Calculating Orbital Period of Satellites

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To calculate the orbital period of a satellite using the radius of its orbit and the mass of the central object, the key equation is T^2 = (2π)²r³/GM. This formula derives from equating gravitational force and centripetal force, where G is the gravitational constant, M is the mass of the central object, and r is the orbital radius. The small mass of the satellite can be neglected in this calculation. The discussion emphasizes the relationship between gravitational and centripetal forces in determining orbital dynamics. Understanding this equation is crucial for accurately predicting satellite motion.
Bugsy23
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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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