• Effects of Triaxiality, Oblateness and Gravitational Potential from a Belt on the Linear Stability of 𝐿4,5 in the Restricted Three-Body Problem

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    • Keywords


      Restricted three-body problem (R3BP); potential from the belt; triaxiality effect; oblateness effect.

    • Abstract


      In this paper we have considered the restricted three body problem (R3BP) in which the more massive primary is triaxial, the less massive primary and infinitesimal body are oblate spheroids, and are encompassed by a belt of homogenous material points. Analytically and numerically, we have studied the effects of triaxiality of the more massive primary, oblateness of both the less massive primary and infinitesimal body and the gravitational potential generated by the belt on the location of the triangular libration points 𝐿4,5 and their linear stability. 𝐿4,5 do not form equilateral triangles with the primaries in the presence of all or any of the aforementioned perturbations. Due to triaxiality of the more massive primary and oblateness of the infinitesimal body the triangular libration points are seen to move away from the line linking the primaries, whereas they shift closer to the line owing to the oblateness of the less massive primary and the potential from the belt. The range 0 < 𝜇 < 𝜇c of stability of the triangular points is reduced in the presence of any of the perturbations, except when considering the potential from the belt the range increases, where 𝜇c is the critical mass ratio. The oblateness of a test particle (of infinitesimal mass) shifts the location of its libration positions away from the primaries and reduces its range of stability.

    • Author Affiliations


      Jagadish Singh1 Joel John Taura2

      1. Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria.
      2. Department of Mathematics and Computer Science, Federal University, Kashere, Gombe State, Nigeria.
    • Dates

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