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Ive only taken physics 101, but I recently became fascinated with Einstein’s theory of general relativity and have watched many YouTube videos on it. My question may be an indication that I completely misunderstand it, however.

Doesn’t the theory of relativity (I think this part predates Einstein) state that if you have two objects in constant velocity, there is no experiment you can do to prove which object is in motion and which object is still? In other words, both prospectives (that you are in motion or you are still) are perfectly legitimate?

So if I claim that the earth is stationary and the universe, along with the sun, is in motion, how can you prove this is not the case?

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    $\begingroup$ There are many equally "correct" ways to describe the world. Some of those descriptions are more convenient for doing some calculations and others are more convenient for doing other calculations. I think you'll find that your proposed description is exceptionally inconvenient for almost any calculation you'll ever want to do. $\endgroup$
    – WillO
    Commented Aug 8, 2021 at 21:48
  • $\begingroup$ Most certainly it’s inconvenient. The main reason I ask this question is because some religious folks claim the sun revolves around the earth. So I’m wondering if that can be disproven. $\endgroup$
    – Mike Olson
    Commented Aug 8, 2021 at 21:48
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    $\begingroup$ Of course it can't be disproven, because it has no content. It's an aesthetic preference about how to describe things, and is no more susceptible to disproof than "We should paint the bathroom blue". You can, however, point out that the blue will clash with the pink tile, or that the geocentric description will lead to some mighty complicated equations. $\endgroup$
    – WillO
    Commented Aug 8, 2021 at 21:51
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    $\begingroup$ Does this answer your question? Why do we say that the Earth moves around the Sun? $\endgroup$
    – Tobias Fünke
    Commented Aug 8, 2021 at 21:52
  • $\begingroup$ @MikeOlson Without invoking special relativity, you just need to track the movements of 3 bodies, or you figure out the mass of the sun with the help of general relativity, by measuring its gravitational pull via bending of light close to its surface. $\endgroup$
    – Leviathan
    Commented Aug 8, 2021 at 22:18

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If the Solar System contained only Earth and the Sun, the best description of their behaviour would be that both orbit their mutual barycentre, which is in the Sun's interior. As it happens, there are many other bodies in the Solar System, and their barycentre ends up just outside the Sun, primarily due to Jupiter. The "moons orbit planets which, like asteroids, comets etc., orbit the Sun (well, maybe a point just outside it)" description provides an especially convenient choice for a coordinate system's origin if it must track all bodies' movements. You can centre everything on e.g. Earth (or Ganymede, for all I care) instead, but this is especially inconvenient. The other planets in our Solar System end up moving in a very complicated path in the night sky; the ancient Greek etymology of "planet" is "wanderer", because this was recognized a long time ago.

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There is an important difference between velocity and acceleration: velocity is always relative, but acceleration is not. The Earth's velocity is not constant; the Earth is accelerating around the Sun, so the principle of relativity does not apply.

If you wish, you can assume that the Earth is fixed and everything else in the Universe moves relative to it, but you would find it impossible to construct a law of gravity that could account for that in a consistent way- in other words, it would be a totally irrational belief.

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    $\begingroup$ This is a question about GR. There is no acceleration. $\endgroup$
    – m4r35n357
    Commented Aug 9, 2021 at 9:00
  • $\begingroup$ I am thinking aloud here, but does this mean that Newtonian gravitational force/acceleration fails the "Galileo's Ship" test? It looks like it must. $\endgroup$
    – m4r35n357
    Commented Aug 9, 2021 at 9:50

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