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.

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

scholarly journals Periodic Attitudes of Libration Point Spacecrafts in the Earth-Moon System

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qiwei Guo ◽  
Bo Xu ◽  
Hanlun Lei
Keyword(s):  
Body Problem ◽  
Libration Point ◽  
Space Mission ◽  
Attitude Motion ◽  
Three Body Problem ◽  
Moon System ◽  
Libration Point Orbits ◽  
The Earth ◽  
Rigid Spacecraft ◽  
Three Body

The attitude motion of a rigid spacecraft is studied in the Earth-Moon circular restricted three-body problem. Firstly, the equilibrium attitude and its stability as functions of the moments of inertia are discussed when the spacecraft is assumed at the libration points. Then, periodic attitudes of a spacecraft with mass distribution given in the stable regions are obtained. Regarding space mission applications, the Sun orientation is discussed, and the orbit-attitude resonances are constructed for spacecrafts working on the libration point orbits by means of a continuation procedure.

scholarly journals Qualitative Dynamics of the Sun-Jupiter-Saturn System

1978 ◽  
Vol 41 ◽  
pp. 53-55
Author(s):  
V. Szebehely
Keyword(s):  
Body Problem ◽  
Stellar Systems ◽  
The Sun ◽  
Three Body Problem ◽  
Moon System ◽  
The Earth ◽  
Qualitative Dynamics ◽  
Binary Orbit ◽  
The Stability ◽  
Three Body

AbstractThe stability of the three-body problem formed by the Sun, Jupiter and Saturn is investigated using surfaces of zero velocity. The results obtained with the models of the restricted and general problems of three bodies are compared with numerical integration. The system is found to be stable in the sense that Saturn will neither interrupt the (perturbed) binary orbit of Jupiter around the Sun, nor will it escape from the system. It is shown that the known classical triple stellar systems are “more stable” than the solar system, which in turn is “more stable” than the Earth-Moon system.

DIFFERENT TYPES OF ATTRACTORS IN THE THREE BODY PROBLEM PERTURBED BY DISSIPATIVE TERMS

2011 ◽  
Vol 21 (08) ◽  
pp. 2195-2209 ◽  
Author(s):  
JOHN D. HADJIDEMETRIOU ◽  
GEORGE VOYATZIS
Keyword(s):  
Hamiltonian System ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Large Mass ◽  
Three Body Problem ◽  
Resonant Orbits ◽  
Different Types ◽  
Families Of Periodic Orbits ◽  
Three Body ◽  
Special Case

We study the evolution of a conservative dynamical system with three degrees of freedom, where small nonconservative terms are added. The conservative part is a Hamiltonian system, describing the motion of a planetary system consisting of a star, with a large mass, and of two planets, with small but not negligible masses, that interact gravitationally. This is a special case of the three body problem, which is nonintegrable. We show that the evolution of the system follows the topology of the conservative part. This topology is critically determined by the families of periodic orbits and their stability. The evolution of the complete system follows the families of the conservative part and is finally trapped in the resonant orbits of the Hamiltonian system, in different types of attractors: chaotic attractors, limit cycles or fixed points.

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