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If all motion is relative, how do we know that the Earth revolves around the sun? Or we are just making the above statement from the frame of reference in which Sun is at the origin?

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marked as duplicate by Dan, Waffle's Crazy Peanut, Qmechanic Jul 6 '13 at 17:58

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Duplicate: physics.stackexchange.com/q/10933 $\endgroup$ – Greg Jul 6 '13 at 6:36
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    $\begingroup$ On the one hand, that is something of a duplicate. On the other - wow, that thread got bogged down in tangential stuff, to the point where it's hard to find any (accurate) physics there. This is what happens when physicists try to be historians, theologians, and philosophers I guess. $\endgroup$ – user10851 Jul 6 '13 at 6:43
  • $\begingroup$ Also possible duplicate: physics.stackexchange.com/q/55444/2451 $\endgroup$ – Qmechanic Jul 6 '13 at 17:58
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Motion may be relative, but only in certain reference frames will Newton's Second Law, $$ \vec{F} = m \vec{a}, $$ hold without having to invoke ad hoc forces $\vec{F}$.

In this case, suppose we did look at everything in the reference frame where the Earth is not moving. Then the Sun would be moving in a giant circle, $1\ \mathrm{AU}$ in radius, every year. But since even before Newton we've known that objects should just move at the same speed and in the same direction unless acted upon by an external force. Uniform circular motion requires something to be accelerating you ($\vec{a}$) all the time.

What, then, is acting on the Sun to accelerate it? Since $m$ is so large for the Sun, you need quite a large $\vec{F}$ to make the necessary $\vec{a}$. The Earth's gravity won't suffice. In fact, the "force" here is known as centrifugal force, and it is "fictitious" in the sense that a better choice of reference frame would eliminate it.

So yes, you can say that the Sun moves around the Earth, but only subject to the caveat that you are not talking about an inertial frame. Instead, that statement only holds in a reference frame where objects experience some centrifugal "force," which does not come from any fundamental interaction like gravity or electromagnetism.

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This is really a footnote to Chris' answer, but the Earth doesn't revolve around the Sun. The Earth and the Sun revolve around their common centre of gravity. In other words the situation is symmetrical since both bodies rotate about the other. The only reason it looks as if the Sun doesn't move is because it's so much heavier than the Earth.

Actually the Sun revolves around the centre of mass of the Solar System, to which Jupiter makes a considerably bigger contribution than the Earth does.

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No, all motion is not relative in this classical sense. You can determine if you are accelerating by noting fictitious forces -- in this case centrifugal forces which would not arise if the Earth were inertial and the Sun orbiting it. The classic way to do this a Foucalt's pendulum.

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Well because earth, sun and all planets moves in spiral way w.r.t. to galaxy .Simple as that.

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