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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(re / re + 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 a3/2 / (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.


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