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
F is the F in f=ma
The force of gravity is Fg=G*M*m / r^(2)
So A = F/m as always.
A = Fg=G*M*~~m~~ / r^(2) / ~~m~~
leaving
A = Fg=G*M / r^(2)
The only mass that matters is the other object, not the accelerating object.
This because mass does double duty. It has an attractive force towards another object, but it ALSO resists acceleration.
It just so happens that the gravitational mass (in Fg) and inertial mass (f=ma) are the same. And that is puzzling, and we don’t know why. There is currently no reason that *has* to be true, it just is empircally true.
So, a brief take on your scenario: Your engine produces a fixed amount of thrust, this is why a larger rocket accelerates slower.
Gravitational attraction is not fixed, it increases when you have more mass. So a larger rocket feels more gravitational force (2x the mass, 2x more force, 2x more acceleration). But larger rockets are *also* harder to move (2x the mass, 2x less acceleration), so in the end you get the exact same result for every object attracted to the mass in question (a.k.a. the planet)
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