scholarly journals Invariant Relative Orbits Taking into Account Third-Body Perturbation

2012 ◽  
Vol 03 (02) ◽  
pp. 113-120 ◽  
Author(s):  
Walid Ali Rahoma ◽  
Gilles Metris
Keyword(s):  
Third Body ◽  
Third Body Perturbation

scholarly journals Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Carlos Renato Huaura Solórzano ◽  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Semimajor Axis ◽  
The Moon ◽  
Orbital Elements ◽  
Third Body ◽  
Short Period ◽  
Time Histories ◽  
Physical Reasons ◽  
Averaged Model ◽  
The Mathematical Model ◽  
Third Body Perturbation

The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.

scholarly journals Studying the behaviour of averaged models in the third body perturbation problem

2013 ◽  
Vol 465 ◽  
pp. 012017 ◽  
Author(s):  
R C Domingos ◽  
A F Bertachini de Almeida Prado ◽  
R Vilhena de Moraes
Keyword(s):  
Third Body ◽  
The Third ◽  
Perturbation Problem ◽  
Averaged Models ◽  
Third Body Perturbation

Third-Body Perturbation Effects on Satellite Formations

2013 ◽  
Vol 60 (3-4) ◽  
pp. 408-433 ◽  
Author(s):  
Christopher W. T. Roscoe ◽  
Srinivas R. Vadali ◽  
Kyle T. Alfriend
Keyword(s):  
Third Body ◽  
Satellite Formations ◽  
Third Body Perturbation

scholarly journals A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
R. C. Domingos ◽  
A. F. Bertachini de Almeida Prado ◽  
R. Vilhena de Moraes
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Second Order ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Elliptic Orbits ◽  
Three Body ◽  
The Impact ◽  
Third Body Perturbation

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

Third-Body Perturbation in Orbits Around Natural Satellites

2003 ◽  
Vol 26 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Third Body ◽  
Natural Satellites ◽  
Third Body Perturbation

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

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