COMBINED EFFECTS OF OBLATENESS AND RADIATION ON THE NONLINEAR STABILITY OF L₄IN THE RESTRICTED THREE-BODY PROBLEM

Abstract

The nonlinear stability of the triangular libration point, L 4 , when both of the primaries are oblate spheroids as well as sources of radiation has been studied. It is found that L 4 is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon oblateness coefficients and mass reduction factors.

The effect of perturbations on the circular restricted four-body problem with variable masses

“…Shrivastava et al in [46] evaluated the equilibrium points in the Robes restricted problem of three-bodies with effect of perturbations in the coriolis and centrifugal forces. Singh et al in [50][51][52][53][54][55][56][57][58][59] studied the restricted problem of three-bodies and four-bodies in circular and elliptic cases with different perturbations. Khanna et al in [29,30] explored the existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid and observed that there are five libration points in which three collinear libration points are unstable and two triangular points are stable for the particular mass parameter.…”

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

“…The Earth, Jupiter, Saturn, Ragulus, Neutron stars and black dwarfs are oblate. Some studies which have considered the non sphericity of the primaries include: SubbaRao and Sharma [23], Elipe and Ferrer [3], Sharma et al [12], Singh [15], Singh and Leke [19] and Singh [16]. Some of these cited studies have also included one or more parameters aside the bodies not being a sphere.…”

Nonlinear stability in the restricted three-body problem with oblate and variable mass

“…Verhulst (1972) described the two-body problem with slowly decreasing mass according to Jean's (1928) law. The restricted problem dealing with variable mass of one or two bodies under different aspects was studied by Shrivastava and Ishwar (1983), Singh andIshwar (1984, 1985), Das et al (1988), Luk'yanov (1990), El-Shaboury (1991 and Bekov (1992).…”

“…The nonlinear stability in the restricted three-body problem under various aspects was carried out by Deprit and Deprit-Bartholome (1967), Bhatnagar and Hallan (1983), Niedzielska (1994), Subba Rao and Sharma (1997), Hallan et al (2000, Gozdiewskii (2003) and Singh (2009).…”

“…Our aim is to study the combined effects of oblateness and varying mass on the nonlinear stability of triangular points as it has been found that they produce significant changes in the location and stability (Singh andIshwar 1984, 1985;AbdulRaheem and Singh 2006) of the triangular points. We also know that the inclusion of nonlinear terms sometimes changes the entire pattern of the stability and hence, we intend to examine the stability in the nonlinear sense as well.…”