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Satellite Orbit Variables Problem

A satellite in a 322km circular orbit has onboard a 300MHz transponder. Calculate the following parameters with a 322km high circular orbit, and determine the maximum frequency range over which the received signal would Doppler shift if received by a stationary observer in space. That being, a delta in frequency equivalent to a signal shift from plus frequency to minus frequency; or put mathematically 2Δf.

a) Determine the orbital angular velocity in radians per second.
b) Determine the orbital period in minuets.
c) Determine the orbital linear velocity in meters per second.


a) rs = a = 6370km + 322km = 6692km

T = 2π a3/2 / μ1/2 = 2π (6692km)1.5 / sqrt (3.986E5) = 5448 seconds

η = 2π / T = 2π rad / 5448 seconds = 1.15E-3 rad/second

b) Calculated in part a, T = 5448 seconds = 90.8 minuets

c) v = rs η = (6692km)(1.15E-3rad/s) = 7696m/s

d) It was determined the Orbital Linear Velocity was Vt = 7696 m/s

Δf / ft = VT / VP

Δf = VTfT / VP

Δf = (7696m/s)(3E8m/s) / 3E8m/s = 7.696kHr

So the Maximum Doppler Shift = 2Δf = 15.4kHr

Satellite key words: angular velocity, orbital period, linear velocity, radians, polar coordinates, geosynchronous, Doppler shift, delta, signals, orbital variables, circular orbit, elliptical, bandwidth, frequency shift, UT, universal time, transmitter, receiver.

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