fixed Earth, the Sun appears to be revolving the Earth, and vice-versa. He's not saying that the overall model was right or wrong, just that if you ignore EVERYTHING ELSE (planets, etc), you can argue that both statements are correct.

Also, I believe that some models had the Earth fixed, with the Sun orbiting the Earth, and all other objects orbiting the Sun. Not a very convenient coordinate system, but none-the-less a correct one.

 

[DaveC426913]

That depends on what the OP wants to do, as he said in post #3: "...its harder to work with..."

If he only wants to work with the Earth the Sun and the Moon, then I see your point. And his.

 

[Swapnil]

According to Einstein, in an inertial frame, if one sees a person "fly by," one cannot say if he/she is moving or that other person is moving because there is no universal rest frame.

All I am saying that if we apply the same concept to the motion of planets, then we can't really prove that if the all the planets (including the Earth) revolve around the Sun or if all the planets (excluding the Earth) and the Sun revolve around the Earth. Am I right?

According to Guillochon, the response seems to be yes.

 

[russ_watters]

No, you are not right. Guillochon outlined an extremely limited domain under which the geocentric model would not be wrong, but it appears with your last post here, you are looking for a much more general use.

There is a difference between a theory and a model. A geocentric mathematical model has no predictive power and thus can't be a theory and can't be proven. You would not be able to use geocentric calculations to, for example, send a probe to Jupiter or discover and analyze an exoplanet.

 

[selfAdjoint]

You're pushing my math, but doesn't that just yield a potentially endless series of bandaid terms who'se overall length depends on how precise you want the model to be?

Sure. And doesn't the Fourier method, which AFAIK is still the standard method for calculating epherimedes, involve a potentially endless series of terms of higher and higher frequencies? Far as that goes, what about perturbative solutions? Power series in the coupling coefficient. It was in celestial mechanics that they were introduced, centuries before they became the method of choice, or necessity, in quantum theory.

The idea of converging approximations for celestial motions goes back to the Babylonians who took an admirably "algebraic" approach. The Greeks with their visual imagination could never free the epicycle method from their preconceptions.

 

[Swapnil]

Here's a quote from Elements of Relativity Theory by D.F Lawden. I think that this should put an end to this discussion.

In the terrestrial frame employed by medieval astronomers, the trajectories of the planets are exceedingly complicated, their overall forward motions being frequently checked by phases of retrograde motion which insert loops into their paths; ... To explain such trajectories, the medieval astronomers (following Ptolemy) were compelled to develop a theory in which the planets were fixed to wheels, which rolled around the circumferences of other wheels, which in turn rolled around on a third set of wheels, and so on -- the theory of epicycles. By switching to the solar frame, Copernicus was able to demonstrate that the planetary paths become very nearly circular and, after a more precise determination of their orbits by Kepler, this opened the door to a theory of the planetary motions based on Newton's law of gravitation. Again, we are not to regard the Copernican description of the planetary motion as being the true account, whereas the Ptolemain one as invalid. Both are valid in their respective frames, but the Copernican point of view is overwhelmingly the more convenient and seminal.

 

[franznietzsche]

According to Einstein, in an inertial frame, if one sees a person "fly by," one cannot say if he/she is moving or that other person is moving because there is no universal rest frame.

All I am saying that if we apply the same concept to the motion of planets, then we can't really prove that if the all the planets (including the Earth) revolve around the Sun or if all the planets (excluding the Earth) and the Sun revolve around the Earth. Am I right?

According to Guillochon, the response seems to be yes.

Am I the only one remembering that rotational motion is NOT inertial motion? There is a measureable difference between the sun going around the Earth and the Earth rotating. Motion is only relative between two intertial frames. The sun and the Earth are not in inertial frames.

 

[GeorgeSol]

Yes, revolving planets require angular acceleration. I assume this is a GR issue not a simple SR case.

The ancient Greeks demonstrated the sun is larger than the earth. A larger body revolving around a smaller body should be an issue for GR, but I suspect the math still allows any point of reference to work. This is over my head, but there is one idea I had about this that has intrigued me...

Assuming GR does allow any point as a workable reference, would the math become more difficult in a progressive manner? In other words, to calculate a path to some new giant dwarf planet, wouldn't the math be easiest if one starts from the solar system's barycenter, and progressively more difficult as one calculates from further places?

[Copernicus model was slightly less accurate than Ptolemy but easier. His introduction, though altered, was very critical of Ptolemy's model due to the obvious flaw in the appearance of Venus (not phases)]

 

[subzero]

It's interesting that the geocentric theory won't completely die though. It can accurately predict planetary motion even though it becomes complicated. It reminds me of when some scientists continued to look for the mythical planet Vulcan because they didn't like, or didn't believe, Einstein's sheet theory. I actually know a geocentrist and I like teasing him (in a good natured way ;)