Find the radius of a geostationary orbit. We proceed in a manner analogous to the previous section, but with the intent of substituting values with units attached for G and M, and obtaining a value for R with units attached.
The expression for circular orbital velocity around a spherically symmetric body is:
where is the gravitational constant, is the mass of the body, and is the radius of orbit.
Now, for geostationary orbit, an orbital velocity of meters per day is required, which in meters per second is:
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Equate this to .
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Solve for . To disregard non-real solutions, use the RealDomain package.
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Replace with its value and with the mass of the Earth and then evaluate.
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The result is the radius in kilometers (km) of a geostationary orbit.