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mogley76
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Homework Statement
by using Newtons law of universal gravitaion and the relationship for the centripetal force, show that the orbital period T for a satellite circling a planet of mass M in orbit of radius r is given by :
T= 2pi sqrt r^3/GM
Homework Equations
none given
The Attempt at a Solution
consider a satellite of mass m orbiting the Earth of mass M with a constant speed v along a circular path of radius r.
the centripetal force : mv^2/r is provided by the gravitational attraction of the earth
so F= mv^2/r = GmM/r^2
v of robit = sgrt GM/r
the orbital period T = 2pi/w
since v=wr T now eqauls : 2pi r /v
therefore T= 2 pi sqrt r^3/GM
as both G and M are constants it can be seen that both the orbital speed and period depend only on the orbital radius.
have i derived this correctly?