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Effective potential
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Combines gravity with the centrifugal barrier.
U_eff = −GMm/r + L²/2mr²For radial motion, add a centrifugal barrier: U_eff = −GMm/r + L²/2mr². Minimum gives the circular orbit; energies between give ellipses.
A comet with low L plunges close to the Sun.
Only the radial motion appears in U_eff.
In more detail
The effective potential combines gravitational potential and the centrifugal term from angular momentum. Its minima and maxima define the allowed circular orbits and the stability of orbits.
Real-world uses
- Orbit stability is analysed using effective potentials.
- Mission designers check orbit stability for satellites in complex fields.
- Engineers use the effective potential to see which orbits are stable and whether a spacecraft can escape a planet.
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Frequently asked questions
What is the centrifugal term?
The effective energy due to angular momentum, which pushes the object outward.
What does a minimum mean?
A stable circular orbit, where small changes give small oscillations.
Why add a centrifugal term?
The angular momentum of an orbit creates a repulsive barrier that keeps a body from falling straight into the centre.
Related topics in Gravitation & Orbits
Roche limit · Lagrange points · Two-body problem · Binary stars · Weighing the Sun and planets · Gravitational lensing