oblivimous wrote:Imagine a rocket (mass = m1) that is able to exert a constant force (F) while maintaining a constant mass. This rocket is fired away from a planet (mass = m2) which exerts a gravitational force in the expected manner.
Is it possible to give an equation for the rocket's height at time=t? To simplify, we should consider the planet to be a point mass, and note that there are no other gravitational forces or planetary motion at play.
Helpful Hint wrote:Recall that the radius of a timelike geodesic behaves as though it has mass 1 and is in a potential of
(Where L is r^2 phi', of course.)
Hawknc wrote:I'm having a pretty summarily awful day so far, but I'll take a look when I get back. My instinct is to say that it would be difficult to give a simple equation for it, but what would I know, I'm just a rocket scientist.
Hawknc wrote:since I'm kinda weak on relativity and I don't think it's really relevant.
Edit: alright, time to put my money where my mouth is. I'm going to approach this from a Newtonian point of view, since I'm kinda weak on relativity and I don't think it's really relevant.
If the rocket is putting out a constant thrust F, that will be counteracted by the gravitational force . So the net force at any point is equal to:
Solving this for acceleration gives:
Obviously because it's not a constant acceleration we can't use Newton's equations of motion, so we integrate twice between 0 and some time t, which gives us:
Now I'm almost guaranteed to have screwed something up here, so someone please check that what I'm doing isn't completely stupid.
It's a magic rocket.Though, won't the rocket loose mass according to
Imagine a rocket (mass = m1) that is able to exert a constant force (F) while maintaining a constant mass.
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