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Evolution of Periodic Orbits in the sun-saturn system

International Journal of Astronomy and Astrophysics 2016年第2期6卷 175-197页

作者： Niraj Pathak R. K. Sharma V. O. Thomas Department of Mathematics Dharmsinh Desai University Nadiad India Department of Aerospace Engineering Karunya University Coimbatore India Department of Mathematics Faculty of Science The Maharaja Sayajirao University of Baroda

We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational sun-saturn system incorporating actual oblateness of saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of sun centered and saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits ***-ther, the periodic orbits around saturn and sun moves towards sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of saturn centered periodic orbits is observed.

关键词： Restricted Three Body Problem sun-saturn system Periodic Orbits Quasi Periodic Orbits Chaotic Orbits Photo Gravitation Oblateness Poincare Surface Section

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Evolution of the “f” Family Orbits in the Photo Gravitational sun-saturn system with Oblateness

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International Journal of Astronomy and Astrophysics 2016年第3期6卷 254-271页

作者： Niraj Pathak V. O. Thomas Department of Mathematics Dharmsinh Desai University Nadiad India Department of Mathematics The Maharaja Sayajirao University of Baroda Vadodara India

We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around saturn in the photo gravitational sun-saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of sun saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around saturn move towards the sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.

关键词： Restricted Three Body Problem sun-saturn system “f” Family Periodic Orbits Region of Quasi Periodic Orbits Photo Gravitation Oblateness Poincare Surface of Section

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