  Custom Search  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.

 Parameters: 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.

Solution:

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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