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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.

d = 42,242km (GEO Orbit)

Plus or minus 0.1 degrees, corresponds to a total excursion of 0.2 degrees or 0.00349 radians.

So define: Δ θ = 0.00349rads




Figure 1: Satellite Station Keeping Diagram

Solution:

The arc length involved is, r Δ θ = (42,242km)(0.00349rads) = 147.44km

The radial excursion, Δ r = rmax - rmin = 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.


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