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

There are two ways to look at this. The first is the classical way, Newton’s laws of motion and gravity.

The force due to gravity is “coincidentally” proportional to the mass. Compare this to electrostatic forces. The electrostatic force is proportional to electric charge, so that, in a given electrostatic field, an object with a strong charge and a small mass will accelerate a lot, while an object with a weak charge and a large mass will accelerate only a little.

With gravity, the “gravitational charge” is exactly proportional to the mass. So if you double the mass, you double the “gravitational charge”, and therefore double the force. When you double the force and double the mass, the acceleration is the same.

In classical mechanics, the “gravitational charge” being exactly proportional to the mass for any substance is a “coincidence”. There is no explanation for it, but for centuries all experiments confirmed it.

The second way to look at it is with general relativity – Einstein’s great theory. Here, gravity is not a force like electromagnetism (or chemical stuff, which is really just electromagnetism). Instead, objects in space bend space and time itself, and then other objects move along that bent space in what seem to them to be “straight lines” (straight in an obscure sense).

It’s a bit like how planes follow great circle routes when traveling long distances. Great circle routes are sort of straight lines on a globe, but they look like curves on a flat map. Objects move through this warped space-time in what look like four dimensionally straight lines to them, but looks like acceleration to us.

This is how general relativity provided an explanation for why gravitational acceleration does not depend on mass. The objects are just following these odd straight-ish lines.