Is this correct?"Calculating Time of Astronaut's Trip Across 15 Light-Years

[sexy_brittany]

Homework Statement

An astronaut travels from the Earth at a speed of 0.999c to a star that us 15 light-years away (as measured by someone from earth). she spends 10 years on one of the star's planets (as measured by someone on that planet) and then returns to Earth at 0.999c. How long has she been away (1) as measured by someone on the Earth and (2) as measured by her?

Homework Equations

Δt = γ Δt'

The Attempt at a Solution

I am trying to measure the time it took for her to go to the planet and come back by
Δt = γ(1+(1/2)* β^2 )
and then the time she spent on the planet counted by someone on the Earth by
Δt = γ Δt'
where ...Δt' = 10 yr ...is this right
and add all the values ...

For the B part I calculated the distance for her in the ship
by L = Lp √ 1- β*β
and based on this new distance did the same calculation as part A ...

 

[Simon Bridge]

Homework Statement

An astronaut travels from the Earth at a speed of 0.999c to a star that us 15 light-years away (as measured by someone from earth). she spends 10 years on one of the star's planets (as measured by someone on that planet) and then returns to Earth at 0.999c. How long has she been away (1) as measured by someone on the Earth and (2) as measured by her?

Depends on the relative speed of the planet doesn't it. Can you assume the Earth and Exoplaten clocks share a reference frame?

I am trying to measure the time it took for her to go to the planet and come back by
Δt = γ(1+(1/2)* β^2 )
and then the time she spent on the planet counted by someone on the Earth by
Δt = γ Δt'
where ...Δt' = 10 yr ...is this right
and add all the values ...

In her reference frame, the Earth and the planet are moving at 0.999c, and their distance is contracted.

You should draw the space-time diagrams for each reference frame to compare them.
http://www.physicsguy.com/ftl/html/FTL_part2.html#sec:twin