I know that acceleration due to gravity is independent of mass : $$a = \frac{F}{m} = G\frac{M}{r^2}$$
Meaning that a hammer and a feather fall with the same acceleration on the moon.
I am confused, let's say that instead of a regular hammer, it is a "super hammer" with the same mass as moon. If you drop it on the moon, the "super hammer" will accelerate toward the moon and the moon will accelerate toward the "super hammer". Wouldn't the moon's acceleration make the "super hammer" falls faster than the feather?
In other words, when an object falls, the body it is attracted to "receive" a smaller acceleration in the opposite direction. Wouldn't that acceleration make the object falls faster?
What am I missing?
