[Mentor Note: thread split off from a different thread]Assume m2 masses a significant percentage of Earth, like the moon say.
We have a controlled Earth (not spinning, a perfect sphere, no air) all alone in space (so the sun isn't accelerating it for instance) and I have a stationary moon-size rigid balloon at the same altitude as the orbit of the moon. We let go of it and time how long it takes to hit. Now we let go of something the mass of the moon (and stronger to avoid Roche effects) from the same altitude and it will hit the ground in significantly less time. It accelerates more or less at the same rate at first, but gains speed quicker because the Earth is accelerating up towards the massive moon but not the balloon moon. Each travels a different distance because the Earth is not sitting still.
Since seeing this thread yesterday, I have been trying to derive the time equation for the collision of two masses due to Newtonian gravity. Unfortunately, this seems to be much more difficult than I thought before, so I haven't made much progress yet. 🤔
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