

Satellite Orbit Position Problem
Most commercial communications satellites must maintain their orbital positions to within plus or minus 0.1 degrees of arc.
If a satellite meets this condition and is in an orbit with an eccentricity of 0.001, describe the station keeping box in
which the satellite in constrained to move. Calculate the maximum variation in range to an earth station that could occur
as the satellite moves about within the confines of the box. Assume a geosynchronous satellite orbit for your calculation.
Solution:
The arc length involved is, r Δ θ = (42,242km)(0.00349rads) = 147.44km
The radial excursion, Δ r = r_{max}  r_{min} = a (1 + e) – a (1  e) = 2ae
Therefore, Δ r = 2 (42,242km)(0.001) = 84.48km
The satellite is bound by the following figure (i.e. station keeping box)
Diagonal box dimension = sqrt [ (147.44)^{2}  2 + (84.48)^{2} ] = 225km
Next, given an Earth Station on the equator, the maximum variation to an earth station (ES) is, ES to point B minus ES to point A
The mean distance from ES to the center of the station keeping cube (note all three dimensions need to be accounted for) is = 35,872km.
ES to point A = 35,872km – 42km = 35,830km
ES to point B = sqrt [ (35,872 + 42)^{2} + 2 (74)^{2} ] = 35,914km
Therefore, the maximum variation is:
Δ = 35,914km – 35,830km = 84km
Satellite key words: SATCOM, station keeping, orbital limits, position, arc, communication satellite, eccentricity,
geostationary orbit constrains, earth station, GEO, range, kilometers, orbit drift, vector.
