Halo Orbits around Sun-Earth L1 in Photogravitational Restricted Three-Body Problem with Oblateness of Smaller Primary

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.

Halo Orbits around $L_1$ and $L_2$ in the Photogravitational Sun-Earth System with Oblateness

“…Halo orbits are important for spacecraft mission design. Many researchers have obtained the halo orbits upto third order approximation (Richardson 1980;Howell 1984;Breakwell and Brown 1979;Koon et al 2011;Chidambararaj and Sharma 2016;Pushparaj and Sharma 2016;Ghotekar and Sharma 2019). Tiwary and Kushvah (2015) have computed halo orbits upto fourth order approximation with the Sun as a radiating body and the Earth as an oblate spheroid using Lindstedt-Poincaré method.…”

Halo Orbits in the Photo-Gravitational Restricted Three-Body Problem

“…The variation in size, shape of the halo orbits is observed by comparing it with the plots of classical case and the effects of radiation pressures on the halo orbit is observed. The numerical computation of halo orbits is referred from Chidambararaj P. and Sharma R. K. [14].…”

Searching for g modes: Part I. A new calibration of the GOLF instrument

“…5 shows that the time delay in this time series is modulated with a periodicity of almost 6 months. This is due to the SoHO halo orbit 9 , which has a periodicity of 178 days resulting in a time modulation of 1.54 s. The periodicity of 178 days is primarily constrained by the solar radiation pressure (Chidambararaj & Sharma 2016).…”