Secular Resonance and Chaos in N Body problem

Abstract

Chapter one is the historical development of the Solar system dynamics along with the definition of some technical terms. newlineChapter two is devoted to understand the effect of secular resonances of other inner satellites of Saturn on Mimas-Tethys system. Here it is investigated that the system is more chaotic if considered to be locked in i1i3 resonance compared with i12 resonance. The effect of Saturn s oblateness and the interaction of its other inner satellites is also considered. By the help of Poincare surface of section and time-series graphs it is concluded that oblateness of Saturn plays significant role in the dynamics of Mimas-Tethys system and also it partially controls the chaos. newlineChapter three explains the impact of radiation pressure of Sun on halo orbits. It explains the stability of these orbits through frequency analysis. The result shows that the radiation pressure increases the time period and the eccentricity of the orbits around L1 but decreases around L2. With the effect of radiation pressure the halo orbits are shifting towards the Sun. The time-frequency analysis method is implemented to confirm its stability. newline The equations of motions are numerically integrated and found a signal with the help of solutions. In ridge-plot it is evident that instantaneous frequency is constant throughout the time interval considered. Thus it is concluded that the orbit is periodic. newlineChapter four is the extension of chapter three where the Radiation Pressure and its effect on the Halo orbits of Venus-Sun and Satellite system are studied. It is very attractive because Indian Space Research Organization (ISRO) has proposed to send an orbiter named Shukrayann-1 in year 2023. At last it is concluded that radiation pressure is directly proportional to eccentricity and the time period of the orbits around L1 but it is inversely proportional in case of L2. Also due to the effect of radiation pressure the halo orbits are shifting towards the Sun. newline newline