In space, why do thrust and gravity behave differently when accelerating objects?

Question

If I attach the same engine to a 1,000 kg spacecraft and a 10,000 kg spacecraft in orbit, the 1,000 kg spacecraft will accelerate more quickly. If I drop a 1 kg rock and a 10 kg rock on the moon, they accelerate at the same rate. What is the difference?

I think what I may be asking is “why is gravity the a and not the f in f=ma.”

EDIT: BY all means please feel free to discuss, but I consider the question answered by u/mmmmmmBacon12345

mmmmmmm….. Bacon…..

In: 0

Answer 1

Because the force of gravity is proportional to the mass of an object. Gravity *is* the F in F = ma, but it just so happens that an *m* also shows up in that F in such a way that the two m’s cancel out and you always get the same a.

…or at least that’s the classical Newtonian-gravity picture. Relativity changes the story somewhat, but the notion of acceleration in relativity is pretty different from how it is in classical mechanics.