INVESTIGATIONS ON INSTABILITY OF PERIODIC ORBITS OF NIGCOMSAT AROUND TRIANGULAR LAGRANGIAN POINTS IN THE EARTH-MOON SYSTEM WITH RADIATION PRESSURE AND VARIABLE MASSES

The Nigerian Space Agency launched the Nigerian Communication Satellites (NigComSat) into orbit in 2007. The satellite was designed to have a lifespan of 15 years and to remain in orbit for that duration. Unfortunately, after a year, the orbit became unstable and the satellite left orbit. In this paper, the focus is to investigate instability of the periodic orbits of the NigComSat around triangular Lagrangian points (TLPs) using the model of the restricted three-body problem with radiation pressure and variable masses. The masses of the host bodies are assumed to vary with time and the smaller bodyisa radiation emitter. We compute explicit expressions for the frequency, angle of rotation of the principal axis, eccentricity and lengths of semi-axes of the orbits of the satellite. Since some facts are not directly discernable from the analytic solutions, numerical evidences are provided to analyze the structure of the orbits, when the host bodies are assumed to be the Earth and Moon. Our numerical explorations reveal that due to the mass variation parameter, the orientation and paths around the TLPs differ and at some points, the NigComSat travels around the Earth and TLP while for some value of the mass variation parameter, the NigComSat does not travel around the TLP and the Earth. Further, as the mass variation increases the orbit flattens and the NigComSat leaves orbit. Further, the zero velocity curves around TLPs are explored and it is seen that the most significant perturbing effect is the mass variation of the main bodies. Additionally, when the Earth and Moon gain sufficient mass, large region becomes dynamically forbidden for the NigComSat and it leaves the vicinity of the TLPs and escape into space. Consequently, the NigComSat leaves the orbits due to the instabilities posed by the increasing mass of the Earth and the Moon coupled with the radiation pressure of the Moon. The orbits about Lagrangian points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies.