Higher Order Resonant Periodic Orbits in Photo–Gravitational Planar Restricted Three–Body Problem

What is it about?

The study of resonance has wide ranging applications in the solar system dynamics and theories related to satellite formation. It also plays an important role in the study of formation of rings around planets. A numerical relationship between frequencies or periods of two bodies gives rise to resonance. Resonance can be due to spin–orbit coupling or orbit–orbit coupling of two or more bodies. The reason for the moon always keeping the same face towards the Earth is due to the spin–orbit resonance between them. That the thin ring around Jupiter is due to the resonance in the magnetic field of the Jupiter with motion of dust particles in its gravitational field.

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Photo by Markus Spiske on Unsplash

Photo by Markus Spiske on Unsplash

Why is it important?

We have studied the first order exterior resonant orbits and the first, third and fifth order interior resonant periodic orbits within frame of the perturbed photo–gravitational restricted three–body problem. The location, eccentricity and period of the first order exterior and interior resonant orbits are investigated in the unperturbed and perturbed cases for a specified value of Jacobian constant C. We have extended study for resonance on the photo–gravitational planar restricted three–body problem as the analysis of orbits involving higher order resonance are seldom found in literature. In this work we have analyzed the higher order resonant periodic orbits (seventh, ninth and eleventh) in the framework of photo–gravitational planar restricted three–body problem.

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