Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

Zotos, Euaggelos E.; Papadakis, K. E.

doi:10.1016/j.ijnonlinmec.2019.02.007

“…In a periodic orbit, the dynamic system repeats the same motion at equal intervals of time, including the motions that are repeated in a relative sense, whereas the quasi-periodic orbit is an orbit that is close to but is not quite periodic [15]. In general, a quasi-periodic orbit is preferable to a periodic one, owing to the larger number of parameters that characterize a quasi-periodic orbit [16]. Periodic solutions of the three-body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics [17].…”

Section: Methodsmentioning

confidence: 99%

A study of the nonlinear dynamics inside the exoplanetary system Kepler-22 using MATLAB® software

Hysa

2024

Eureka: PE

0

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Kepler is a discovery-class mission designed to determine the frequency of Earth-radius planets in and near the habitable zone of solar-type stars. A habitable zone of a star is defined as a range of orbits within which a rocky planet can support liquid water on its surface. The most intriguing question driving the search for habitable planets is whether they host life. The aim of this paper is to study the motion of a “test particle” inside the exoplanetary system Kepler-22. This system consists of a sun-like star, Kepler-22, and a terrestrial exoplanet, Kepler-22b. This exoplanet is situated in the habitable zone of its star. Kepler-22b is located about 180 pc from Earth in the constellation of Cygnus. It was discovered by NASA’s Kepler Space Telescope in December 2011 and the planet is about 2.4 times the radius of Earth. Scientists don't yet know if Kepler-22b has a rocky, gaseous or liquid composition. In this study, let’s derive Lagrange points and perform several numerical tests to discover different possible orbits around the star Kepler-22. From many numerical tests performed, it is also possible to found two tadpole orbits around the Lagrange points L4 and L5 and a tadpole orbit around the exoplanet Kepler-22b, which encircles the two Lagrange points L1, and L2. Some of these orbits are found in the habitable zone and others outside. We have also examined the possibility of the existence of an exomoon around the terrestrial exoplanet Kepler-22b. In this case we have considered the mass of this exomoon. The Circular Restricted Three-Body Problem is used in this study. If it is further assumed that the third body (for example a planet, satellite, an asteroid or just a “test particle”) travels in the same plane as the two larger bodies, then there is the Planar Circular Restricted Three-Body Problem

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“…In order to detect appropriate initial conditions for the accurate computation of the basic families of the Hill's problem we use the grid search method as it was described by Markellos et al [41]. This method is appropriate for the detection of planar symmetric periodic orbits and has been used by several authors in order to sketch the skeleton of the basic families of periodic orbits in several dynamical models of two degrees of freedom (see, e.g., [42][43][44], among others).…”

Section: Families Of Planar Periodic Orbitsmentioning

confidence: 99%

Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Kalantonis

¹

2020

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The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

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“…[7][8][9][10][11][12][13][14][15] (for latest publications on CCs, cf. Suraj et al [16], Zotos, and Papadakis [17], and Cornelio et al [18]). e three-body problem has been a great challenge for the scientists as it needed some special assumptions for the third body.…”

Section: Introductionmentioning

confidence: 96%

The Restricted Six-Body Problem with Stable Equilibrium Points and a Rhomboidal Configuration

Siddique

¹

,

Kashif

²

2022

Advances in Astronomy

1

0

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We explore the central configuration of the rhomboidal restricted six-body problem in Newtonian gravity, which has four primaries m i (where i = 1 , … 4 ) at the vertices of the rhombus a , 0 , − a , 0 , 0 , b , and 0 , − b , respectively, and a fifth mass m 0 is at the point of intersection of the diagonals of the rhombus, which is placed at the center of the coordinate system (i.e., at the origin 0,0 ). The primaries at the rhombus’s opposite vertices are assumed to be equal, that is, m 1 = m 2 = m and m 3 = m 4 = m ˜ . After writing equations of motion, we express m 0 , m , and m ˜ in terms of mass parameters a and b . Finally, we find the bounds on a and b for positive masses. In the second part of this article, we investigate the motion and different features of a test particle (sixth body m 5 ) with infinitesimal mass that moves under the gravitational effect of the five primaries in the rhomboidal configuration. All four cases have 16, 12, 20, and 12 equilibrium points, with case-I, case-II, and case-III having stable equilibrium points. A significant shift in the position and the number of equilibrium points was found in four cases with the variations of mass parameters a and b . The regions for the possible motion of test particles have been discovered. It has also been observed that as the Jacobian constant C increases, the permissible region of motion expands. We also have numerically verified the linear stability analysis for different cases, which shows the presence of stable equilibrium points.

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Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

Cited by 9 publications

References 56 publications

A study of the nonlinear dynamics inside the exoplanetary system Kepler-22 using MATLAB® software

A study of the nonlinear dynamics inside the exoplanetary system Kepler-22 using MATLAB® software

Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

The Restricted Six-Body Problem with Stable Equilibrium Points and a Rhomboidal Configuration

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