1. Jun 7, 2009

### EskShift

A satellite is being prepared for take-off on the surface of the fictitious planet Zeta. The planet Zeta has a radius of R and the satellite experiences a gravitational force, F, from the planet at the surface. A single moon, Eta, completes one orbit of the planet every 50 days at a distance of 5R from the center of the planet.
The satellite is now placed into orbit 2R from the surface of the planet.

Determine the Period of the satellite.

2. Relevant equations
Well i assume you use (R^3 / T^2)A = (R ^ 3 / T ^ 2)B

3. The attempt at a solution
Therefore
5R ^3 / 50^2 = 3R^2 / T^2
T is what we need, but i seem to always get 540 and am not exactly sure as to how to work it out.
Am i using the wrong equation? or is my working out wrong?

thanks.

2. Jun 7, 2009

### LowlyPion

Welcome to PF.

Don't you need to take the square root of 540?

3. Jun 7, 2009

### EskShift

I thought so too, but that is approximately 23. The answer says 40 days? I still don't understand what I'm doing wrong, and i have an exam tomorrow!

4. Jun 7, 2009

### LowlyPion

Working backwards from 40 days that suggests an orbital radius of 4.3R from the center doesn't it?

5. Jun 8, 2009

### EskShift

It certainly does, possibly the answer is a miss-type, everyone i have asked have all said they don't understand. but i haven't asked my teacher yet, he might know. but ill be happy if my working is correct at least?

6. Jun 8, 2009

### LowlyPion

Perhaps there is a misstatement in the problem?

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