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Time Dilation and Mass Increase in Special Relativity

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This question illustrates the problem of long distance space travel. Let us say that we want to travel to a planet that is 200 light years away.

a) How fast (fraction of c) must we travel if we want to age only 10 years on the trip?
b) Assume the spacecraft's mass is 5 tons. What will be the mass (MeV) be in-flight?

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Solution Summary

We calculate how fast a spaceship would need to go in order to reach a star system 200 light years away in a proper time of just 10 years, as well as how much its mass would increase.

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a) The Lorentz factor gamma = 1/sqrt(1 - v^2/c^2) = 1/sqrt(1 - beta^2) tells us by what factor time appears to slow down for us as we approach the speed of light, where beta = v/c is the fraction of the ...

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