I'm considering doing a sci-fi comic or novel in an Einsteinian universe, no wormholes or faster-than-light travel. I haven't seen this done very often. It's been a while since I've worked with math, though, so I'm having some trouble.(adsbygoogle = window.adsbygoogle || []).push({});

First, I just want you to check my math. The relativistic mass of an object is

[tex]m(v) = m_o / \sqrt{1-v^2/c^2}[/tex]

From that I've arrived at

[tex]v = c - m_o c / m(v)[/tex]

How's my algebra? Now, just to be sure, m(v) is defined as the kinetic energy of my spaceship converted into mass plus the rest mass of the spaceship, correct? So, supposing the ship is powered by anti-matter or otherwise can perfectly convert its fuel into kinetic energy, than the amount of fuel needed would then be:

[tex]m(f) = m(v) - m_o[/tex]

Is that right?

Now here's where I'm running into trouble. I can't figure out how much fuel is needed for the spaceship to accelerate up to speed, and then decelerate back to zero velocity. My instincts are saying to square the mass of the fuel, but I can't prove it.

And here's where it's starting to get really complicated. I'm probably going to want to have the spaceship constantly accelerating at 1G up until the midpoint in the trip, and then decelerating at 1G until it reaches its destination. I don't remember anything about differential equations, so I don't trust myself enough to figure out the length a trip would take either from the reference frame of the ship or the reference frame of the planets. Furthermore, would that even work, or would I need to incorporate general relativity as well? I'm hoping that would be negligible, as 1G is basically Newtonian.

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# Math of an accelerating spaceship

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