Orbital period

  • Thread starter Bugsy23
  • Start date
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?
 
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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....
 
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
 

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