Related papers: Approximating Periodic Orbits with Algebraic Curve…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We…

Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincar\'e maps to search for a suitable path through the interconnected web of periodic…

The goal of this paper it to prove existence theorems for one parameter families (branches) of ejection-collision orbits in the planar circular restricted three body problem (CRTBP), and to study some of their bifurcations. The orbits…

The elliptic isosceles restricted three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. The primaries of masses…

Near-Earth Objects (NEOs) are attractive exploration targets due to their accessibility, scientific value, and resources. Although trajectory design has revealed efficient pathways to these bodies, systematic strategies for Earth-NEO…

We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits. Asymmetric orbits exist in the restricted circular three body problem only…

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…

High-dimensional visual computer models are poised to revolutionize the space mission design process. The circular restricted three-body problem (CR3BP) gives rise to high-dimensional toroidal manifolds that are of immense interest to…

The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.

The halo orbits of the spatial circular restricted three-body problem are largely considered in space-flight dynamics to design low-energy transfers between celestial bodies. A very efficient analytical method for the computation of halo…

The goal of this paper is to obtain an approximate solution of the restricted three-body problem in the case of small perturbations in the vicinity of, but not in exact resonance. In this paper, we study the restricted threebody problem…

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this…

We propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle is in an orbit exterior to the one of the…

In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…

Our aim is to identify and classify mean-motion resonances (MMRs) for the coplanar circular restricted three-body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an…

Multi-revolution elliptic Halo (ME-Halo) orbits are a special class of symmetric and periodic solutions within the framework of the elliptic restricted three-body problem (ERTBP). During a single period, an M:N ME-Halo orbit completes $M$…

The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple…

With an increasing interest in the design of long and complex space missions, the search for orbits that require the least amount of fuel is of fundamental interest. This paper develops existing computational models for locating Unstable…

This paper presents a novel fuel-optimal guidance and control methodology for spacecraft swarm reconfiguration in Restricted Multi-Body Problems (RMBPs) with a guarantee of passive safety, maintaining miss distance even under abrupt loss of…