How much did Scott Carpenter age less when he orbited the earth 22 times?

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Homework Statement



Scott Carpenter orbited the Earth 22 times in 1962. Assuming he was 160 km above Earth in a circular orbit, determine the time difference between someone on the Earth and Carpenter for the 22 orbits.

Homework Equations


L = Lp(1 - v^2/c^2)^.5 delta t = t /(1 -v^2/c^2)^.5 Note the t on right hand side of equation is the proper time.


The Attempt at a Solution


All that is given in the problem is the proper length 160,000m. The problem does not specify how fast Carpenter is moving or how long it took to complete one orbit. Obviously Carpenter is going to be measuring proper time and delta t is the time someone measures on the Earth. I have tried solving for v in the first equation and substitute in the second equation. Still leaves you with three unknown variables.
 
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If you know the radius of the orbit, you can determine how fast he is moving and how long it took. He is in orbit so the acceleraton must be the acceleration due to gravity at that height.