Classification of Swing-By Trajectories Using the Moon

1995 ◽  
Vol 48 (11S) ◽  
pp. S138-S142 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado ◽  
Roger Broucke
Keyword(s):  
Large Range ◽  
Initial Conditions ◽  
Close Approach ◽  
The Body ◽  
The Moon ◽  
Three Body Problem ◽  
Jacobian Constant ◽  
Three Body ◽  
The Mathematical Model

In the present paper we study and classify the swing-by maneuvers that use the Moon as the body for the close approach. The goal is to simulate a large variety of initial conditions for those orbits and classify them according to the effects caused by the close approach in the orbit of the spacecraft. Special attention is given to identify the regions where the captures and escapes occur. The classical three parameters (Jacobian constant, pericenter distance and angle of approach) used to identify a Swing-By maneuver are varied in large intervals to cover a large range of possibilities for the maneuver. Letter-plots figures are made to show the results obtained in a compact form. The theoretical prediction that for 0° ≤ ψ ≤ 180° the spacecraft losses energy and for 180° ≤ ψ ≤ 360° the spacecraft gains energy is confirmed. Regions containing trajectories that are candidates to generate Belbruno-Miller trajectories are identified. The well-known planar restricted circular three-body problem is used as the mathematical model. The equations are regularized (using Lamaiˆtre’s regularization), so it is possible to avoid the numerical problems that come from the close approach with the Moon.

scholarly journals Libration of Retrograde Satellite Orbits in the Circular Plane Restricted Three-Body Problem

1979 ◽  
Vol 81 ◽  
pp. 41-44
Author(s):  
Daniel Benest
Keyword(s):  
Body Problem ◽  
Initial Conditions ◽  
The Body ◽  
Satellite Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Limited Region ◽  
Lagrange Points ◽  
Three Body ◽  
Circular Plane

In the circular plane restricted three-body problem, we study the stable large retrograde non-periodic satellite orbits. We use rotating axes with the origin in the body around which turns the satellite, called its primary. We choose the initial conditions such as Yo=0 and Uo=0, so that an orbit can be represented by a point in the (Xo,Vo) plane. In this plane, the set of stable orbits is represented by a limited region, which we call the stability zone. This zone is composed in general by a large continental region, approximately limited by Lagrange points, and a peninsula more or less elongated.

Triple close approach in the three-body problem: A limit for the bounded orbits

1984 ◽  
Vol 32 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Jacques Laskar ◽  
Christian Marchal
Keyword(s):  
Body Problem ◽  
Close Approach ◽  
Three Body Problem ◽  
Three Body

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

scholarly journals Trapping Time of Resonant Orbits in Presence of Poynting - Robertson Drag

1983 ◽  
Vol 74 ◽  
pp. 397-410 ◽  
Author(s):  
R. Gonczi ◽  
Ch. Froeschlé ◽  
C. Froeschlé
Keyword(s):  
Initial Conditions ◽  
Gravitational Interaction ◽  
Resonance Region ◽  
Three Body Problem ◽  
Trapping Time ◽  
Resonant Orbits ◽  
Numerical Exploration ◽  
Orbital Resonances ◽  
Three Body ◽  
Special Case

AbstractWe study numerically the competition between the Poynting-Robertson drag and the gravitational interaction of grains with Jupiter near orbital resonances. The computations are based on the plane elliptic restricted three body problem. Numerical investigations show that the grains always cross the resonance region without any oscillation, except in the special case where the grains were initially inside the resonance. Such grains are temporarily trapped, then due to the drag they are ejected out of the resonance. The trapping time of a particle turns out to be much more important in the 3/2 and 2/1 commensurabilities than in the others.A numerical exploration of numerous orbits for different initial conditions and different sizes of grains has been performed. The trapping time appears to be closely connected to the size of the librator-type orbits regions; it increases with the initial eccentricity of the orbit, and is also proportional to the radius and the density of the particle.

scholarly journals New relativistic effects in the motion of the Moon

1986 ◽  
Vol 114 ◽  
pp. 407-410
Author(s):  
Bahram Mashhoon
Keyword(s):  
Body Problem ◽  
Gravitational Constant ◽  
Relativistic Effects ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
The Moon ◽  
Three Body Problem ◽  
Novel Approach ◽  
Lunar Motion ◽  
Three Body

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.

scholarly journals Making the moon reverse its orbit, or, stuttering in the planar three-body problem

2008 ◽  
Vol 10 (2/3, September) ◽  
pp. 569-595 ◽  
Author(s):  
Richard Montgomery ◽  
Mark Levi ◽  
Samuel Kaplan
Keyword(s):  
Body Problem ◽  
The Moon ◽  
Three Body Problem ◽  
Three Body

The role of the mass ratio in ballistic capture

2020 ◽  
Vol 498 (1) ◽  
pp. 1515-1529
Author(s):  
Zong-Fu Luo
Keyword(s):  
Initial Conditions ◽  
Massless Particle ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Ballistic Capture ◽  
Jacobi Constant ◽  
Celestial Bodies ◽  
Three Body ◽  
Gravity System

ABSTRACT A massless particle can be naturally captured by a celestial body with the aid of a third body. In this work, the influence of the mass ratio on ballistic capture is investigated in the planar circular restricted three-body problem (CR3BP) model. Four typical dynamical environments with decreasing mass ratios, that is, the Pluto–Charon, Earth–Moon, Sun–Jupiter, and Saturn–Titan systems, are considered. A generalized method is introduced to derive ballistic capture orbits by starting from a set of initial conditions and integrating backward in time. Particular attention is paid to the backward escape orbits, following which a test particle can be temporarily trapped by a three-body gravity system, although the particle will eventually deviate away from the system. This approach is applied to the four candidate systems with a series of Jacobi constant levels to survey and compare the capture probability (quantitatively) and capture capability (qualitatively) when the mass ratio varies. Capture mechanisms inducing favourable ballistic capture are discussed. Moreover, the possibility and stability of capture by secondary celestial bodies are analysed. The obtained results may be useful in explaining the capture phenomena of minor bodies or in designing mission trajectories for interplanetary probes.

scholarly journals Initial Parameter Analysis about Resonant Orbits in Earth-Moon System

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Li-Bo Liu ◽  
Ying-Jing Qian ◽  
Xiao-Dong Yang
Keyword(s):  
Body Problem ◽  
Parameter Analysis ◽  
Initial Parameter ◽  
The Moon ◽  
Three Body Problem ◽  
Ballistic Capture ◽  
Moon System ◽  
Two Body Problem ◽  
Resonant Orbits ◽  
Three Body

The initial parameters about resonant orbits in the Earth-Moon system were investigated in this study. Resonant orbits with different ratios are obtained in the two-body problem and planar circular restricted three-body problem (i.e., PCRTBP). It is found that the eccentricity and initial phase are two important initial parameters of resonant orbits that affect the closest distance between the spacecraft and the Moon. Potential resonant transition or resonant flyby may occur depending on the possibility of the spacecraft approaching the Moon. Based on an analysis of ballistic capture and flyby, the Kepler energy and the planet’s perturbed gravitational sphere are used as criteria to establish connections between the initial parameters and the possible “steady” resonant orbits. The initial parameter intervals that can cause instability of the resonant orbits in the CRTBP are obtained. Examples of resonant orbits in 1:2 and 2:1 resonances are provided to verify the proposed criteria.

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