Related papers: Semi-Analytical Perturbative Approaches to Third B…
Various astrophysical processes are known, where the fly-by of a massive object affects matter initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs or planetary systems. We…
Starting from the Hamiltonian representation of the dynamics in \cite{rosengren2015chaos,colombo2019long}, this work proposes an innovative procedure to design fully-analytical maneuvers for post-mission disposal of HEOs satellites,…
The proposal of increasingly complex and innovative space endeavours poses growing demands for mission designers. In order to meet the established requirements and constraints while maintaining a low fuel cost, the use of low-energy…
We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum ${\boldsymbol S}_\textrm{X}$ of a rotating mass $M_\textrm{X}$ orbited at distance $r_\textrm{X}$ by a local gravitationally bound restricted…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
We consider the planar circular restricted three-body problem (PCRTBP), as a model for the motion of a spacecraft relative to the Earth-Moon system. We focus on the Lagrange equilibrium points $L_1$ and $L_2$. There are families of Lyapunov…
Based on the value of the orbital eccentricity of a particle and also its proximity to the exact resonant orbit in a three-body system, the Pendulum Approximation (Dermott & Murray 1983) or the Second Fundamental Model of Resonance (Andoyer…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
Hierarchical three-body systems offer a compelling framework to explore the subtle interplay between Newtonian and relativistic gravitational effects in astrophysical environments. In this work, we investigate post-Newtonian corrections to…
We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…
In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials…
We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away…
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 use the planar circular restricted three-body problem in order to numerically investigate the orbital dynamics of orbits of a spacecraft, or a comet, or an asteroid in the Saturn-Titan system in a scattering region around the Titan. The…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
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…
We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This phenomenon, known as Kozai-Lidov mechanism in the…
We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the…