do I have any physics folk on my list?

[jmtorres]

You know the whole time is relative thing where at speeds approaching c, time dilates? I need someone smarter than me who can talk to me about [time in ship]/[time outside ship] rates, factoring in acceleration and deceleration.

Pulling numbers out of my ass, I've been writing a ten-year round-trip jaunt to Alpha Centauri (approx four light-years away, which is to say, eight round-trip), which takes a year from the perspective of the folks on the ship. I figure making any two of those numbers (distance, external time, internal time) jive should be simple, but the third would be determined by those two rather than being something I could pick.

(I'm also vaguely aware of the problem mass increasing as you approach the speed of light, requiring more fuel to accelerate you, increasing your mass... Vaguely, I know of it. I'm kind of ignoring it for now.)

You know what would be cool? An equation relating journey distance, external journey time, internal journey time, and the length of acceleration and deceleration, that I could plug stuff into to my heart's content.

Does anyone want to help me?

Comments

[mecurtin.livejournal.com]

you might be able to use this:

http://www32.brinkster.com/snefru/space/srcalc/srcalc.htm

[jmtorres.livejournal.com]

Okay, this is useful for cruising speed, wish I could figure in acceleration though. Thanks.

[silly-dan.livejournal.com]

So do I! I was about to give the easy answer -- that if your ship is going 4.36 light years in 5 years, or 87.2% of the speed of light, you can just plug in the formula given on that website -- the clocks run slower by a factor of (1 / sqrt (1 - (v^2/c^2))), means the clocks go slower by a factor of 2.043, and the round trip takes 4.895 years for an Earth observer's 10.

That's the answer if you neglect acceleration, possibly by assuming that your ship gets to top speed very fast, "coasts" at a constant velocity with respect to Earth on its way there, quickly decelerates once it gets to Alpha C, and then does the same on the way back. It might be more realistic to assume the ship accelerates slowly to its top speed until it's halfway there, then decelerates until it's almost as rest with respect to Alpha Centauri at the end of the trip. Then, after doing whatever, it repeats the process on the return trip. This site has some examples of what would happen if you accelerated at 9.81 m/s^2, which is equal to the acceleration due to gravity on Earth: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html