# Homework Help: Twin paradox with circular motion

1. Oct 30, 2007

### Urd

1. The problem statement, all variables and given/known data
A variation on the twin paradox, with uniform circular motion. The travelling sibling moves so that his acceleration is g at all times, pointing to the centre of his circular path, constant velocity. There is given that the trip takes twenty years in the frame of the traveller. Then how long will the astronaut be gone as seen by the inertial observer?

2. Relevant equations

3. The attempt at a solution
I have an expression for the time elapsed (as seen by the inertial observer) in function of radius and velocity. And as I'm unable to calculate radius or velocity for this problem, I am stuck.

Last edited: Oct 30, 2007
2. Oct 30, 2007

### clem

You have two equations:
2pi R=vT (T=20 years), and v^2=Rg.
Solve for R and v.

3. Oct 30, 2007

### Urd

When I use these equations, the velocity is more then three times the speed of light?

4. Oct 31, 2007

### Meir Achuz

The statement "his acceleration is g at all times" is ambiguous.
If it refers to his acceleration in the Earth system, you do get v~3c.
It must mean his acceleration in his rest system. In that case,
a in the Earth system is a=g(1-v^2/c^2), and
The centripetal equation becomes v^2=Ra=Rg(1-v^2/c^2), which eventually gives v<c.
Incidentally, if you work with LY (light years), then c=1 and g~1.