A friend and I were talking about relativistic time dialation, and the question was asked: If you're travelling to Alpha Centauri and it takes you 4.5 years to arrive, (as observed by the traveller) then a) how fast were you going, and b) how much time has elapsed on Earth?
morningfoxnorth
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Alpha Centauri is 4.35 light years away (more or less), so if you traveled at 69.5% of light-speed (constant speed), it would feel like 4.5 years to the traveler.
Dilation factor = square root (1 - (v^2 / c^2))
... = 0.7190
... (4.5 / 0.695) x 0.7190 = 4.5 years
How much time has elapsed on Earth? That can be a hard question, with multiple answers. It's best to ask it in terms of what is observed. Here is one: assume that Earth broadcasts a radio signal with time information.
Time 0: you leave Earth.
Time 4.5 years: you arrive at Alpha Centauri.
... you receive the signal with time = 6.259 years.
... (4.35 / 0.695 = 6.259)
... you add the 4.35 light years distance.
... time back on Earth is 10.009 years.