Introduction
Finding planets around other stars is extremely difficult because the planets are faint compared to the star that they orbit. However, we have been very sucessful at finding planets through indirect methods that observe the effect of the planet on its star. The two most sucessful methods are the transit method and the radial velocity method. In the transit method, we observe a periodic dimming of the star as the planet passes in front of it. The radial velocity measures the motion of the star as the planet orbits around it. We have found about 5000 exoplanets so far, including many in multiplanet systems.
Exoplanet Dynamics
The planets in the solar system have well ordered orbits. They are all close to circular, and their orbital planes are nearly coplanar and almost aligned to the spin of our Sun. The small, rocky terrestrial planets are close to the Sun, while the gaseous giant planets are farther away. However, many of the exoplanetary systems observed are quite different to our Solar System. For example, some of the first exoplanets discovered were “Hot Jupiters”. These are planets with masses similar to Jupiter but with orbits even closer to their star than Mercury is to our Sun. Standard planet formation theories are unable to explain how these planets could form so close to their star. Instead, we think they may have formed farther away from their host stars and later migrated inwards. Planet migration can occur early within the protoplanetary disk or later through gravitational interactions with other planets and bodies. Exoplanets are also observed in orbits that can be highly eccentric or highly misaligned, meaning that the orbital plane of the planet is misaligned to the spin of the star. Planets that form in a gas disk are expected to be in circular and coplanar orbits. These planets must have undergone some later gravitational interactions to be found in these orbits.
Resonances can occur when there are multiple bodies orbiting around a star, and they exert a periodic gravitational tug on each other. In most cases, this leads to an unstable interaction. The bodies exchange angular momentum until the resonance no longer exists. However, in some cases, it can lead to a stable resonant orbit. Mean motion resonances occur when the orbital period of two objects are related by a ratio of integers.
Post-Main Sequence and White Dwarf Pollution
When our Sun dies, it will undergo significant mass loss on the red-giant branch and the asymptotic giant branch phases. The outer envelope expands during these phases and may engulf planets that are close in. The Earth is close to the survival limit. As a result of the mass loss, any surviving bodies expand outwards. The asteroid belt and the giant planets should survive this process.
The Sun will eventually become a white dwarf. White dwarfs are made up of electron-degenerate material. They have a mass similar to the Sun but a volume similar to the Earth. A white dwarf is no longer undergoing nuclear fusion, and so its luminosity comes from its residual thermal energy.
A large fraction of white dwarfs are observed to have metal-polluted atmospheres. Metals (elements heavier than helium) in the white dwarf atmosphere should sink rapidly into the interior. Since we observe pollution for up to 600 million years after the white dwarf forms, there must be continuous accretion of metal-rich material on to these white dwarfs. The currently favored mechanism for feeding the pollution is planetary material that gets tidally disrupted through close encounters with the white dwarf. This material forms a debris disk around the white dwarf before it gets accreted. In order to feed the white dwarf with asteroids, there must be some instability in the remaining debris.
Circumbinary Planet Dynamics
While all of the currently observed circumbinary planets are in orbits that are close to coplanar to the binary orbit, this may be a result of selection effects. Many circumbinary gas disks are observed to be misaligned to the orbital plane of the binary, so planet formation may be able to proceed in a misaligned disk.
There are two inclinations for stationary orbits around an eccentric binary (meaning orbits that do not undergo nodal precession): first, when the planet orbit is coplanar to the binary orbit; and second, when the planet orbit is polar to the binary orbit.