What is the orbital distance for a satellite with a 125 min period around Earth?

[choyphin]

Homework Statement

At what distance about Earth would a satellite have a period of 125 min?
G=6.673x10^-11
T=125 Min
Mass=5.97x10^24
Radius of Earth=6.38*10^6

Homework Equations

T=2pi*Square root of (R^3/constant*mass)

The Attempt at a Solution

125=2*3.14*Square root of ((6.38x10^6)^3+R^3/6.673x10^-11*5.97x10^24)
I got a negative #... Which i know is wrong!

 

[mgb_phys]

Put the units in - it will help !

 

[choyphin]

I did that, but still got an unreasonable answer: 2.6x10^26

 

[mgb_phys]

T=2pi*sqrt(R^3/GM)
so T/2pi = sqrt(R^3/GM)
Square both sides (T/2pi)^2 = R^3/GM
Finally R = cube root ( GM * (T/2pi)^2 )

Check the units (m^3 kg^01 s^-2 * kg * s^2)^1/3 = (m^3 )^1/3 = m

 

[choyphin]

Is the answer 106.6 KM? Thanks so much for the explanations by the way!

 

[mgb_phys]

I think you have a slight mistype there, do you have T in seconds?
Remember that the result is the radius of the orbit from the centre of the Earth - if you want the altitude you need to subtract the radius of the Earth.