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

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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…..

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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.

I’m no expert but I believe the official answer is “we don’t know.” Ask the top theoretical physicists and they can’t explain gravity other than “it just works the way we have observed.” Redditors, please correct me if I’m wrong.

The difference is that a mass at rest wants to stay at rest. The object that you are thrusting has to fight it’s rest state. The object that is falling into a gravity well is at rest the whole time while it’s canvas is being guided towards it’s source of attraction.

The gravitational force on an object is proportional to that object’s mass, but so is the object’s inertia. If you increase an object’s mass tenfold, you increase the gravitational force on it tenfold—but you also make it ten times harder to accelerate, and these factors offset one another perfectly.

You’ve said it yourself by quoting “f=ma”: the force (f) grows by a factor of ten, but so does mass (m). Since they’re on opposite sides of the equation, they cancel each other out. Better yet, rewrite it as “a=f/m”: increase the mass and thereby the gravitational force, and your acceleration increases by a factor of 10/10, which simplifies to 1/1, which is just 1, which means your acceleration remains the same.

Because the gravity-force depends on the mass of both objects: F = M1*M2*G/R^2 where M1 and M2 are the two objects’ masses, G is the gravitational constant, and R is the distance between the centers of the two masses M1 and M2. So when you put that together with the acceleration equation, you get this (assuming Earth is M1 and the object is M2)

F = M2*A = M1*M2*G/R^2

A = M1*G/R^2

The mass of the Earth (M1) and the gravitational constant (G) are relatively constant, so the only real factor for the acceleration of gravity is how far from the Earth you are.

On the other hand, the thrust of the rocket engine has nothing to do with the mass of the rocket. It pushes with 1000 Newtons whether the rocket has a mass of 1 kilogram or 10^6 kilograms.

F = M*A
1000N = (1kg)*A
A = 1000N/1kg = 1000 m/s^2

F = M*A
1000N = (1000000kg)*A
A = 1000N/1000000kg = 0.001 m/s^2