# Acceleration in space?

Sorry if this is the wrong section or a post like this has been already created. I had a thought but the question remains unanswered. I have limited knowledge of physics and was hoping someone on this forum could help me.

First assume you were in the vacuum of space. Next assume you had some sort of propulsion device ( engine, motor, jet, etc). Lastly assume you had infinite fuel.

If you began to accelerate would you,
A.) Accelerate to a peak speed pre-determined by the output of the device and continue at that speed. Also limited by numerous factors
B.) Accelerate at constant rate
or
C.) Accelerate exponentially.

Nugatory
Mentor
You have to be careful to about stating the exact conditions. For example, If you have infinite fuel, you don't move at all - your infinite fuel supply will have infinite mass - and I don't think that's the answer you're looking for.

If you are asking what happens to an object that starts out at rest relative to you and is subjected to a constant force by some external agency, classical mechanics says the object will accelerate away from you according to Newton's ##F=ma## for as long as the force is applied. If neither the mass nor the force change the acceleration will be constant.

If you allow for the effects of special relativity (which only start to show up after the object has already reached a significant fraction of the speed of light) the acceleration is more complicated. The object's speed gets closer and closer to the speed of light, never stops increasing, but never quite reaches ##c##.

jbriggs444
Homework Helper
If the infinite fuel supply is modelled as a kind of tanker truck that pulls alongside and transfers fuel as needed then the result is constant acceleration as measured in the instantaneously co-moving inertial frame.

Like Nugatory said, you'd never quite reach the speed of light. The reason is that as matter moves faster, its mass increases. When matter reaches the speed of light, its mass becomes infinite (which would require infinite force to accelerate further). If you keep applying the same force for acceleration, the ever-increasing mass means the acceleration gradually decreases (because the same force won't accelerate an increased mass as much) and you'll never quite reach the speed of light. To accelerate an infinite mass, you would need infinite energy, with neither being possible.

Nugatory
Mentor
If the infinite fuel supply is modelled as a kind of tanker truck that pulls alongside and transfers fuel as needed then the result is constant acceleration as measured in the instantaneously co-moving inertial frame.

Indeed it is, and interestingly that will hold for both classical and relativistic mechanics.

Nugatory
Mentor
The reason is that as matter moves faster, its mass increases. When matter reaches the speed of light, its mass becomes infinite (which would require infinite force to accelerate further). If you keep applying the same force for acceleration, the ever-increasing mass means the acceleration gradually decreases (because the same force won't accelerate an increased mass as much) and you'll never quite reach the speed of light. To accelerate an infinite mass, you would need infinite energy, with neither being possible.

There's an FAQ over in the relativity section of the forum: https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-is-it-not-used-much.783220/#post-4919337 [Broken]

Last edited by a moderator:
rcgldr
Homework Helper
Just in case your'e wondering about a more realistic situation with a limited supply of fuel: if ~63.2121% ((e-1) / e) or more of the initial mass of a rocket is fuel, then as the fuel is depleted, the rockets speed can increase greater than the speed of the exhaust fuel (relative to the rocket).

Khashishi