Mike Beede wrote:
But
there's only one earth, and if you drop them both at the same time,
don't they both hit the rising earth at the same time? You didn't
say they were released at the same time, but that was the implication
in the thread.

I was treating the case where only two objects were in motion at any one
time - it's a lot simpler.

Since the implied problem is a three body problem it isn't going to be so
easy to prove that two objects of different masses released at the same
time will accelerate at the same rate towards the center of the earth. The
actual trajectories are going to be surprisingly complex.