# Do all planets rotate around the sun with the same acceleration?

I have this question in mind. suppose if by any chance, all planet around sun stopped rotating. then as per formula F= M * A. all planet should fall with same acceleration towards sun and ultimately fall into sun. but even when they are rotating around sun in an orbit then they should have same acceleration, as change of direction is also acceleration. So my question is that do scientist have calculated that all planet around sun rotate with same acceleration ? My guess is that off course they would have, but i just want to know if i am thinking it correctly.

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Somewhat related: physics.stackexchange.com/q/6074/2451 – Qmechanic Jan 4 '12 at 15:13

No, the acceleration obviously depends on the distance. It is given by Newton's inverse square law: $$a = \frac{GM_{\rm Sun}}{r^2}$$ so if you double the distance from the Sun, the acceleration decreases by a factor of four. The planets sit into elliptical orbits. If we approximate them by circles, the acceleration above has to be equal to the centrifugal acceleration $$a_{\rm centri} = r \omega^2$$ which also allows one to calculate the angular frequency.