Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P506
Venus is our sister planet which is less explored because of its atmosphere. It is unique in the sense of its rotation. It rotates in opposite direction. Its brightness as natural objects comes as second after Moon in the night sky. Indian space research organization (ISRO) has planned to send Shukrayan-I in 2023 to explore the surface and atmosphere of Venus. In this paper Venus-satellite and sun are considered in the mathematical model of "circular restricted three body problem".Since Venus is very near to the Sun so it is important to study the radiation pressure and its effect on the halo orbit through more accurate and modern technique. Here the continuation method up to fourth order approximation (recently introduced) have been used to analyze halo orbits around L-points i.e. L1 and L2.
[1] Kulkarni, T. R., and Mortari, D., “Low energy interplanetary transfers using halo orbit hopping method with STK/Astrogator,” Advances in the Astronautical Sciences, Vol. 120, 2005, pp. 155–168.
[2] Lo, M. W., “Libration point trajectory design.” Numerical Algorithms, Vol. 14, 1997, pp. 153–164. doi:10.1023/A: 1019108929089.
[3] Koon, W. S., Lo, M. W., Marsden, J. E., and Ross, S. D., “Low Energy Transfer to the Moon,” Celestial Mechanics and Dynamical Astronomy, Vol. 81, 2001, pp. 63–73.
[4] Koon, W., Lo, M., and Marsden, J., Dynamical Systems: The Three-body Problem and Space Mission Design, Interdisciplinary Applied Mathematics, Springer-Verlag New York Incorporated, 2011.
[5] Gomez, G., Jorba, A., Masdemont, J., and Simo, C., “Study of the transfer from the Earth to a halo orbit around the equilibrium point L1,” Celestial Mechanics and Dynamical Astronomy, Vol. 56, 1993, pp. 541–562. doi:10.1007/BF00696185.
[6] Jorba, À., and Masdemont, J., “Dynamics in the center manifold of the collinear points of the restricted three body problem,” Physica D Nonlinear Phenomena, Vol. 132, 1999, pp. 189–213. doi:10.1016/S0167-2789(99)00042-1.
[7] Romagnoli, D., and Circi, C., “Lissajous trajectories for lunar global positioning and communication systems,” Celestial Mechanics and Dynamical Astronomy, Vol. 107, 2010, pp. 409–425. doi:10.1007/s10569-010-9279-1.
[8] Eapen, R. T., and Sharma, R. K., “Mars interplanetary trajectory design via Lagrangian points,” Astrophysics and Space science, Vol. 353, No. 1, 2014, pp. 65–71.
[9] Burns, J. A., Lamy, P. L., and Soter, S., “Radiation forces on small particles in the solar system,” Icarus, Vol. 40, No. 1, 1979, pp. 1–48.
[10] McCuskey, S. W., “Introduction to celestial mechanics.” Reading, Mass., Addison-Wesley Pub. Co.[1963], 1963.
[11] Sharma, R. K., “The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid,” Astrophysics and Space Science, Vol. 135, No. 2, 1987, pp. 271–281.
[12] Verhulst, F., Nonlinear differential equations and dynamical systems, Springer Science & Business Media, 2006.
[13] Richardson, D. L., “Analytic construction of periodic orbits about the collinear points,” Celestial Mechanics, Vol. 22, 1980, pp. 241–253. doi:10.1007/BF01229511.
[14] Tiwary, R. D., and Kushvah, B. S., “Computation of halo orbits in the photogravitational Sun-Earth system with oblateness,” Astrophysics and Space Science, Vol. 357, No. 1, 2015, p. 73.
[15] Mishra, H. K., and Jha, G. K., “Frequency analysis of Halo orbits in the Sun-Mercury System,” Manuscript submitted for publication, 2019.
[16] Thurman, R., and Worfolk, P. A., “The geometry of halo orbits in the circular restricted three-body problem,” University of Minnesota: Geometry Center Research Report GCG95, 1996.
Hemant Kumar Mishra, Govind Kumar Jha, "Radiation Pressure and its effect on the Halo orbits of Venus-Sun and Satellite system," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 33-45, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P506