Synchronous Orbit Parameters

## Question:

A communications satellite is to be placed into an equatorial
orbit around the Earth so that it always remains above a fixed
point on the Earth's surface. Assume this requires the period
to be 24 hours. Determine the radius of the orbit and the
satellite's velocity.
## Answer:

As we have seen for a circular orbit
r=G*M/v^{2}. If the period is to be 8.64e4 seconds
(24 hours) then

2*pi*r/v=8.64e4, or
r=(8.64e4/6.28)*v so,

1.376e4*v=6.673e-11*5.976e24/v^{2}

v^3=3.988e14/1.376e4=2.9e10

v=3.07e3m/s

Plugging this back into
r=G*M/v^{2} we get

r=4.23e7m
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