Effects of mass ratio on halo orbits about L1 and L2

In the determination of location of Lagrangian points, the mass ratio of primaries in Restricted Three Body Problem (RTBP) plays an important role. Due to change in the value of mass ratio, the corresponding variations in different parameters of Halo Orbits (HO) are studied. It has been observed that halo orbits around L1 move towards the first primary, X altitude, AX , corresponding to a fixed Z altitude, AZ , and period around L1 decreases whereas X altitude, AX , corresponding to a fixed Z altitude, AZ , and period around L2 increases with the increase in mass ratio. Further, orbits around L2 move away from the second primary until μ≈ 0.17894 and then move towards the primaries with the increase in mass ratio. Variations in other parameters such as the initial distance from the origin of a spacecraft and its initial velocity in a halo orbit around L1 and L2 are also obtained corresponding to variation in mass ratio. The results are validated by comparing with the data obtained for various Sun-Planet systems. Also, different parameters of halo orbits around the Sun-Earth and the Sun-Earth+Moon system are compared.