Specialy theory of relativity [Answer Check]

AI Thread Summary
A discussion revolves around a physics problem involving time dilation in the context of special relativity. An astronaut traveling at 0.90c to a star 40 light-years away will age less than her child on Earth. Initial calculations suggested the astronaut would be 118 years old upon return, but this was corrected to 68 years after applying the proper equations. The child, meanwhile, will age to approximately 88 years. The conversation highlights the importance of accurately applying relativistic formulas to determine the correct ages.
AClass
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Homework Statement



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

Homework Equations



\Delta t = \frac{\Delta t_o}{\sqrt{1 - \frac{ v^2 }{ c^2 }}}

The Attempt at a Solution



40 years (2) +(0.20)(40 years)= 88 years

The astronaut will be 30+88 years = 118 years old when she returns

Using the above equation.

\Delta t = 118 years

v=0.90c

Obtained \Delta t_o = 51.44 years

The astronaut's son will be 51 years old when she returns.

Wondering if I did this correct, I don't have any answers to check from It looks right to me.
 
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AClass said:
40 years (2) +(0.20)(40 years)= 88 years
Ummm, I'm not following you there. :rolleyes:
The astronaut will be 30+88 years = 118 years old when she returns
Something went wrong again. You're not applying the right time to the right person.

You might want to just start in the child's frame of reference. Then use x = vt for that frame.
Using the above equation.

\Delta t = 118 years

v=0.90c

Obtained \Delta t_o = 51.44 years

The astronaut's son will be 51 years old when she returns.
No, that's not the right application of the formulas.

For starters, the astronaut will age the slowest.
 
40 years (2) +(0.20)(40 years)= 88 years
Means, the parent is on route for 80 years [40 Years there, then 40 years back], plus since she is traveling 10% slower than the speed of light 20% slower since she is going there and back.

I realize where I went wrong. I went to verify my notes.

The child will be 88 years old.

\Delta t = 88 years [Earth Observer]

Using the equation,

Obtained \Delta t_o = 38.36 Years

Therefore the child will be 88 years old, and the parent will be [30 years+38.36 years] 68 years old.

That should be right. Thanks for the help!
 
AClass said:
40 years (2) +(0.20)(40 years)= 88 years
Means, the parent is on route for 80 years [40 Years there, then 40 years back], plus since she is traveling 10% slower than the speed of light 20% slower since she is going there and back.
That's not the correct math. :rolleyes:

Please, start over. First calculate the total distance (in light years). Then write down the velocity (v = 0.90c). It's also helpful to note that c = 1 ly/y. Now go back to one of your most basic kinematics equations for a uniform velocity, x = vt. Solve for t.
I realize where I went wrong. I went to verify my notes.

The child will be 88 years old.

\Delta t = 88 years [Earth Observer]

Using the equation,

Obtained \Delta t_o = 38.36 Years

Therefore the child will be 88 years old, and the parent will be [30 years+38.36 years] 68 years old.

That should be right. Thanks for the help!
That's almost right. But you should go back and redo the child's age for better precision. It's not exactly 88 years. :wink:
 
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