Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

Zotos, Euaggelos E.; Dubeibe, F. L.

doi:10.1142/s0218271818500360

Cited by 18 publications

(9 citation statements)

References 34 publications

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“… Our findings are in agreement with previous studies related to the influence of perturbing terms in the dynamics of open and closed astrophysical systems [17,18,19].…”

Section: Discussionsupporting

confidence: 93%

Exit basins for the Sitnikov problem with variable mass

2020

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In the present paper, we perform a numerical study of the Sitnikov problem aiming to characterize the orbits of a variable mass particle (e.g., comet, rocket, asteroid or spacecraft) and determine the uncertainty in the prediction of the final state of the test particle. The classification of final states was done through the well-known exit basins, while the determination of the uncertainty was calculated using a new tool named Basin entropy. It is found that for small values of the initial mass of the test particle, the number of initial conditions leading to bounded orbits gets increased, thus reducing the uncertainty in the final states. The same behavior in uncertainty is observed for increasing values of the exponent in Jeans law for the variation of the mass. Our results allow us to conclude that: i) an accelerated fuel consumption in the initial stages of stabilization of a satellite can keep the object in an oscillatory state around the primaries and ii) if the mass of the satellite is less than one hundredth of the mass of each primary, it is possible to predict with a very high certainty the final state of the satellite, regardless of the accuracy in the initial conditions of the system.

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“… Our findings are in agreement with previous studies related to the influence of perturbing terms in the dynamics of open and closed astrophysical systems [17,18,19].…”

Section: Discussionsupporting

confidence: 93%

Exit basins for the Sitnikov problem with variable mass

2020

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“…For simplicity, in all that follows we shall use canonical units, such that the sum of the masses, as well as the distance between the primaries, the angular velocity, and the gravitational constant, are set to 1. Additionally, as we consider the non-relativistic limit of the model, the speed of light will be chosen to the value c = 1 × 10 4 [19,20], unless otherwise is specified. Taking into account the previous definitions, the equations of motion in a synodic frame of reference r = (x, y) read as…”

Section: Equations Of Motionmentioning

confidence: 99%

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Osorio-Vargas

González

Dubeibe

2020

Int. J. Bifurcation Chaos

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The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

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“…From Eqs. (1)(2)(3)(4)(5)(6), the location of the primaries (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), are respectively…”

Section: Casementioning

confidence: 99%

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

2020

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We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, and regardless of their mass distribution, they will always lie at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model more realistically the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the repulsive character of the solar radiation pressure, there exist two stable libration points roughly located at the position ofL 4 and L 5 in the Sun-Jupiter system.

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Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

Cited by 18 publications

References 34 publications

Exit basins for the Sitnikov problem with variable mass

Exit basins for the Sitnikov problem with variable mass

Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

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