Time Dilation/Twin paradox Question

[wilson_chem90]

Homework Statement

A 30 year old femal astronaut leaves her newborn child on Earth and goes on a round-trip voyage at a star that is 40 light-years away in a spaceship traveling at 0.90 c. What will be the ages of the astronaut and her son when she returns?

Homework Equations

t = to / {1 - v^2/c^2} ( { } = Square Root)

The Attempt at a Solution

Since its 40 light years away traveling at .90 c. That means it'll take 48 years for the whole trip. ( 0.20 x 40 light years + 40 = 48 years)

to = t {1 - v^2/c^2}
= 48 years { 1 - (0.90c)^2/c^2}
= 48 years(0.43589)
= 20.923 years

Therefore, the mother will have aged approx. 21 years, making her 51 years old when she returns and her son will have aged 48 years, making him 48 years old when his mother returns.


I'm not entirely sure if this is correct. Hopefully it is...

 

[kuruman]

Your reasoning is incorrect. If the star is 40 l.y. away, this means that it takes light 80 years to make the round trip. Surely it can't take the astronaut less than that, baby or no baby. Begin by calculating (correctly) how many years baby thinks mama is gone. Find gamma and then find mama's age.

 

[wilson_chem90]

OHHHH the calculation is 80 l-y + (0.2)(40 l-y) = so its 88 years. I hope...

to = t {1 - v^2/c^2}
= 88 years { 1 - (0.90c)^2/c^2}
= 88 years(0.43589)
= 38.36 years

Therefore, the mother will have aged approx. 38 years, making her 68 years old when she returns and her son will have aged 88 years, making him 88 years old when his mother returns.

thats one old baby!