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This is a common example physics teachers use. As far as I know, it never actually holds true.

There are point masses: A(light, eg. feather), B(heavy, eg. hammer) and, C(eg. the Earth). They are all stationary relative to each other and there are no forces acting on them other than that of gravity's up until the impact. A and B are an equal distance away from C. At no point do any of them occupy the same point in spacetime.

In all possible configurations, B will always be closer to the barycenter of the system and thus impact C first.

Additionally, if there are two, two body experiments; one with A-C and, one with B-C, B will still impact sooner. While C exerts an equal gravitational force on both A and B, B exerts a stronger force on C than A does.

Sac_Winged_Bat
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1 Answers1

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I think you are technically correct. If a hammer and a feather are placed at equal distance from and at rest with respect to the Earth, both will accelerate toward the Earth equally. However, the Earth will also accelerate toward the feather and the hammer. Since the hammer has more mass, the earth will accelerate toward it slightly faster than toward the feather, so the hammer-Earth collision will occur slightly sooner. All this of course assume (1) no effects of air resistance, and (2) we can achieve the stupendous accuracy required to measure the difference.

It might be a little easier to visualize if taken to extremes. Imagine two planets and a feather, all equal distance from each other and initially stationary. The two planets will slam together significantly before the feather hits either planet.

David Rose
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