Journal :   International Journal of Technology

Volume No. :   6

Issue No. :  2

Year :  2016

Pages :   150-160

ISSN Print :  2231-3907

ISSN Online :  2231-3915


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Perturbed Robe’s Restricted Problem of 2+2 Bodies when the primaries form a Roche Ellipsoid - Triaxial System



Address:   Bhavneet Kaur1, Rajiv Aggarwal2, Sushil Yadav3
1Lady Shri Ram College for Women, Delhi University, Delhi, India
2Shri Aurobindo College, Delhi University, Delhi, India
3Maharaja Agrasen College, Delhi University, Delhi, India
*Corresponding Author
DOI No: 10.5958/2231-3915.2016.00024.9

ABSTRACT:
The aim of this paper is to study the effect of perturbations in the Coriolis and centrifugal forces on the location and stability of the equilibrium solutions in the Robe’s restricted problem of 2+2 bodies under the assumption that the hydrostatic equilibrium figure of the first primary is a Roche ellipsoid and the shape of the second primary is triaxial.The third and the fourth bodies (of mass m_3 and m_4 respectively) are small solid spheres of density ?_3 and ?_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. The linear stability of this configuration is examined. It is observed that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. The equilibrium solutions of m_3 and m_4 lying on x_1-axis are unstable for ?>0,?'>0 and ?<0,?'>0 and stable for ?>0,?'<0 and ?<0,?'<0, using the data of submarines in the Earth -Moon system. The equilibrium solutions of m_3 and m_4 respectively when the displacement is given in the direction of x_2 or x_3- axis are conditionally stable.We observe that the conditions of stability are influenced by the small perturbations in the Coriolis and centrifugal forces.
KEYWORDS:
Robe’s Restricted Problem; Roche Ellipsoid; Triaxial; Stability.
Cite:
Bhavneet Kaur, Rajiv Aggarwal, Sushil Yadav. Perturbed Robe’s Restricted Problem of 2+2 Bodies when the primaries form a Roche Ellipsoid - Triaxial System. Int. J. Tech. 2016; 6(2): 150-160.
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