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Satellite Data Relay Problem

An inter-satellite relay allows data to be transferred between satellites without having to pass through an earth station. Given the diagram in Figure 1, calculate the path length and the minimum distance between the data signal path and the surface of the earth for a link between two geosynchronous satellites that are exactly 110 degrees apart. Ignore any atmospheric effects. What is the maximum separation between two geosynchronous satellites with a line-of-sight link between them?


P = path length
d = earth clearance
re = 6370km (earth radius)
rs = 42,242km (GEO radius)
θ = satellite angular separation



Figure 1: Satellite Orbit Diagram

Solution:

With the following relations:

sin (θ / 2) = (P / 2) / rs

cos (θ / 2) = (d + re) / rs

P = 2 rs sin (θ / 2)

d = rs cos (θ / 2) - re

a) The calculated path length and minimum distance between the data link path is:

Angular value for θ = 110 degrees

P = 2 (42,242) sin (55 degrees) = 69,205km

d = (42,242) cos (55 degrees) - 6370km = 17,859km


b) The maximum separation of two GEO satellites with a LOS link is:

Solve for, d = 0

θmax = 2 cos-1(re / rs)

θmax = 2 cos-1(6370km / 42,242km) = 162.65 degrees

Pmax = 2 rs sin (θmax / 2)

Pmax = 2 (42,242) sin (162.65 degrees / 2) = 83,518km


Satellite key words: data relay, 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, relay, handoff, handshaking, data pipe, angular dimensions.


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