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Abstract
This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.
Highlights
The subject of halo orbits in restricted three-body problem (RTBP) has received considerable attention in the last four decades
Tiwary and Kushvah [12] followed the model of Sharma [11] to study the halo orbits around the Lagrangian points L1 and L2 analytically
They did not consider the z term in oblateness in their study. We have considered both the terms due to oblateness of the smaller primary in the photogravitational restricted three-body problem to study the halo orbits analytically as well as numerically around L1
Summary
The subject of halo orbits in restricted three-body problem (RTBP) has received considerable attention in the last four decades. (2016) Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary. Sharma [11] studied the periodic orbits around the Lagrangian points in the planar RTBP by considering Sun as source of radiation and smaller primary as an oblate spheroid with its equatorial plane coincident with the plane of motion. Tiwary and Kushvah [12] followed the model of Sharma [11] to study the halo orbits around the Lagrangian points L1 and L2 analytically They did not consider the z term in oblateness in their study. We have considered both the terms due to oblateness of the smaller primary in the photogravitational restricted three-body problem to study the halo orbits analytically as well as numerically around L1. Solar Heliospheric Observatory (SOHO), launched in 1975 by NASA succeeded ISEE-3.We have taken data of the path of the SOHO mission from the mission website over a period of January-June 2008, to validate our analytical and numerical solutions
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