The Journal of the Astronautical Sciences

, Volume 64, Issue 3, pp 231–250

On the R4BP when Third Primary is an Ellipsoid

  • Md Chand Asique
  • Umakant Prasad
  • M. R. Hassan
  • Md Sanam Suraj

DOI: 10.1007/s40295-016-0104-2

Cite this article as:
Asique, M.C., Prasad, U., Hassan, M.R. et al. J of Astronaut Sci (2017) 64: 231. doi:10.1007/s40295-016-0104-2


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 m3 is not influencing the motion of the dominating primaries m1 and m2. We have studied the motion of m4, moving under the influence of the three primaries mi, i = 1, 2, 3, but the motion of the primaries is not being influenced by infinitesimal mass m4. Further, we have developed the equations of motion of infinitesimal mass m4 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.


R4BP Ellipsoid Libration points ZVCs 

Copyright information

© American Astronautical Society 2016

Authors and Affiliations

  • Md Chand Asique
    • 1
  • Umakant Prasad
    • 2
  • M. R. Hassan
    • 3
  • Md Sanam Suraj
    • 4
  1. 1.Research Scholar, Department of PhysicsTilka Manjhi Bhagalpur UniversityBhagalpurIndia
  2. 2.Department of Physics, TNB College, BhagalpurTilka Manjhi Bhagalpur UniversityBiharIndia
  3. 3.P.G.Department of Mathematics, S M College BhagalpurBhagalpurIndia
  4. 4.Department of Mathematics, SGTB Khalsa CollegeUniversity of Delhi North CampusNew DelhiIndia

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