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Combined Effects of Finite Straight Segment and Oblateness on the Libration Points in the Restricted-Three Body Problem


Affiliations
1 Shyama Prasad Mukherji College (For Women), University of Delhi, New Delhi, India
2 Sri Aurobindo College, University of Delhi, New Delhi, India
3 Bhagini Nivedita College, University of Delhi, New Delhi, India
     

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This paper deals with the existence and stability of the libration points in the restricted-three body problem when the smaller primary is a finite straight segment and bigger primary is an oblate spheroid. We have observed that five libration points do exist in this problem, out of which three are collinear and two are non-collinear with the primaries. The collinear libration points are unstable for all values of mass parameter μ and the non-collinear libration points are stable if μ < μc, where μc is a critical value of mass parameter μ. The range of stability depends length of the finite straight segment and oblateness factor.

Keywords

Restricted Three-Body Problem, Libration Points, Stability, Finite Straight Segment, Oblate Spheroid.
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  • Combined Effects of Finite Straight Segment and Oblateness on the Libration Points in the Restricted-Three Body Problem

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Authors

Dinesh Kumar
Shyama Prasad Mukherji College (For Women), University of Delhi, New Delhi, India
Rajiv Aggarwal
Sri Aurobindo College, University of Delhi, New Delhi, India
Mamta Jain
Bhagini Nivedita College, University of Delhi, New Delhi, India

Abstract


This paper deals with the existence and stability of the libration points in the restricted-three body problem when the smaller primary is a finite straight segment and bigger primary is an oblate spheroid. We have observed that five libration points do exist in this problem, out of which three are collinear and two are non-collinear with the primaries. The collinear libration points are unstable for all values of mass parameter μ and the non-collinear libration points are stable if μ < μc, where μc is a critical value of mass parameter μ. The range of stability depends length of the finite straight segment and oblateness factor.

Keywords


Restricted Three-Body Problem, Libration Points, Stability, Finite Straight Segment, Oblate Spheroid.