Related papers: Sir John Herschel and the Stability of Saturn's Ri…

The true reason for partition of the Saturn ring as well as rings of other planets into great many of sub-rings is found. This reason is the theorem of Zelikin-Lokutsievskiy-Hildebrand about fractal structure of solutions to generic…

As it has already done for Earth, the sun, and the stars, seismology has the potential to radically change the way the interiors of giant planets are studied. In a sequence of events foreseen by only a few, observations of Saturn's rings by…

We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition…

After early work of Henon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by…

We find an interesting fact that fictitious retrograde co-orbitals of Saturn, or small bodies inside the retrograde 1:1 resonance with Saturn, are highly unstable in our numerical simulations. It is shown that in the presence of Jupiter,…

This article reviews Michel Henon's contributions to a diverse set of problems in astrophysical dynamics, including violent relaxation, Saturn's rings, roundoff error in orbit integrations, and planet formation.

Magnet stability and reproducibility have become increasingly important as greater precision and beams with smaller dimension are required for research, medical and other purpose. The observed causes of mechanical and electrical instability…

We elaborate on a criterion for the emergence of instability in the fundamental mode recently observed by Cheung {\it et al.}, as a universal phenomenon in the context of black hole perturbations. Such instability is characterized by an…

With recent advances in the modeling of the solar system giant planets, rapid progress has been made in understanding the remaining questions pertaining to their formation and evolution. However, this progress has largely neglected the…

The law of centripetal force governing the motion of celestial bodies in eccentric conic sections, has been established and thoroughly investigated by Sir Isaac Newton in his Principia Mathematica. Yet its profound implications on the…

In 1925 Sir James Jeans calculated that a star made up of an ideal gas, generating energy as a moderately positive function of temperature and density, could not exist. Such stars would be unstable to oscillations of increasing size. It…

The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities. After its formation, some dynamical mechanism must therefore have tilted Saturn up to its…

The magnetization relationships for magnetically uniform spherical particles of the Saturn rings are derived. The problem of a solitary magnetized sphere and spherical particle among identical particles scattered in a disk-like structure is…

This study is motivated by the observation, based on photographs from the Cassini mission, that Saturn's rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in…

Seismology allows for direct observational constraints on the interior structures of stars and planets. Recent observations of Saturn's ring system have revealed the presence of density waves within the rings excited by oscillation modes…

Saturn's C ring contains multiple structures that appear to be density waves driven by time-variable anomalies in the planet's gravitational field. Semi-empirical extensions of density wave theory enable the observed wave properties to be…

The astronomer E.V. Pitjeva, by analyzing with the EPM2008 ephemerides a large number of planetary observations including also two years (2004-2006) of normal points from the Cassini spacecraft, phenomenologically estimated a statistically…

Context: As a result of Titan's migration and Saturn's probable capture in secular spin-orbit resonance, recent works show that Saturn's obliquity could be steadily increasing today and may reach large values in the next billions of years.…

Poincar\'e's work more than one century ago, or Laskar's numerical simulations from the 1990's on, have irrevocably impaired the long-held belief that the Solar System should be stable. But mathematical mechanisms explaining this…

The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of…