

Satellite Orbital Velocity Problem
A rocket launches a satellite into geostationary orbit from the launch site located at Kourou in French Guiana.
Kourou’s latitude is 5.3 degrees. For the following problem, determine the incremental velocity required to correct
the orbit inclination and to achieve orbit circularization assuming the perigee altitude of the elliptical transfer
orbit is 450km and the apogee radius is 42,164km. Use the earth radius as 6,378km.
Solution:
With the given parameters the distance to perigee must first be obtained as:
V_{apogee} = [ μ ((2 / r_{a})  (1 / a)) ]^{1/2} =
[3.986E5 ((2 / 42,164km)  (1 / 24,496km)) ]^{1/2} = 1.62km / sec
Now for a geo orbit satellite the orbit is circular so, a = r_{a}
V_{geo} = [ μ / a ]^{1/2} = [ 3.986E5 / 42,164km ]^{1/2} = 3.07km / sec
So the incremental velocity required is,
ΔV_{elevation} = [ (V_{apogee})^{2} + (V_{geo})^{2}
 2(V_{apogee})(V_{geo})(cos i) ]^{1/2}
ΔV_{elevation} = 1.47km / sec is the incremental velocity required.
Satellite key words: velocity, meters per second, achieve orbit, apogee, perigee, eliptical orbit, inclination, RF transmission,
orbit, GEO, geosynchronous, earth station, station keeping, orbital parameters, signal path, atmospheric attenuation, path length,
data transfer, line of sight, LOS, ES, uplink, downlink, angular dimensions.
