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Pulsating Zero Velocity Surfaces and Fractal Basin of Oblate Infinitesimal in the Elliptic Restricted Three Body Problem

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Abstract

The pulsating surfaces of zero velocity of the elliptic restricted three body problem when both the primaries are luminous oblate spheroids is investigated considering the effect of the oblateness of the infinitesimal. It is observed that if the third participating body in the restricted problem has sufficiently high value of the oblateness factor, the shape of the pulsating zero velocity surfaces changes for certain values of true anomaly. The projection of the zero velocity surfaces on xy- and xz-plane is also studied along with the low-velocity sub-regions in the respective planes. Employing the multivariate Newton–Raphson iterative scheme, the basins of attraction of the equilibrium points on the xy- and xz-plane is determined. Simulation technique is applied to demonstrate the influence of the oblateness of the infinitesimal on the basins of attraction.

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Acknowledgements

The financial assistance from Chattisgarh Council of Science and Technology is duly acknowledged with gratitude (Endt. No. 2260/CCOST/MRP/2015).

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Authors and Affiliations

  1. Department of Mathematics, Bhilai Institute of Technology, Durg, C. G., 491001, India

    Ashutosh Narayan, Anindita Chakraborty & Akanksha Dewangan

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  1. Ashutosh Narayan
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  2. Anindita Chakraborty
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  3. Akanksha Dewangan
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Correspondence to Ashutosh Narayan.

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Narayan, A., Chakraborty, A. & Dewangan, A. Pulsating Zero Velocity Surfaces and Fractal Basin of Oblate Infinitesimal in the Elliptic Restricted Three Body Problem. Few-Body Syst 59, 43 (2018). https://doi.org/10.1007/s00601-018-1368-9

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