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A Note on Modified Restricted Three-Body Problem

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Abstract

The belief that celestial bodies as perfect spheres results in certain idealistic conditions because most often they are in irregular shapes. With this in mind, we conduct an analysis to study the restricted three-body problem by taking the primaries as oblate spheroids. The modified mean motion expression [1] is used by incorporating the secular perturbation effect due to oblateness of the primaries on mean anomaly, argument of perigee and right ascension of ascending node. The model possesses five equilibrium points, which are subsequently affected by the oblateness parameters. Furthermore, we have studied the stability of the equilibrium points and it is observed that the collinear equilibrium points are always unstable. However, the non-collinear equilibrium points are stable for some combinations of the involved parameters. We have also plotted the zero velocity curves of the infinitesimal body for different values of the Jacobian constant and oblateness parameter. It has been observed that the value of the Jacobian constant has been playing a vital role in obtaining the permissible regions of motion of the infinitesimal body. Further, the results obtained of the study are applied to study the motion of a satellite in the Saturn–Titan system.

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Notes

  1. https://ssd.jpl.nasa.gov/sbdb.cgi.

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Funding

This study was funded by Science and Engineering Research Board, Department of Science and Technology, India, under the scheme MATRICS (MTR/2018/000442). The author, Rajiv Aggarwal, has received a research grant by Department of Science and Technology, India.

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Authors and Affiliations

  1. Department of Mathematics, Deshbandhu College, University of Delhi, Delhi, India

    Dinesh Kumar, Rajiv Aggarwal & Shipra Chauhan

  2. DBC i4 Center, Deshbandhu College, University of Delhi, New Delhi, India

    Dinesh Kumar, Rajiv Aggarwal & Shipra Chauhan

  3. Center for Fundamental Research in Space Dynamics and Celestial Mechanics (CFRSC), New Delhi, India

    Dinesh Kumar, Rajiv Aggarwal & Shipra Chauhan

  4. Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, India

    Ram Krishan Sharma

  5. Department of Mathematics, Keshav Mahavidyalaya, University of Delhi, Delhi, India

    Arpana Sharma

Authors
  1. Dinesh Kumar
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  2. Ram Krishan Sharma
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  3. Rajiv Aggarwal
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  4. Shipra Chauhan
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  5. Arpana Sharma
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Corresponding authors

Correspondence to Dinesh Kumar, Ram Krishan Sharma, Rajiv Aggarwal, Shipra Chauhan or Arpana Sharma.

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Kumar, D., Sharma, R.K., Aggarwal, R. et al. A Note on Modified Restricted Three-Body Problem. Astron. Rep. 66, 710–724 (2022). https://doi.org/10.1134/S1063772922090049

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  • DOI: https://doi.org/10.1134/S1063772922090049

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