Please explain where my logic is wrong.
a) Ignoring air, the same bowling ball will fall faster on Earth than on the Moon.
b) Now, for the feather and hammer on the Moon, reverse your point of view and consider the Moon to be a big ball, and the hammer and feather to each be planets.
c) The Moon ball will fall faster on Planet Hammer than it will on Planet Feather.
d) Ergo, returning to our familiar point of view, the hammer will fall faster than the feather on the Moon.
Of course, the difference may be beyond our current technological capabilities to measure, but that's a different issue.
We can get more complicated and say that the hammer and Moon are both falling towards their common center of gravity (as are the feather and Moon) and that this congruence towards the center of gravity will happen faster for the hammer/Moon combo than for the feather/Moon combo because there is more mass (=> gravity) involved in the former case.
The same logic can be conceptualized through GR because the hammer will bend its space-time just a tad more than the feather will, so the Moon will reach rendezvous point with a smaller transition on the time axis.
