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On the R4BP when Third Primary is an Ellipsoid

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Abstract

The present paper deals with the restricted four-body problem (R4BP), when the third primary placed at the triangular libration point of the restricted three-body problem is an ellipsoid. The third primary m 3 is not influencing the motion of the dominating primaries m 1 and m 2. We have studied the motion of m 4, moving under the influence of the three primaries m i , i = 1, 2, 3, but the motion of the primaries is not being influenced by infinitesimal mass m 4. Further, we have developed the equations of motion of infinitesimal mass m 4 which involves elliptic integrals and shows the existence and locations of equilibrium points. We have also discussed the zero velocity curves(ZVCs) for various value of Jacobian constant.

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Authors and Affiliations

  1. Research Scholar, Department of Physics, Tilka Manjhi Bhagalpur University, Bhagalpur, 812007, Bihar, India

    Md Chand Asique

  2. Department of Physics, TNB College, Bhagalpur, Tilka Manjhi Bhagalpur University, Bihar, 812007, India

    Umakant Prasad

  3. P.G.Department of Mathematics, S M College Bhagalpur, Bhagalpur, 812007, India

    M. R. Hassan

  4. Department of Mathematics, SGTB Khalsa College, University of Delhi North Campus, New Delhi, 110007, India

    Md Sanam Suraj

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  1. Md Chand Asique
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  2. Umakant Prasad
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  3. M. R. Hassan
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  4. Md Sanam Suraj
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Correspondence to Md Chand Asique.

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Asique, M.C., Prasad, U., Hassan, M.R. et al. On the R4BP when Third Primary is an Ellipsoid. J of Astronaut Sci 64, 231–250 (2017). https://doi.org/10.1007/s40295-016-0104-2

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  • DOI: https://doi.org/10.1007/s40295-016-0104-2

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