When a satellite is (h) km above Earth, the time, (t), in minutes, to complete one orbit is given by the formula (t) = square root of (6370 + h)^3 / 6024
A satellite is placed in a geosynchronous orbit about Earth. What must it's altitude be?
t = time
h = height
A satellite is placed in a geosynchronous orbit about Earth. What must it's altitude be?
t = time
h = height
-
Geosynchronous or Geostationary means that the Starlite orbits around the earth once every 24 hours, the same as a day on earth. So all you have to do is to solve the equation for h, when t 24*60 or t = 1440 minutes.
1440 = sqrt( (6370 + h)^3 ) / 6024
6024*1440 = sqrt( (6370 + h)^3 )
(6024*1440)^2 = (6370 + h)^3
(6024*1440)^(2/3) = 6370 + h
h = (6024*1440)^(2/3) - 6370
h = 35848.06299 km
1440 = sqrt( (6370 + h)^3 ) / 6024
6024*1440 = sqrt( (6370 + h)^3 )
(6024*1440)^2 = (6370 + h)^3
(6024*1440)^(2/3) = 6370 + h
h = (6024*1440)^(2/3) - 6370
h = 35848.06299 km