An Aside: ........ Resonances
- Mean motion resonances: Between orbital periods.
- Secular resonances: Between precession periods.
Simplest System: ........ 2D with 2 planets.
Also can happen with the nodes.
- Model planets as elliptical rings.
- Two elliptical Rings will exert a torque on one another.
- They precess.
- Precession periods range from 50,000 to 2 million years in outer solar system.
- Include a massless particle and it will also precess.
- If particle precesses as same rate as a planet
- Secular Resonance .
- Angular momentum can transfer because the particle sees a non-axisymmetric potential.
- These can be very strong.
Notation: is periapse resonance, is nodal resonance,
where X refers to a frequency (planet).