

Satellite Shadow Region Problem
For this problem, take a satellite in a circular orbit around the earth at an altitude of 10,000km.
Find the maximum time the satellite is in eclipse, also referred to as the shadow region, at its equinox.
Take the radius of the earth to be 6,378km. The figure below provides a graphical representation of the problem.
Solution:
θ = sin^{1}(r_{e} / r_{e} + h) = sin^{1}(6,378km / 6,378km + 10,000km)
= sin^{1}(0.389) = 22.92 degrees
Therefore, the Shadow Region (i.e. eclipse angle) = 2θ = 45.84 degrees
Now that we have calculated the angular distance in the satellites orbit it is within the shadow region,
we can now calculate the time (T):
T = 2π a^{3/2} / (μ)^{1/2}
T = 2π (16,378)^{3/2} / (3.986E5)^{1/2} = 20,859 seconds
So the maximum time the satellite is in eclipse is:
(45.84 degrees / 360 degrees) T = 2,656 seconds = 44.27 minuets
Satellite key words: eclipse, data relay, interference, RF transmission, orbit, GEO, geosynchronous, earth station, station keeping, orbital
parameters, stellar obstruction, signal path, atmospheric attenuation, path length, data transfer, line of sight, LOS, ES, uplink, downlink,
relay, handoff, handshaking, data pipe, angular dimensions.
