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I am doing my special relativity homework and since the ideas are quite counter-intuitive it's hard to know if I'm doing the right things. So i'd like to post some work here and see if it is correct. Also, I am stuck on the final part of the question.

1. Homework Statement

1. Homework Statement

A space traveler takes off from Earth and moves at speed 0.990c toward the star Vega, which is 26 ly (light-years) distant. How much time will have elapsed by Earth clocks

(a) When the traveler reaches Vega?

(b) When the Earth observers receive word from her that she has arrived?

(c) How much older will the Earth observers calculate the traveler to be when she reaches Vega that she was when she started the trip?

## Homework Equations

## The Attempt at a Solution

a) The proper time interval, i.e the time measured by the space traveler is found using the standard method.

[itex]\Delta t_{0} = \frac{d}{s} = \frac{26}{0.990} = 26.26[/itex] years.

[itex] \gamma = \frac{1}{(1- \frac{v^{2}}{c^{2}})^{0.5}}[/itex]

Earth time, [itex]\Delta t = \gamma \Delta t_{0} = \frac{\Delta t_{0}}{(1- \frac{v^{2}}{c^{2}})^{0.5}} = 186.17[/itex]years

I think this is correct, but that's a whole lot of time dilation...

b) 186.17 years go by, according to the Earth clock until the traveler reaches vega. It will then take a further 26 years for her signal to reach earth. So the Earth clocks will measure 206.17 years.

c) I am finding this part very confusing... Do Earth observes consider the traveler to have aged 186.17 years?