Calculating Orbital Period of Satellites

[Bugsy23]

How do you calculate the orbital period of an object, eg. a satellite, if the only known values are the radius of the orbit and the mass of the central object?

 

[Naty1]

The equations that come to mind are a = 1/r v² = wr = 2(pi)r/T and mw2r =Mw2R (the two centripetal forces are equal)...M is the big mass, like the Earth with circular radius orbit R..

if the gravitalional force equals the centripetal...F = ma.. so
GMm/(R+r)2 = mw2r and the small m's drop out...

Then just assume R (radius of orbit of the big central mass) is negligible...
and you are right near the answer...

 

[Sakriya]

it comes out to be:

T^2= ((2*pi)^2*r^3)/GM

where r is radius and M is mass of central object. T is time period