

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.
Solution:
a) r_{s} = a = 6370km + 322km = 6692km
T = 2π a^{3/2} / μ^{1/2} = 2π (6692km)^{1.5} / sqrt (3.986E5) = 5448 seconds
η = 2π / T = 2π rad / 5448 seconds = 1.15E3 rad/second
b) Calculated in part a, T = 5448 seconds = 90.8 minuets
c) v = r_{s} η = (6692km)(1.15E3rad/s) = 7696m/s
d) It was determined the Orbital Linear Velocity was V_{t} = 7696 m/s
Δf / f_{t} = V_{T} / V_{P}
Δf = V_{T}f_{T} / V_{P}
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.
