Posted by Anonymous on Monday, October 31, 2011 at 11:10pm.
Equate the gravitational force,
GmM/R^2, to the centripetal force, m V^2/R
M is the Earth's mass and G is the universal constant, which you need to look up. Satellite mass m cancels out.
Substitute 2 pi R/(139*60) for the velocity, V (in m/s).
Solve for the remaining variable R.
The satellite altitude is H = R - Rearth
The orbital period of a satellite derives from
T = 2(Pi)sqrt(r^3/µ) where T = the period in seconds
Pi = 3.14
r = the orbital radius in feet and
µ = the earth's gravitational constant = 1.407974x10^16 ft^3/sec^2.
139(60)= 2(3.14)sqrt(r^3/1.407974x10^16)
Solving for r = 5523.6 miles making the altitude 1560.6 miles = 2511km.
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