Out-of-plane equilibrium points in the restricted  three-body problem with oblateness

Douskos, Christos; Markellos, V. V.

doi:10.1051/0004-6361:20053828

Cited by 78 publications

(64 citation statements)

References 3 publications

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“…The generalization of R3BP yields equilibrium points located out of the orbital plane (out-of-plane, L 6,7 ) (Douskos & Markellos, 2006). L 6,7 also have been found in the generalized Elliptic Restricted Three-Body Problem (ER3BP) (Singh & Umar, 2012).…”

Section: Introductionmentioning

confidence: 92%

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Locations of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem Under Radiation and Oblateness Effects

Huda¹,

Dermawan²,

Wibowo³

et al. 2015

Publications of The Korean Astronomical Society

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This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points (L 6,7 , out-of-plane). We determine the existence of L 6,7 in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of L 6,7 and assume initial approximations of (µ − 1, ± √ 3A 2 ), where µ and A 2 are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of L 6,7 are periodic and affected by A 2 and the radiation factor (q 1 ).

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Section: Introductionmentioning

confidence: 92%

“…The relation between f and the position of L 6 are shown in Figures 1 and 2. Following Douskos & Markellos (2006) we also calculate the position of L 6 using numerical methods. We use the software package Mathematica and applyξ 0 = µ − 1 andζ 0 = ± √ 3A 2 as the initial approximations.…”

Section: Location Of Out-of-plane Pointsmentioning

confidence: 99%

Locations of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem Under Radiation and Oblateness Effects

Huda¹,

Dermawan²,

Wibowo³

et al. 2015

Publications of The Korean Astronomical Society

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“…Fig.3(right) shows that the differential Mars-J 2 perturbation is negligible inside the moon's SOI. In particular, the inclusion of the oblateness of the massive bodies in the CR3BP has been investigated in Douskos and Markellos (2006), Arredondo et al (2012), Abouelmagd and Sharaf (2013): in addition to the direct gravitational effect, the inclusion of J 2 of the primary body affects also the apparent acceleration, by increasing the angular velocity of the frame of reference by a factor 1…”

Section: The Mars-phobos Cr3bp-ghmentioning

confidence: 99%

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

Zamaro

Biggs

2015

Celest Mech Dyn Astr

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The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

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“…They found five libration points, in which three are collinear unstable points and two are triangular stable points and these stable points have short and long periodic orbits. Douskos [4] found the existence of nonplanar equilibrium points in the three-dimensional restricted threebody problem with oblateness. Mittal [11] have studied the periodic orbits generated by Lagrangian solutions of the restricted three body problem when one of the primaries is an oblate body and shown the effect of oblateness on the periodic orbits.…”

Section: Introductionmentioning

confidence: 99%

Stability of the equilibrium points in the circular restricted four body problem with oblate primary and variable mass

Ansari

2016

IJAA

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This paper investigates the liberation points and stability of the restricted four body problem with one of the primaries as oblate body and the infinitesimal body is taken as variable mass. Due to oblateness, the equilateral triangular configuration is no longer exists and becomes an isosceles triangular configuration. Moreover, we have found seven equilibrium points out of which three are asymptotically stable (dark black in the tables) and rest four are unstable.

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Out-of-plane equilibrium points in the restricted three-body problem with oblateness

Cited by 78 publications

References 3 publications

Locations of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem Under Radiation and Oblateness Effects

Locations of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem Under Radiation and Oblateness Effects

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

Stability of the equilibrium points in the circular restricted four body problem with oblate primary and variable mass

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