Periodic orbit in the photo-gravitational restricted three body problem around the collinear Lagrangian points when more massive primary is an oblate spheroid and source of radiation

Authors

  • Derick John Karunya Institute of Technology and Sciences
  • Ram Krishan Sharma Karunya Institute of Technology and Sciences

DOI:

https://doi.org/10.14419/ijaa.v9i1.31627

Published:

2022-01-02

Keywords:

Angular Frequency, Collinear Lagrangian Points, Oblateness, Periodic Orbits, Radiation Pressure, Restricted Three Body Problem.

Abstract

The circular Restricted Three Body Problem is considered with the more massive primary as an oblate spheroid and source of radiation. A new mean motion expression given by n2=1+6A is used in the present study, when the secular effect of the oblateness on the mean motion, argument of perigee and right ascension of the ascending node is considered. The locations of the collinear Lagrangian points are found. It is found to have some variation from the previous study conducted on the same because of the new mean motion that is considered in this study. The variations of the location of the Lagrangian points due to the unperturbed as well as the perturbed problem due to oblateness and radiation pressure are studied. A study on the eccentricity e and angular frequency s at L1, L2 and L3 is carried out. It is observed how the change in effect of oblateness and radiation pressure has affected the location, angular frequency and eccentricity at L3, though there are only small changes noticed in the case of L1 and L2.

 

 

References

[1] Arohan, R., Sharma, R. K. (2020) Periodic orbits in the planar restricted photo-gravitational problem when the smaller primary is an oblate spheroid. Indian Journal of Science and Technology 13(16), 1630 – 1640. https://doi.org/10.17485/IJST/v13i16.401.

[2] Chernikov, V.A. (1970) The Photogravitational Restricted three-body problem. Astronomicheskii Zhurnal 47, 217. Available at: https://articles.adsabs.harvard.edu/pdf/1970SvA....14..176C (accessed 21 December 21).

[3] Kumar, S., Ishwar, B. (2011) Location of collinear equilibrium points in the generalised photogravitational elliptic restricted three body problem. International Journal of Engineering, Science and Technology 3(2), 157-162. https://doi.org/10.4314/ijest.v3i2.68143.

[4] Namboodiri, N. I. V, Reddy, D. S., Sharma, R. K. (2008) Effect of oblateness and radiation pressure on angular frequencies at collinear points. Astrophysics Space Science 318, 161 – 168. https://doi.org/10.1007/s10509-008-9934-0.

[5] Radzievsky, V.V. (1950) the restricted problem of three-bodies taking account of light pressure. Astronomicheskii Zhurnal 27, 250-256

[6] Radzievsky, V.V. (1953) the spatial case of the restricted problem of three radiating and gravitating bodies. Astronomicheskii Zhurnal 30, 265-273

[7] Raheem, A., A.R., Singh, J. (2006) Combined effects of perturbations, radiation, and oblateness on the stability of equilibrium points in the restricted three-body problem. The Astronomical Journal 131(3), 1880–1885. https://doi.org/10.1086/499300.

[8] Raheem, A., A.R., Singh, J. (2008) Combined effects of perturbations, radiation, and oblateness on the periodic orbits in the restricted three-body problem. Astrophysics Space Science 317, 9–13. https://doi.org/10.1007/s10509-008-9841-4.

[9] Sharma, R.K. (1975) Perturbations of Lagrangian points in the restricted three-body problem. Indian Journal of Pure and Applied Mathematics 6, 1099–1102.

[10] Sharma, R. K. (1987) The Linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid. Astrophysics and Science 135, 271 – 281. https://doi.org/10.1007/BF00641562.

[11] Sharma, R. K., Sellamuthu, H., Jency, A. A. (2020) Perturbed Trojan dynamics in the solar system. AAS AIAA Astrodynamics Specialist Conference 20 – 704. Available at: https://www.researchgate.net/publication/343547691 (accessed 21 December 2021).

[12] Sharma, R.K., Subba Rao, P.V. (1975) collinear equilibria and their characteristics exponents in the restricted three-body problem when the primaries are oblate spheroids. Celestial Mechanics and Dynamical Astronomy 12, 189–201. https://doi.org/10.1007/BF01230211.

[13] Sharma, R.K., Subba Rao, P.V. (1976) Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid. Celestial Mechanics and Dynamical Astronomy 13, 137–149. https://doi.org/10.1007/BF01232721.

[14] Sharma, R.K., Subba Rao, P.V. (1978) A case of commensurability induced by oblateness. Celestial Mechanics and Dynamical Astronomy 18, 185–194. https://doi.org/10.1007/BF01228715.

[15] Simmons, J.F.L., McDonald, A.J.C., Brown, J.C. (1985) The restricted 3-body problem with radiation pressure. Celestial Mechanics and Dynamical Astronomy, 35 145–187. https://doi.org/10.1007/BF01227667.

[16] Singh, J., Umar, A. (2012) Motion in the photogravitational elliptic restricted three-body problem under an oblate primary. The American Astronomical Society 143(5), 109-131. https://doi.org/10.1088/0004-6256/143/5/109.

[17] Subba Rao, P.V., Sharma, R.K. (1975) A note on the stability of the triangular points of equilibrium in the restricted three-body problem. Astronomy and Astrophysics 43, 381–383. Available at: https://articles.adsabs.harvard.edu/pdf/1975A%26A....43..381S (accessed 21 December 2021).

[18] Szebehely, V. (1967) THEORY OF ORBITS the Restricted Problem of Three Bodies. New York and London: Academic Press. https://doi.org/10.1016/B978-0-12-395732-0.50016-7.

[19] Vidyakin, V. (1974) Astronomicheskii Zhurnal 51, 1087–1094.

View Full Article: