Energy of Orbiting Satellites

Understanding the energy of orbiting satellites brings together concepts of kinetic energy, gravitational potential energy, and orbital mechanics. The relationships between these energy forms explain why satellites behave the way they do when their orbits change, and why a satellite in orbit has negative total energy.

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Kinetic Energy of an Orbiting Satellite

For a satellite of mass m in a circular orbit of radius r around a body of mass M, the orbital speed is v = √(GM/r). The kinetic energy is:

$KE = \frac{1}{2}mv^2 = \frac{1}{2}m \times \frac{GM}{r} = \frac{GMm}{2r}$KE=21​mv2=21​m×rGM​=2rGMm​

Notice that kinetic energy is always positive and decreases as the orbital radius increases. A satellite in a higher orbit moves more slowly and has less kinetic energy. This may seem counterintuitive — you might expect that moving a satellite to a higher orbit (giving it energy) would increase its speed. In fact, the opposite happens: adding energy to a satellite slows it down.

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Gravitational Potential Energy of an Orbiting Satellite

The gravitational potential energy of a satellite at orbital radius r is:

$PE = -\frac{GMm}{r}$PE=−rGMm​