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It is often stated that masses fall at the same rate towards the Earth at the same rate (barring things like friction), and this seems to be quoted as the Equivalence Principle. Is this statement correct? I was thinking that the force of $M$ on $m$ causes $m$ to accelerate towards $M$ with $a_m = GM/r^2$, and similarly the force of $m$ on $M$ to accelerate towards $m$ with acceleration $a_M = Gm/r^2$. Isn't the relative acceleration $a_m + a_M = G(M+m)/r^2$, and if you're stationary on $M$ it will appear that $m$ is accelerating towards you with an acceleration that depends slightly on $m$? If correct, I assume the correct statement should be something more like "objects of different masses fall in a constant gravitational field at the same rate"? (It may even be that it is?)

jim
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    The equivalence principle is described here: https://en.wikipedia.org/wiki/Equivalence_principle – Peter Diehr May 15 '16 at 20:40
  • Thanks, but there is the comment "During the Apollo 15 mission in 1971, astronaut David Scott showed that Galileo was right: acceleration is the same for all bodies subject to gravity on the Moon, even for a hammer and a feather." that suggests that the equivalence principle is about objects falling in the gravitational field of a mass. I don't think this is strictly true. – jim May 15 '16 at 20:47
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    Possible duplicate of Equivalence principle question – Peter Diehr May 15 '16 at 20:49
  • Seems quite different? – jim May 15 '16 at 20:53
  • Possible duplicate: http://physics.stackexchange.com/q/3534/2451 – Qmechanic May 15 '16 at 20:53
  • That is correct and, at the same time, irrelevant for the equivalence principle. The reduced mass is a kinematic term that you can already observe in collisions and that appears in all force interactions, as well. The usual formulation of the equivalence principle is for small test masses, which do not modify the reduced mass sufficiently to be of interest. For a 1kg hammer and Earth's $6\times 10^{24}kg$ that a very good approximation. – CuriousOne May 15 '16 at 20:54
  • Yes, this seems to be what I am asking. – jim May 15 '16 at 20:55
  • Correct - falling towards the earth at the same rate is something that is often attributed to Galileo, and described as Galileo's Leaning Tower of Pisa experiment (1589). – Peter Diehr May 15 '16 at 21:01

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