Research ArticleOpen AccessGoogle Scholar indexed
Solar Radiation Pressure Effects on Stability of Periodic Orbits in Restricted Four-Body Problem
Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
- 1 Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
- 2 Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt
- 3 Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
- 4 Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
- 5 Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
- 6 Mathematics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt
World Journal of Mechanics·Volume 09 (2019)·Pages 191–204·Published 29 August 2019·DOI10.4236/wjm.2019.98013
Copy link · social · email
Abstract
In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).
KeywordsRestricted Four-Body ProblemPoincare Surface SectionsLibration PointsStabilityPeriodic Orbits
- Sweatman, W.L. (2002) The Symmetrical One-Dimensional Newtonian Four-Body Problem: A Numerical Investigation. Celestial Mechanics and Dynamical Astronomy, 82, 179-201. https://doi.org/10.1023/A:1014599918133
- Kalvouridis, T.J., Arribas, M. and Elipe, A. (2006) The Photo-Gravitational Version of the Restricted Four-Body Problem. AIP Conference Proceedings, 848, 637-646.
- álvarez-Ramírez, M. and Vidal, C. (2009) Dynamical Aspects of an Equilateral Restricted Four-Body Problem. Mathematical Problems in Engineering, 2009, Article ID: 181360. https://doi.org/10.1155/2009/181360
- Baltagiannis, A.N. and Papadakis, K.E. (2011) Families of Periodic Orbits in the Restricted Four-Body Problem. Astrophysics and Space Science, 336, 357-367. https://doi.org/10.1007/s10509-011-0778-7
- Burgos-Garcia, J. and Delgado, J. (2012) Periodic Orbits in the Restricted Four-Body Problem with Two Equal Masses. Astrophysics & Space Science, 345, arXiv:1205.3446v1.
- Kumari, R. and Kushvah, B.S. (2013) Equilibrium Points and Zero Velocity Surfaces in the Restricted Four-Body Problem with Solar Wind Drag. Astrophysics and Space Science, 344, 347-359. https://doi.org/10.1007/s10509-012-1340-y
- Papadouris, J.P. and Papadakis, K.E. (2013) Equilibrium Points in the Photogravitational Restricted Four-Body Problem. Astrophysics and Space Science, 344, 21-38. https://doi.org/10.1007/s10509-012-1319-8
- Sanam, S. and Hassan, M.R. (2014) Sitnikov Restricted Four-Body Problem with Radiation Pressure. Astrophysics and Space Science, 349, 705-716. https://doi.org/10.1007/s10509-013-1687-8
- Papadouris, J.P. and Papadakis, K.E. (2014) Periodic Solutions in the Photogravitational Restricted Four-Body Problem. Monthly Notices of the Royal Astronomical Society, 442, 1628-1639. https://doi.org/10.1093/mnras/stu981
- Burgos-García, J. and Gidea, M. (2015) Hill’s Approximation in a Restricted Four-Body Problem. Celestial Mechanics and Dynamical Astronomy, 122, 117-141. https://doi.org/10.1007/s10569-015-9612-9
- Jain, P., Aggarwal, R., Mittal, A. and Abdullah (2016) Periodic Orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies. International Journal of Astronomy and Astrophysics, 6, 111-121. https://doi.org/10.4236/ijaa.2016.61009
- Ismail, M.N., Khalil, I.K.H. and Ibrahim, A.H. (2016) The Effect of Solar Radiation Pressure on the Libration Points of the Restricted Four-Body Problem. Global Journal of Advanced Research, 3, 901-906.