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Alpha Centauri is located 4 light years away. A spacecraft travels at 0.8c towards this star, as seen from earth. How long will the spacecraft take to reach its destination?

The spacecraft sees the distance to Alpha Centauri as 2.4 light years due to length contraction.

This means that the spacecraft will reach Alpha Centauri in:

t = d/v = 2.4/0.8 = 3 years (spacecrafts reference frame)

Then, because of time dilation, the observer on earth sees:

3 * gamma = 5 years go by.

This then matches up with:

t = d/v = 4/0.8 = 5 years (according to earths observer).

Is this all correct?

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# Quick question on Special Relativity

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