Lesson 17, Topic 2
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Orbital Energy

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Overview of Formulae

Potential EnergyKinetic EnergyTotal Energy
[katex]U=-\frac{GMm}{r}[/katex][katex]K=\frac{GMm}{2r}[/katex][katex]E=-\frac{-GMm}{2r}[/katex]

Potential Energy

Gravitational potential energy is always less than zero, unless a body is an infinite distance away from other bodies or gravitational fields.

Kinetic Energy

The formula for orbital kinetic energy may be derived by substituting the equation for orbital velocity into the standard equation for kinetic energy.

Total Energy

The total energy of an orbiting object, like any other object, is the sum of its potential and kinetic energies. Creating a formula specific to orbital energy involves simply adding the specific formulae for orbital potential and kinetic energies.

E=U+K=-\frac{GMm}{r} + \frac{GMm}{2r}=-\frac{GMm}{2r}

Energy Changes due to Changing Orbits

When an object is moved to another position within a gravitational field, energy is converted between gravitational potential and kinetic energy. An object moving to a lower orbit will see a decrease in gravitational potential energy and thus an increase in kinetic energy, for example.

The magnitude of change of potential/kinetic energy will be equal to the work done to alter the orbit.

It is easiest to calculate a change in energy based off the change in potential energy as this change is determined by the difference in orbital radius. Calculate the energy change by subtracting the initial potential energy from the final potential energy, as seen below.

\Delta E_\text p= GMm\Big [\frac{1}{R_\text i - R_\text f}\Big ]