RRJoPHY (2019) 130-136 © STM Journals 2019. All Rights Reserved Page 130 Research & Reviews: Journal of Physics ISSN: 2278-2265 (Online), ISSN: 2347-9973 (Print) Volume 8, Issue 2 www.stmjournals.com Higher Ordered Resonant Periodic Orbits in Perturbed Sun-Mars System Niraj Pathak 1, *, Elbaz I. Abouelmagd 2 1 Department of Mathematics, Dharmsinh Desai University, Nadiad, Gujarat, India 2 Celestial Mechanics Unit, Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt Abstract In this paper, we have studied interior resonant orbits of higher order in the framework of photo–gravitational restricted three-body problem. The seventh, ninth and eleventh order interior resonant periodic orbits are analyzed for Sun-Mars system. The location, eccentricity and period of resonant orbits are investigated in the perturbed case for a given value of Jacobi constant C. It is observed that for a given order of resonance, a period of orbits is increased by 6 or 7 units as the number of loops is increased by 1. This indicates that the time elapsed for making one loop is approximately equal to the period of Mars, which are 6.2827 units. The location of periodic orbits recedes from Sun as the number of loops increase. For an orbit with a given number of loops, the location of periodic orbits shifts towards Sun and the eccentricity of the periodic orbits decrease as the order of resonance increases. Keywords: Interior resonance, oblateness periodic orbits, photo–gravitation, poincare surface of section, restricted three-body problem *Author for Correspondence E-mail: niraj23481@yahoo.com INTRODUCTION 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 the formation of rings around planets. A numerical relationship between frequencies or periods gives rise to resonance. The resonance can be due to spin-orbit coupling or orbit–orbit coupling of two or more bodies. The reason for the moon always keeping its face towards the Earth is due to the spin-orbit resonance between them [1]. It has been discussed, that the thin ring around Jupiter is due to resonance in the magnetic field of the Jupiter with the motion of dust particles in its gravitational field [2]. Like the Earth–Moon system, the majority of natural satellites of planets in the solar system are in a synchronous spin–orbit resonance. The orbit–orbit resonance occurs among three of the major four satellites of Jupiter, known as Galilean satellites. More references in this regard are found in the leteratures [3, 4]. The given useful reviews about orbital evolution are through resonance [5, 6]. A large number of Trans–Neptunian objects (TNOs) having exterior order of resonance 2:3 has received wide attention [7]. There are several objects having resonance close to the 1:2, 1:3 and 1 : 4. In the Trans-Neptunian belt, stable regions close to resonant motion of TNOs is detected by [8-11]. On the PSS resonances can be detected with the help of a number of islands. An extensive study on resonances has been done by [8]. It has observed that in the motion of asteroids and comets, chaotic trajectories can be trapped around a resonance for a long time [12, 13]. studied asteroids with autocorrelation time series function [14]. [15] analyzed the existence of asymmetric liberation and their importance for the stability of the 1:2 and 1:3 resonant motion in satellite and extrasolar planetary systems [15]. [16] studied the number of resonances associated with the dynamical features of the Kuiper belt and located between 30 and 48 AU [16]. This study was based on the computation of resonant periodic orbits and their stability. [17]