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
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
Latest Answers