Related papers: The Outward Radial Offset of Neptune Ring Arcs
By distinguishing the main arc Fraternite from the minor arcs Egalite (2,1), Liberte, Courage, the restricted three-body system is extended to a non-conservative restricted four-body system with the central body Neptune S, the primary body…
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [Astroph. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies,…
Generally, the oblateness of a planet or moon is what causes rings to settle into its equatorial plane. However, the recent suggestion that a ring system might exist (or have existed) about Rhea, a moon whose shape includes a strong prolate…
The Hamiltonian used in classical analyses of von Zeipel-Lidov-Kozai or ZLK oscillations in hierarchical triple systems is based on the quadrupole potential from a distant body on a fixed orbit, averaged over the orbits of both the inner…
Voyager 2 images confirmed the presence of ring arcs around Neptune. These structures need a confinement mechanism to constrain their spreading due to collisions, dissipative forces, and differential keplerian motion. Here we report the…
The boundaries of the Uranian epsilon, alpha, and beta rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of…
The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…
We study the hybrid type of rank one perturbations in $\mathbb{R}^2$ and $\mathbb{R}^3$, where the perturbation supported by a circle/sphere is considered together with the delta potential supported by a point outside of the circle/sphere.…
Neptune's incomplete ring arcs have been stable since their discovery in 1984 by stellar occultation. Although these structures should be destroyed within a few months through differential Keplerian motion, imaging data over the past couple…
According to recent works [Tsui PSS \textbf{55}, 237-242 (2007), \textbf{55}, 2042-2044 (2007)], the Neptune Adams ring main arc Fraternite is regarded as captured by the corotation elliptic resonance (CER) potential of Galatea. The minor…
We analytically work out the long-term orbital perturbations induced by the first term of the expansion of the perturbing potential arising from the local modification of the Newton's inverse square law due to a topology R^2 x S^1 with a…
We first derive the Rayleigh-Schr\"odinger many-body perturbation theory up to third order (RSPT3) for Hamiltonians with three-body interaction. The structure of closed-shell nuclei in a wide mass range from 4He to 48Ca has been…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
Narrow planetary rings are eccentric and inclined. Particles within a given ring must therefore share the same pericenter and node. We solve for the three-dimensional geometries and mass distributions that enable the Uranian Alpha and Beta…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…
It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold.…
Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…
The arcs of Neptune - Fraternit\'e, Egalit\'e, Libert\'e, and Courage - are four incomplete rings immersed in the Adams ring. A recent confinement model for the arcs proposes that the structures are azimuthally confined by four co-orbital…
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the…