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Well, in today's world we know that the earth resolves around the sun. But that is seen from frame of reference of sun or an observer stationary wrt sun.

From frame of reference of the earth, sun revolves around earth. But why modern physics says one is right while the other is wrong?

Shouldn't both be correct? As relativity says no frame of reference is special. And if we are very specific, both of them revolve around each other.

Edit: Please refer this for further answers: Why do we say that the earth moves around the sun?

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    $\begingroup$ The frame of the sun-centric is essentially an inertial frame, whereas you're earth-centric frame is a much more non-inertial one, and will therefore be full of ficticious forces. The situation is analogous to us having to account for the coriolis force on earth because we've chosen a frame of reference with the surface of the earth while it spins. Or, as Galileo said: "eppur si muove". It just makes sense to choose a frame in which ficticious forces are eliminated as much as possible (analogous to a center of mass frame). $\endgroup$
    – R. Rankin
    Commented May 17, 2019 at 1:10

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Considering only the Earth and the Sun, they both revolve around their center of mass. But since the Sun so much more massive, their center of mass is much closer to the Sun than to the Earth. So close, in fact, that it is well within the body of the Sun, just 280 miles from the center.

So the Sun just wiggles a bit, its center moving in a tiny 280-mile-radius “orbit” around that COM. By contrast, the Earth’s orbit has a radius of 93 million miles. Relative to the COM, the Sun’s acceleration is tiny compared with that of the Earth, so we tend to think of the Sun as more or less stationary and the Earth as revolving around it.

The center of mass of the solar system is also accelerating, due to the gravitation in our Milky Way galaxy. And the center of mass of the galaxy is accelerating due to the gravitation in our local cluster of galaxies.

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  • $\begingroup$ Yes true, but why to say earth revolves around sun? I mean it is just practical approximation because we see one motion more than other, right? $\endgroup$
    – sakura
    Commented May 17, 2019 at 3:00
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    $\begingroup$ Yes, it is a practical approximation based on how little the Sun moves relative to the COM. $\endgroup$
    – G. Smith
    Commented May 17, 2019 at 4:15
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This is to point out one key error in your thought process.

As relativity says no frame of reference is special.

(Classical) relativity says that no inertial frame of reference is special.

The frame of reference that has the Earth stationary is not an inertial frame, because the Earth must accelerate to maintain (roughly) circular motion around the sun.

The reference frame that has the Sun stationary is also not strictly an inertial frame, since the Sun is orbiting around the galactic center. But the acceleration associated with that orbit is affecting the Earth as much as it is the Sun, so the errors resulting in treating this frame as an approximately inertial frame are not significant in the analysis of the Sun-Earth system.

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    $\begingroup$ The Sun also orbits Sun-Earth center of mass, which may be more important than acceleration due to orbiting the galactic center. But anyway, if we use General Relativity, both the Sun and the Earth are in free fall, so corresponding frames of reference are both inertial. $\endgroup$
    – Ruslan
    Commented May 16, 2019 at 21:34
  • $\begingroup$ If both frames are inertial then should we still say earth revolves around sun? Or it is just a practical approximation $\endgroup$
    – sakura
    Commented May 17, 2019 at 2:59
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    $\begingroup$ @sakura, like the other answer said, they both orbit around the center of mass of the system, so pretty much (but not exactly), around the Sun. $\endgroup$
    – The Photon
    Commented May 17, 2019 at 5:19

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