The final giant-impact phase of terrestrial planet formation is believed to begin with a large number of planetary embryos on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits
cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the dynamical temperature, that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.
This article reviews Michel Henons contributions to a diverse set of problems in astrophysical dynamics, including violent relaxation, Saturns rings, roundoff error in orbit integrations, and planet formation.
Numerous telescopes and techniques have been used to find and study extrasolar planets, but none has been more successful than NASAs Kepler Space Telescope. Kepler has discovered the majority of known exoplanets, the smallest planets to orbit normal
stars, and the worlds most likely to be similar to our home planet. Most importantly, Kepler has provided our first look at typical characteristics of planets and planetary systems for planets with sizes as small as and orbits as large as those of the Earth.
Quasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of
between $10^6$ and $10^{10}$ solar masses---dead quasars---are present at the centers of most galaxies. Our own galaxy contains a black hole of $4.3times10^6$ solar masses. The mass of the central black hole appears to be closely related to other properties of its host galaxy, such as the total mass in stars, but the origin of this relation and the role that black holes play in the formation of galaxies are still mysteries.
The broad emission lines commonly seen in quasar spectra have velocity widths of a few per cent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the redshift of t
he broad H-beta line in the quasar rest frame (determined from the core component of the [OIII] line) for over 20,000 quasars from the Sloan Digital Sky Survey DR7 quasar catalog. The mean redshift as a function of line width is approximately consistent with the relativistic redshift that is expected if the line originates in a randomly oriented Keplerian disk that is obscured when the inclination of the disk to the line of sight exceeds ~30-45 degrees, consistent with simple AGN unification schemes. This result also implies that the net line-of-sight inflow/outflow velocities in the broad-line region are much less than the Keplerian velocity when averaged over a large sample of quasars with a given line width.
