this post was submitted on 28 May 2024
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One definition for a "rate of falling" would comfortably be "the time it takes the surfaces of two free gravitational separated by some distance to meet." With this in mind, the imperceptible but very real difference in the acceleration of the earth towards the bowling ball would become part of that equation, as it shortens the distance between the two from the other side.
Think of it like a head on collision of two vehicles. You can do the math as two bodies colliding with opposite velocity vectors, or you can arrive at the same mathematical result (at least for some calculations) by considering one of them to be stationary and the other to have the sum of the two speeds in the direction of its original velocity. "Two cars colliding head on at 60mph is the same as one car hitting a brick wall at 120mph." It is rough and doesn't work for all calculations, but the idea is the same.
Mythbusters did this one and, surprisingly, the crash is way more fucked up at twice the speed on the wall
Yeah, that's why I used the heavy caveats. The wall produces an inelastic collision which will do WAY more damage as all of the energy is arrested rather than an elastic collision of the two vehicles in which a good portion of energy is spread between the two bodies as they separate.
Well, considering the scales, the difference is not only imperceptible, I'm pretty sure it's impossible to measure.