Part of JME-05 — Gravitation

Satellite Energetics

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A satellite in circular orbit of radius r has well-defined energy relationships:

QuantityFormulaSign
KEGMm2r\frac{GMm}{2r}+
PE-GMm/r-
Total E-GMm2r\frac{GMm}{2r}-
Binding EGMm2r\frac{GMm}{2r}+

Key relations: Total E = -KE = PE/2. Binding energy = -Total E = KE.

As orbit radius increases: KE decreases, PE increases (less negative), Total E increases (less negative), satellite becomes less tightly bound.

To move to a higher orbit: supply energy = difference in total energies. To escape from orbit: supply energy = binding energy = GMm2r\frac{GMm}{2r} = current KE.

The geostationary orbit (T = 24h, r ≈ 42,300 km) is in the equatorial plane. All geostationary satellites orbit at the same altitude regardless of mass.

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