Related papers: Planetary Orbital Equations in Externally-Perturbe…
Binary and multiple star systems are extreme environments for the formation and long-term presence of extrasolar planets. Circumstellar planets are subject to gravitational perturbations from the distant companion star, and this interaction…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These…
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
This work focuses on the dynamics and the detection methods of co-orbital exoplanets. We call "co-orbital" any configuration in which two planets orbit with the same mean mean-motion around the same star. First, we revisit the results of…
Terrestrial exoplanets are on the verge of joining the ranks of astronomically accessible objects. Interpreting their observable characteristics, and informing decisions on instrument design and use, will hinge on the ability to model these…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We study the long-term time-scale (i.e. period comaprable to the orbital period of the outer perturber object) transit timing variations in transiting exoplanetary systems which contain a further, more distant (a_2>>a_1) either planetary,…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
Non-gravitational forces play surprising and, sometimes, centrally important roles in shaping the motions and properties of small planetary bodies. In the solar system, the morphologies of comets, the delivery of meteorites and the shapes…
The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements…
We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
Aims. The aim of this work is to study the dynamical effects of the Galaxy on binary star systems with physical and orbital charac- teristics similar to those of the population of known wide binary stars with exoplanets. As secondary goal…
Research in extrasolar-planet science is data-driven. With the advent of radial-velocity instruments like HARPS and HARPS-N, and transit space missions like Kepler, our ability to discover and characterise extrasolar planets is no longer…
Consider the Restricted Planar Circular Three Body Problem (RPC3BP), which models the motion of a massless particle (Asteroid) under the gravitational influence of two massive bodies (the primaries) moving on circular orbits. By considering…
We extend the description of equivalent-barotropic equations for exoplanets to the diabatic case -- that is, with explicit heating and/or cooling representation, rather than with a stationary deflection of the bottom bounding surface. In…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…