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 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 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 Alternative paths to Earth-Moon transfer

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Cristiano Fiorilo de Melo ◽  
Othon Cabo Winter
Keyword(s):  
Body Problem ◽  
Low Cost ◽  
Flight Time ◽  
The Moon ◽  
Three Body Problem ◽  
The Earth ◽  
Probe System ◽  
Four Body Problem ◽  
Low Altitude ◽  
Three Body

The planar, circular, restricted three-body problem predicts the existence of periodic orbits around the Lagrangian equilibrium point L1. Considering the Earth-lunar-probe system, some of these orbits pass very close to the surfaces of the Earth and the Moon. These characteristics make it possible for these orbits, in spite of their instability, to be used in transfer maneuvers between Earth and lunar parking orbits. The main goal of this paper is to explore this scenario, adopting a more complex and realistic dynamical system, the four-body problem Sun-Earth-Moon-probe. We defined and investigated a set of paths, derived from the orbits around L1, which are capable of achieving transfer between low-altitude Earth (LEO) and lunar orbits, including high-inclination lunar orbits, at a low cost and with flight time between 13 and 15 days.

scholarly journals The special case of the three body problem, when gravitational potential is given as the Kislik potential

2014 ◽  
Vol 9 (S310) ◽  
pp. 45-48
Author(s):  
A. Shuvalova ◽  
T. Salnikova
Keyword(s):  
Body Problem ◽  
Relative Equilibria ◽  
Point Mass ◽  
Restricted Three Body Problem ◽  
The Moon ◽  
Three Body Problem ◽  
The Earth ◽  
The Difference ◽  
Three Body ◽  
Special Case

AbstractIn this paper we consider the special case of the planar circular restricted three-body problem by the example of the problem of the Earth, the Moon and a point mass, where the gravitational potentials of the Earth and the Moon are given as the Kislik potential. The Kislik potential takes into account the flattening of a celestial body on the poles. We find the relative equilibria solutions for a point mass and analyze their stability. We describe the difference between the obtained points and the classical solution of the three-body problem.

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