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Title of Journal: Astrophys Space Sci

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Abbravation: Astrophysics and Space Science

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Springer Netherlands

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DOI

10.1002/9781444303339.ch2

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1572-946X

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Robe’s restricted problem of 2+2 bodies with one o

Authors: Rajiv Aggarwal Bhavneet Kaur
Publish Date: 2014/05/17
Volume: 352, Issue: 2, Pages: 467-479
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Abstract

In this problem one of the primaries of mass m 1 is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ1 The smaller primary of mass m2 is an oblate body outside the shell The third and the fourth bodies of mass m3 and m4 respectively are small solid spheres of density ρ3 and ρ4 respectively inside the shell with the assumption that the mass and the radius of the third and the fourth body are infinitesimal We assume that m2 is describing a circle around m 1 The masses m3 and m4 mutually attract each other do not influence the motions of m 1 and m2 but are influenced by them We also assume that masses m3 and m4 are moving in the plane of motion of mass m2 In the paper equilibrium solutions of m3 and m4 and their linear stability are analyzed There are two collinear equilibrium solutions for the system The non collinear equilibrium solutions exist only when ρ3=ρ4 There exist an infinite number of non collinear equilibrium solutions of the system provided they lie inside the spherical shell In a system where the primaries are considered as earthmoon and m3m4 as submarines the collinear equilibrium solutions thus obtained are unstable for the mass parameters μμ3μ4 and oblateness factor A In this particular case there are no noncollinear equilibrium solutions of the system

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