Evolution of the “f” Family Orbits in the Photo Gravitational Sun-Saturn System with Oblateness

What is it about?

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.

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Photo by NASA on Unsplash

Photo by NASA on Unsplash

Why is it important?

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.

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