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Robe’s Restricted Problem of 2 + 2 Bodies with a Roche Ellipsoid - Triaxial System

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This paper investigates the motion of two infinitesimal masses on the location and stability of the equilibrium points in Robe’s restricted problem of 2 + 2 bodies with the bigger primary a Roche ellipsoid and the smaller a triaxial body. We suppose the bigger primary of mass m 1 to be filled with a homogeneous incompressible fluid of density ρ 1. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m 2 is describing a circle around m 1. The masses m 3 and m 4 mutually attract each other, do not influence the motion of m 1 and m 2 but are influenced by them. We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m 2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m 3 and m 4 and their linear stability are analyzed.

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Authors and Affiliations

  1. Sri Aurobindo College, University of Delhi, Delhi, India

    Rajiv Aggarwal

  2. Lady Shri Ram College for Women, University of Delhi, Delhi, India

    Bhavneet Kaur

  3. Maharaja Agrasen College, University of Delhi, Delhi, India

    Sushil Yadav

Authors
  1. Rajiv Aggarwal
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  2. Bhavneet Kaur
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  3. Sushil Yadav
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Correspondence to Bhavneet Kaur.

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Aggarwal, R., Kaur, B. & Yadav, S. Robe’s Restricted Problem of 2 + 2 Bodies with a Roche Ellipsoid - Triaxial System. J of Astronaut Sci 65, 63–81 (2018). https://doi.org/10.1007/s40295-017-0119-3

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