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## Homework Statement

If a spacecraft is traveling to a star which is located at a distance of 1 lightyear and it would take the spacecraft 1 year to reach the star in its own frame, how fast would the spacecraft actually fly? Also, how long would the journey take for an observer on Earth (t_e)?

t_sc = 1 y

L_e = 1 ly

t_e = ?

## Homework Equations

gamma = 1/sqrt(1-v^2/c^2)

beta = v^2/c^2

t_sc = t_e / gamma

L_sc = L_e /gamma

## The Attempt at a Solution

I would start by saying that the L_e = v * t_e (v = the velocity). After throwing everything around, I get that the speed should be 25% of the speed of light, which I don't actually think is correct.

My calculations so far:

L_e = t_e * v = t_sc *v *gamma

L_e / t_sc = c = v * gamma

1/gamma^2 = beta^2

1-beta^2 = beta^2 --> beta = 1/4

Hence the time on earth should be 4 years.

Thanks for everyone willing to help me!

Cheers,

Merlin