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/v². 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/v²
v^3=3.988e14/1.376e4=2.9e10
v=3.07e3m/s
Plugging this back into r=G*M/v² we get
r=4.23e7m

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know. JDJ