scholarly journals The Satellite Case of the Three-Body Problem

1979 ◽  
Vol 81 ◽  
pp. 77-83
Author(s):  
Gen'ichiro Hori
Keyword(s):  
Body Problem ◽  
Disturbing Function ◽  
The Sun ◽  
Satellite Theory ◽  
Three Body Problem ◽  
Two Factors ◽  
Three Body

In the lunar or satellite theory, the disturbing function is developed in the form in which each term consists of two factors. The first factor depends on the position of the sun, and the second one that of the satellite.

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 Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem

2010 ◽  
Vol 108 (3) ◽  
pp. 215-232 ◽  
Author(s):  
Marco Tantardini ◽  
Elena Fantino ◽  
Yuan Ren ◽  
Pierpaolo Pergola ◽  
Gerard Gómez ◽  
...  
Keyword(s):  
Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Spacecraft Trajectories ◽  
Three Body

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.

scholarly journals Properties of the lunar gravity assisted transfers from LEO to the retrograde-GEO

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bo-yong He ◽  
Peng-bin Ma ◽  
Heng-nian Li
Keyword(s):  
Body Problem ◽  
Space Debris ◽  
Low Earth Orbit ◽  
Earth Orbit ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Lunar Gravity ◽  
Three Body Problem ◽  
Four Body Problem ◽  
Three Body

AbstractThe retrograde geostationary earth orbit (retro-GEO) is an Earth’s orbit. It has almost the same orbital altitude with that of a GEO, but an inclination of 180°. A retro-GEO monitor-satellite gives the GEO-assets vicinity space-debris warnings per 12 h. For various reasons, the westward launch direction is not compatible or economical. Thereby the transfer from a low earth orbit (LEO) to the retro-GEO via once lunar swing-by is a priority. The monitor-satellite departures from LEO and inserts into the retro-GEO both using only one tangential maneuver, in this paper, its transfer’s property is investigated. The existence of this transfer is verified firstly in the planar circular restricted three-body problem (CR3BP) model based on the Poincaré-section methodology. Then, the two-impulse values and the perilune altitudes are computed with different transfer durations in the planar CR3BP. Their dispersions are compared with different Sun azimuths in the planar bi-circular restricted four-body problem (BR4BP) model. Besides, the transfer’s inclination changeable capacity via lunar swing-by and the Sun-perturbed inclination changeable capacity are investigated. The results show that the two-impulse fuel-optimal transfer has the duration of 1.76 TU (i.e., 7.65 days) with the minimum values of 4.251 km s−1 in planar CR3BP, this value has a range of 4.249–4.252 km s−1 due to different Sun azimuths in planar BR4BP. Its perilune altitude changes from 552.6 to 621.9 km. In the spatial CR3BP, if the transfer duration is more than or equal to 4.00 TU (i.e., 17.59 days), the lunar gravity assisted transfer could insert the retro-GEO with any inclination. In the spatial BR4BP, the Sun’s perturbation does not affect this conclusion in most cases.

scholarly journals Transfers from the Earth to $$L_2$$ Halo orbits in the Earth–Moon bicircular problem

2021 ◽  
Vol 133 (11-12) ◽  
Author(s):  
José J. Rosales ◽  
Àngel Jorba ◽  
Marc Jorba-Cuscó
Keyword(s):  
Direct Effect ◽  
Body Problem ◽  
Time Dependent ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Halo Orbits ◽  
The Earth ◽  
Gravitational Influence ◽  
Three Body

AbstractThis paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.

Special cases of the restricted problem of three bodies

1966 ◽  
Vol 25 ◽  
pp. 187-193 ◽  
Author(s):  
J. Schubart
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Disturbing Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Long Period ◽  
Period Effects ◽  
Special Cases ◽  
Three Body

The long-period effects in nearly commensurable cases of the restricted three-body problem were studied according to the ideas of Poincaré. The secular and critical terms of the disturbing function were isolated by a numerical averaging process, by use of an IBM 7094 computer.

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