How to Calculate the Orbital Period of a Satellite Around Planet Zeta?

[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.

Homework Equations

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

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.

 

[LowlyPion]

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.

Homework Equations

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

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.

Welcome to PF.

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

 

[EskShift]

Welcome to PF.

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

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!

 

[LowlyPion]

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

 

[EskShift]

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

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?

 

[LowlyPion]

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?

Perhaps there is a misstatement in the problem?