Triangular libration points in the R3BP under combined effects of oblateness, radiation and power-law profile

Abstract

We study the effects of oblateness up to J 4 of the primaries and power-law density profile (PDP) on the linear stability of libration location of an infinitesimal mass within the framework of restricted three body problem (R3BP), by using a more realistic model in which a disc with PDP is rotating around the common center of the system mass with perturbed mean motion. The existence and stability of triangular equilibrium points have been explored. It has been shown that triangular equilibrium points are stable for 0 < µ < µ c and unstable for µ c ≤ µ ≤ 1/2, where µ c denotes the critical mass parameter. We find that, the oblateness up to J 2 of the primaries and the radiation reduces the stability range while the oblateness up to J 4 of the primaries increases the size of stability both in the context where PDP is considered and ignored. The PDP has an effect of about ≈ 0.01 reduction on the application of µ c to Earth-Moon and Jupiter-Moons systems. We find that the comprehensive effects of the perturbations have a stabilizing proclivity. However, the oblateness up to J 2 of the primaries and the radiation of the primaries have tendency for instability, while coefficients up to J 4 of the primaries have stability predisposition. In the limiting case c = 0, and also by setting appropriate parameter(s) to zero, our results are in excellent agreement with the ones obtained previously. Libration points play a very important role in space mission and as a consequence, our results have a practical application 1 E-mail: fbjames11@physicist.net; babatunde.falaye@fulafia.edu.ng †Corresponding Author Tel. no: (+52) 1 5521450362 2 E-mail: dongsh2@yahoo.com 3 E-mail: kjoyewumi66@gmail.com 4 E-mail: sesantayo2001@yahoo.com ‡On sabbatical leave from University of Ilorin, Ilorin, Nigeria 5 E-mail: dreamsambo@yahoo.com 6 E-mail: friendsaver1@yahoo.com 7 E-mail: ladiran@gmail.com 8 E-mail: konyekachi@gmail.com 9 E-mail: sameer.ikhdair@najah.edu; sikhdair@gmail.com. 1 in space dynamics and related areas. The model may be applied to study the navigation and stationkeeping operations of spacecraft (infinitesimal mass) around the Jupiter (more massive) -Callisto (less massive) system, where PDP accounts for the circumsolar ring of asteroidal dust, which has a cloud of dust permanently in its wake.

Analysis of albedo as well as disc effects at the Jacobi constant and their stability of equilibrium points in the generalized restricted four-body problem

“…has analyzed all the existing non-collinear equilibrium points as well as their Jacobi Constants for Case.1-2-3, here for a separate planetary system, only numerical fluctuation are found. The remarkable effects of stunning parameters Q A1 , Q A2 , a 21 , a 22 , M d , r c at collinear points L (1,2,3) , Non-collinear points L (4,5,6,7,8,9) and their stability analysis as well as zero-velocity surface and their prohibited region of the motion by infinitesimal body explained in Case.1-2-3. It is also observed that the effect of these stunning parameters at the position of existing collinear points L (1,2,3.)…”

“…Albedo is a dimensionless quantity as well as a non-gravitational force having valuable effects on the movement of masses as well as their stability. The study of the mixed analysis of RTBP with certain perturbations belongs to [36,17,32,7]. Motion and orbit related issues of RTBP studied by [3,26,34].Generally, the albedo effect is measured on a scale of mass 0 to 1.…”

Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

“…In addition to L 1,2,3,4,5 , they have found new collinear equilibrium points JY1 and JY2, known as Jiang-Yeh points, which exist only if the total mass of the galaxy is greater than that of critical mass. Several researchers (Kushvah 2008;Kushvah et al 2012;Kishor & Kushvah 2013;Falaye et al 2016) have also studied the linear stability of equilibrium points of the restricted problem of three bodies with the inclusion of disclike structure. Recently, Jiang & Yeh (2014); Yeh & Jiang (2016) modified the RTBP by taking a star as a test particle, moving in the gravitational influence of super-massive binary black hole and the external galactic potential.…”

The Linear Stability of Collinear Equilibrium Points and Resonances

“…[11], [12] have studied generalized photogravitational Chermnykh-like problem with P-R drag and found that triangular points are stable under Routh's condition but collinear equilibrium points are unstable whereas, [28] have discussed about linear stability of triangular equilibrium point and resonances. [15] analyze the influence of radiation pressure on the nature of orbits whereas, [16] discuss the combined effects of oblateness, radiation and power-law profile.…”

“…The influence of the belt for planetary system is observed by [2], [3] and found that probability of equilibrium points is larger, near the inner part of the belt than outer one. Different aspects of the problem with and without disc are studied by many authors as [8], [9], [10], [7], [11], [12], [13], [14], [15], [16] etc., under some assumptions on mass parameter and angular velocity of the system. They have found that at the mass parameter µ = 0.5, there is a deviation in classical results [10], whereas in the presence of a belt, there exist new equilibrium points [7], [13], called Jiang-Yeh points [14], [17], [18].…”