Quadrupole and octupole order resonances in non-restricted hierarchical planetary systems

Tuning fifth-order aberrations in a quadrupole-octupole corrector.

The resolution of conventional electron microscopes is usually limited by spherical aberration. Microscopes equipped with aberration correctors are then primarily limited by higher order, chromatic, and misalignment aberrations. In particular the Nion third-order aberration correctors installed on machines with a low energy spread and possessing sophisticated alignment software were limited by ...

Orbital Resonances in Planetary Systems

There are two main types of resonance phenomena in planetary systems involving orbital motions: (i) mean motion resonance: This is intuitively the most obvious type of resonance; it occurs when the orbital periods of two planets are close to a ratio of small integers; (ii) secular resonance: this is a commensurability of the frequencies of precession of the orientation of orbits, as described b...

Quadrupole and octupole radiation from 16O near 39 MeV excitation.

Order and Chaos in Planetary Systems

The dynamical stability of the Solar System is one of the oldest problems studied in astronomy. The motion of more than two bodies relative to each other due to their mutual gravitational attraction cannot be described analytically. Instead, the equations of motion need to be integrated using numerical methods in order to predict the orbital evolution of the system. In this way it has been esta...

Planetary Migration and Eccentricity and Inclination Resonances in Extrasolar Planetary Systems

The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected...