

Satellite Data Relay Problem
An intersatellite 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 lineofsight link between them?
Solution:
With the following relations:
sin (θ / 2) = (P / 2) / r_{s}
cos (θ / 2) = (d + r_{e}) / r_{s}
P = 2 r_{s} sin (θ / 2)
d = r_{s} cos (θ / 2)  r_{e}
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
θ_{max} = 2 cos^{1}(r_{e} / r_{s})
θ_{max} = 2 cos^{1}(6370km / 42,242km) = 162.65 degrees
P_{max} = 2 r_{s} sin (θ_{max} / 2)
P_{max} = 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.
