Are heliocentrism and geocentrism both correct?

[larry909]

I'm a layperson, and from what I've read it seems that according to the theory of relativity it's all relative. You can say that the sun is orbiting the Earth, you can say the Earth is orbiting the Sun, or you can say they are both orbiting each other. These are all correct assertions. Is that right?

 

[Drakkith]

The idea of things being relative is partially right. We can always choose to model the universe as seen from any frame of reference we so choose. However this doesn't mean that heliocentrism and geocentrism are equally valid. To quote wiki:

Relativity agrees with Newtonian predictions that regardless of whether the Sun or the Earth are chosen arbitrarily as the center of the coordinate system describing the solar system, the paths of the planets form (roughly) ellipses with respect to the Sun, not the Earth. With respect to the average reference frame of the fixed stars, the planets do indeed move around the Sun, which due to its much larger mass, moves far less than its own diameter and the gravity of which is dominant in determining the orbits of the planets. (In other words, the center of mass of the solar system is near the center of the Sun.) The Earth and Moon are much closer to being a binary planet; the center of mass around which they both rotate is still inside the Earth, but is about 4,624 km (2,873 mi) or 72.6% of the Earth's radius away from the centre of the Earth (thus closer to the surface than the center).[citation needed]

What the principle of relativity points out is that correct mathematical calculations can be made regardless of the reference frame chosen, and these will all agree with each other as to the predictions of actual motions of bodies with respect to each other. It is not necessary to choose the object in the solar system with the largest gravitational field as the center of the coordinate system in order to predict the motions of planetary bodies, though doing so may make calculations easier to perform or interpret. A geocentric coordinate system can be more convenient when dealing only with bodies mostly influenced by the gravity of the Earth (such as artificial satellitesand the Moon), or when calculating what the sky will look like when viewed from Earth (as opposed to an imaginary observer looking down on the entire solar system, where a different coordinate system might be more convenient).

Geocentrism was a model stating that everything orbited around the Earth. This should mean that all planets and the Sun trace ellipses around the Earth, as the wiki quote says. But they don't. The ellipses their orbits form are centered around the Sun, regardless of what coordinate system (reference frame) you choose. This runs counter to the historical geocentric model, and simply placing the Earth at the center of a coordinate system does not mean that you have a geocentric model.

 

[PeroK]

I'm a layperson, and from what I've read it seems that according to the theory of relativity it's all relative. You can say that the sun is orbiting the Earth, you can say the Earth is orbiting the Sun, or you can say they are both orbiting each other. These are all correct assertions. Is that right?

Let me give you another example. Suppose someone didn't believe in the motor car. That the internal combustion engine was a myth and an impossibility.

They could argue that a car driving along a road can be just as validly represented from the car's point of view as the road moving under the car. Which is quite true.

But that in no way supports the argument about the impossibility of motorised transport.

 

[larry909]

@Drakkith

So how were the geocentric proponents able to make correct calculations? Is it that at the end of the day the celestial bodies end up in the same place, just they don't take straight routes in elliptical orbits as it would if you make the Sun as the center reference point?

 

[Drakkith]

So how were the geocentric proponents able to make correct calculations?

They weren't. They always had pretty gross errors in the predictions of the long term positions of the planets. It was only with the heliocentric model that long term predictions became much more accurate.

 

[Ibix]

You can choose a geocentric coordinate system. The price for that is that it isn't remotely inertial, where a heliocentric coordinate system is pretty close to inertial. That means that a geocentric system has so-called "fictitious forces" in it, while a heliocentric one doesn't, and is much more mathematically complex.

So you can have a geocentric system if you're willing to accept the conceptual and mathematical pain.

 

[PeterDonis]

So how were the geocentric proponents able to make correct calculations?

They weren't.

Actually, for the accuracy of observation that was possible before the invention of the telescope, the geocentric model's predictions were pretty good. That's one of the reasons it was so hard to dislodge.

It was only with the heliocentric model that long term predictions became much more accurate.

More precisely, it was only with Kepler's model, which had the planets moving in ellipses with the Sun at one focus, that the heliocentric model began to make more accurate predictions than the geocentric model. The heliocentric model of Copernicus still had the planets moving in circles centered on the Sun, and didn't match observations any better than the geocentric model. (In fact, as Steven Weinberg shows in his excellent book To Explain the World, one can show that with appropriate choices of parameters the geocentric model of Ptolemy and the heliocentric model of Copernicus are mathematically equivalent.)

And even then, at the time Kepler published, the difference wasn't very much; if it hadn't been for the extremely accurate naked eye data collected by Tycho Brahe (much more accurate than any data previously collected), Kepler wouldn't have been able to show that his model was more accurate than that of Copernicus. It wasn't until the telescope was used to make detailed observations of the planets that the data started to really favor Kepler's model.