Back
 IJAA  Vol.6 No.3 , September 2016
Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness
Abstract: 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.
Cite this paper: Pathak, N. and Thomas, V. (2016) Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness. International Journal of Astronomy and Astrophysics, 6, 254-271. doi: 10.4236/ijaa.2016.63021.
References

[1]   Szebehely, V. (1967) Theory of Orbits. Academic Press, San Diego.

[2]   Sharma, R.K. (1987) The Linear Stability of Libration Points of the Photo Gravitational Restricted Three Body Problem When the smaller Primary Is an Oblate Spheroid. Astrophysics and Space Science, 135, 271-281.
http://dx.doi.org/10.1007/BF00641562

[3]   Broucke, R.A. (1968) Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses. Technical Report, 32, Jet Propulsion Lab., Pasadena.

[4]   Murray, C.D. and Dermot, S.F. (1999) Solar System Dynamics. Cambridge University Press, Cambridge.

[5]   Winter, O.C. (2000) The Stability Evolution of a Family of Simply Periodic Lunar Orbits. Planetary and Space Science, 48, 23-28.
http://dx.doi.org/10.1016/S0032-0633(99)00082-3

[6]   Dutt. P. and Sharma, R.K. (2010) Analysis of Periodic and Quasi-Periodic Orbits in the Earth-Moon System. Journal of Guidance, Control, and Dynamics, 33, 1010-1017.
http://dx.doi.org/10.2514/1.46400

[7]   Dutt. P. and Sharma, R.K. (2011) Evolution of Periodic Orbits in the Sun-Mars System. Journal of Guidance, Control, and Dynamics, 34, 635-644.
http://dx.doi.org/10.2514/1.51101

[8]   Safiyabeevi, A. and Sharma, R.K. (2011) Oblateness Effect of Saturn on Periodic Orbits in the Saturn-Titan Restricted Three-Body Problem. Astrophysics and Space Science, 333, 245-261.

[9]   Dutt. P. and Sharma, R.K. (2012) On the Evolution of the “f” Family in the Restricted Three-Body Problem. Astrophysics and Space Science, 340, 63-70.
http://dx.doi.org/10.1007/s10509-012-1039-0

[10]   Hénon, M. (1970) Numerical Exploration of the Restricted Problem. VI. Hill’s Case: Non-Periodic Orbits. Astronomy and Astrophysics, 9, 24-36.

[11]   Douskos, C., Kalantonis, V. and Markellos, P. (2007) Effect of Resonances on the Stability of Retrograde Satellite. Astrophysics and Space Science, 310, 245-249.
http://dx.doi.org/10.1007/s10509-007-9508-6

[12]   Dutt, P. and Sharma, R.K. (2011) Evolution of Periodic Orbits near the Lagrangian Point L2. Advance in Space Research, 47, 1894-1904.
http://dx.doi.org/10.1016/j.asr.2011.01.024

[13]   Perdiou, A.E., Perdios, E.A. and Kalantonis, V.S. (2012) Periodic Orbits of the Hill Problem with Radiation and Oblateness. Astrophysics and Space Science, 342, 19-30.
http://dx.doi.org/10.1007/s10509-012-1145-z

[14]   Pathak. N., Sharma, R.K. and Thomas, V.O. (2016) Evolution of Periodic Orbits in the Sun-Saturn System. International Journal of Astronomy and Astrophysics, 6, 175-197.
http://dx.doi.org/10.4236/ijaa.2016.62015

[15]   Sharma, R.K. and Subbarao, 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, 13, 137-149.
http://dx.doi.org/10.1007/BF01232721

 
 
Top