Abstract
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 decreases.Fur-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.
Highlights
Restricted three body problem (RTBP) describes the motion of an infinitesimal mass which moves under theHow to cite this paper: Pathak, N., Sharma, R.K. and Thomas, V.O. (2016) Evolution of Periodic Orbits in the Sun-Saturn System
In this paper we have studied Poincare surface of section (PSS) method for Sun-Saturn system for periodic and quasi-periodic orbits
As the solar radiation pressure force Fp changes with the distance by the same law as the gravitational attraction force Fg and acts opposite to it, it is possible to consider that the result of the action of this force leads to reducing the effective mass of the sun [8]
Summary
Restricted three body problem (RTBP) describes the motion of an infinitesimal mass which moves under the. [4] have studied RTBP with all perturbation He had considered the case where both primaries are source of radiation and both primaries and secondary bodies are oblate spheroids. He developed the equation of motion for two and three dimensional case with perturbation due to Coriolis and centrifugal forces. [10] and [11] analysed the PSS for Earth-Moon system and Sun-Mars system They have identified periodic, quasi-periodic solutions and chaotic regions. [12] and [13] studied PSS for Saturn-Titan system for periodic orbits, quasi-periodic and chaotic regions. In this paper we have studied PSS method for Sun-Saturn system for periodic and quasi-periodic orbits.
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