A Cartographic Study of the Phase Space of the Elliptic Restricted Three Body Problem: Application to the Sun–Jupiter–Asteroid System

2011 ◽  
pp. 83-96
Author(s):  
Cătălin Galeş
Keyword(s):  
Phase Space ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
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.

Characterization of the Phase Space Structure of Circular Restricted Three-Body Problem: An Alternative Approach

2016 ◽  
Vol 26 (02) ◽  
pp. 1650029
Author(s):  
Beena R. Gupta ◽  
Vinay Kumar
Keyword(s):  
Phase Space ◽  
Frequency Analysis ◽  
Body Problem ◽  
Space Structure ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Phase Space Structure ◽  
Three Body

In this paper, we have considered Time-Frequency Analysis (TFA) and Poincaré Surface of Section (PSS) for the study of the phase space structure of nonlinear dynamical system. We have examined a sample of orbits taken in the framework of Circular Restricted Three-Body Problem (CRTBP). We have computed ridge-plots (i.e. time-frequency landscape) using the phase of the continuous wavelet transform. Clear visualization of resonance trappings and the transitions is an important feature of this method, which is presented using ridge-plots. The identification between periodic and quasi-periodic, chaotic sticky and nonsticky and regular and chaotic orbits are done in comparatively less time and with less computational effort. The spatial case of Circular Restricted Three-Body problem is considered to show the strength of Time-Frequency Analysis to higher dimensional systems. Also, with the help of ridge-plots, we can visualize the phenomenon of transient chaos.

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.

Comets and the Missing Planet

1978 ◽  
Vol 41 ◽  
pp. 101-107
Author(s):  
Michael W. Ovenden ◽  
John Byl
Keyword(s):  
Body Problem ◽  
Heliocentric Distance ◽  
Asteroid Belt ◽  
Random Sets ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Orbital Elements ◽  
Long Period ◽  
Three Body

AbstractIntegrating backwards in time in the circular restricted three-body problem Galaxy-Sun-Comet, for both the real long-period comets and fictitious random sets of orbital elements, we have confirmed van Flandern’s conclusion that there is a statistically-significant clustering of the orbits of real long-period comets, in heliocentric direction, some 5×106 years ago. The clustering is also significant in heliocentric distance, and is more marked if it is assumed that the comets have gone round the Sun more than once since the epoch of maximum clustering. We suggest that the “event” discovered by van Flandern is not the explosive disruption of a planet formerly in the asteroid belt, but the latest in a series of minor catastrophies, such as the collisional break-up of a pair of large asteroids.

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