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Elliptical orbit energy
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Total energy depends only on the semi-major axis.
E = −GMm/2aFor an ellipse E = −GMm/2a, with a the semi-major axis. All orbits with the same a have the same energy, whatever their eccentricity.
A comet's long ellipse has the same energy as a circular orbit of radius a.
Not −GMm/2r with the current r.
In more detail
In an elliptical orbit, the total energy depends only on the semi-major axis. The energy is constant, but the kinetic and potential energies exchange as the object moves around the orbit.
Real-world uses
- Spacecraft in elliptical transfer orbits use energy exchange to reach higher altitudes.
- Comets speed up and slow down along their elliptical paths.
- Mission designers compute the energy of a spacecraft on a transfer orbit to plan its journey between planets.
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Frequently asked questions
Where is kinetic energy greatest?
At perihelion, closest to the central body, where speed is highest.
Does total energy change?
No, in an ideal two-body orbit with no drag, total energy is constant.
Does eccentricity change the total energy?
No. The total energy depends only on the semi-major axis, so orbits with the same long axis share the same energy.
Related topics in Gravitation & Orbits
Kepler's first law · Kepler's second law · Kepler's third law · Eccentricity · Perihelion and aphelion · Orbital transfers