Is it actually possible to formulate a geocentric model of the universe...

[Mangetout]

...that adequately (and simultaneously)explains all observable phenomena?

Sombody on another board told me that there are a few astronomers who had devised a geocentric model that works, but that it was fiendishly complex.

[mcbiggins]

Tycho Brahe was the last of the great geocentric astronomers. His geocentric model of the solar system was exactly right, except for that he couldn't get past the idea that the earth was the centre of the universe. So the Earth stood still, while it was orbited by the moon, and much further away, the Sun. The sun was then orbited by all of the visible planets in their proper order. His protege, Johannes Kepler, even figured out the proper spacing of the planets and devised the laws of planetary motion. Tycho Brahe also gets bonus points for lording over two islands whose entire economies were geared toward paying for his scientific work and having a nose made out of silver.

[mcbiggins]

If you ignore everything outside of our solar system, the Brahian system works just as well as the Copernican system. Its all in your point of view as the observer. It's like riding in a car and pretending you're actually still while eveything else is rushing past you.

[eburacum45]

eh... the earth is at the centre of the observable universe, so what is the problem?

[Mangetout]

Originally posted by mcbiggins
If you ignore everything outside of our solar system, the Brahian system works just as well as the Copernican system. Its all in your point of view as the observer. It's like riding in a car and pretending you're actually still while eveything else is rushing past you.

Does it though? is the erratic movements of the planets (in relation to ourselves) consistent with the laws of motion and gravity?

[Mangetout]

Originally posted by eburacum45
eh... the earth is at the centre of the observable universe, so what is the problem?

What I want to know is whether it is possible to model the universe (and particularly the solar system) with a (relatively) stationary Earth as the centre, without the other bodies having to violate any known laws.

[smiling bandit]

Oh yes, its easy. Simply choose the Earth as a reference point. All other bodies will appear to have very unusual orbits, since they are being puled by gravity around other objects, but its certainly possible. Since in space and physics there is no preffered reference point, you can choose your own.

[Mangetout]

I'm not sure that you're getting the point (or maybe I'm not) - I think I understand about reference frames, but suppose I tie a weight to a piece of string and swing it rapidly about my head, would not choosing the weight as the fixed point, then observing that the entire universe is gyrating rapidly around it, violate the laws of motion etc?

[Achernar]

A geocentric theory is not consistent with Newtonian gravity, if that's what you're asking. You'd have to have some other theory to explain why orbits are the way they are.

[Mangetout]

Thanks Achernar, that's what I was trying to get at.

[Desmostylus]

This is no big deal.

We'll leave GR out of things.

According to Newton, the solar system isn't heliocentric, it's mass-centric.

Two bodies orbit each other in an elliptical path with the centre of mass at one focus of the ellipse.

The solar system is made up of lots of these bodies orbiting each others centre of mass. Earth-moon orbiting each other. Jupiter and her satellites co-orbiting each other.

To calculate the orbits of everything in the solar system, you only need to know masses and velocities. You don't need to posit the sun at the centre.

To say that the earth orbits the sun, or to say that the sun orbits the earth, is meaningless in terms of Newtonian gravity.

It's conceptually useful to say that because the sun is closer to the centre of mass of the earth-sun pair, the earth orbits the sun. But even though it's conceptually useful, it isn't true.

[Mangetout]

I was going to mention that (it is similar to the philosophical debate regarding the two men chasing a squirrel around a tree).

Just out of interest, given that the masses of the planets are relatively insignificant, I'm guessing that the centre of mass of the solar system lies at a point within the sun, is that correct?

[Desmostylus]

And lest anyone argue that the centre of mass of the solar system is the "true" centre of rotation, don't forget the rest of the galaxy.

This co-orbits with that, and the pair co-orbit with something else, and they co-orbit with... etc.

Geocentric is as valid as heliocentric.

[Achernar]

Originally posted by Desmostylus
Geocentric is as valid as heliocentric.

I don't know if I'd go that far. You can go a long way with Newton's law of gravity assuming M_SUN / M_EARTH = infinity, and you'll replicate your observations, to a certain precision. Assuming the other way around will give you results that are qualitatively different from observations.

[Desmostylus]

No, Achernar, you're assuming an approximation, and one which I specifically wasn't.

[Mangetout]

Originally posted by Desmostylus
And lest anyone argue that the centre of mass of the solar system is the "true" centre of rotation, don't forget the rest of the galaxy.

I suppose we should not stop at the galaxy either, although it must become rather confusing at that point (if the universe is finite but boundless)

[Achernar]

Well, if you're not allowed to make approximations, you might as well say that epicycle theory is as valid as Newtonian gravity.

[Desmostylus]

Ah. That's quite good, Achernar.

But they are the same thing.

If you put the sun at the centre, you can use approximations and that simplifies a lot of stuff.

If you put the earth at the centre, you can't use the approximations, and it gets complicated. So what?

Heliocentrism is just a transformation to make the calcs easier.

[Trinopus]

Over at Bad Astronomy, there actually are a handful of (religious based) geocentrists.

They make heavy use of Mach's work, which allows exactly what Mangetout is asking for: a principle of equivalence.

It *could* be that the earth is stationary, and that the cosmos whirls around us, creating a "frame-dragging" effect in GR which emulates all the laws of physics. For instance, this whirling cosmos "pulls" upward, thus keeping (for example) geostationary satellites in orbit (otherwise, not really orbiting, they'd fall, right?)

Of course, the same mathematical equivalence could equally well apply to Venus, or Mars, or any other body anywhere in the cosmos: it's really just a mathematical fiction.

Occam's old-fashioned cut-throat suggests the simpler solution to be the preferred one.

Trinopus