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So I recently learned about a project about using lasers on Earth to propel a spacecraft to 20% of light speed for interstellar traveling. So this brings an interesting question, how much shorter would be time for the spacecraft relative to us? For example, you expect it to take 10 years for it to reach its destination. You plan 10 years worth of battery power, relative to it it wouldn't be 10 years, so would it use 10 years of battery power?

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If it took 10 years from our point of view, it would take 9.8 years from the point of view of the spacecraft travelling at 20% of the speed of light. So a little shorter, but not by much. A bigger effect would be that the spacecraft would be two light years away by the end of it's journey, so if we were watching though a telescope we wouldn't see it reach it's target until 12 years after launch.

The time dilation correction is very small until you get quite close to the speed of light. To get by with five years worth of batteries, you'll need to get the spacecraft to 87% of the speed of light, and to take only one year's worth of batteries you'd want more than 99% of the speed of light.

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  • $\begingroup$ So it's an exponential curve, where the closer you get the more dramatic the effects will be. I didn't account for that. So you do need to take note of the effect of time and calculate the resources needed by that standard. That was very helpful. $\endgroup$ – XTImpossible Apr 4 '17 at 5:47

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