Transfer Trajectory Design using direct method in the photo-gravitational Sun-Earth System

This study employs a direct approach to construct transfer trajectories within the photo-gravitational Sun-Earth system and by considering the Earth as an oblate primary in Circular Restricted Three-Body Problem (CRTBP). Specifically, it explores the transfer trajectories of a spacecraft from an Earth-centered parking orbit to a halo orbit near Lagrangian point in photo-gravitational CRTBP framework. In this work, the Chebyshev collocation method (CCM) is used in combination with the differential correction (DC) method to construct the transfer trajectories. In order to make up for the absence of a general analytical solution in the photo-gravitational CRTBP, this method uses the CCM to produce a trustworthy starting approximation. The DC method is then used to improve the approximation to the required precision for the trajectories. For a comprehensive analysis, we consider six time of flight (TOF) durations ranging from 100 to 200 days, with increments of 20 days (i.e., 100, 120, 140, 160, 180, and 200 days). For each TOF, we compute the departure velocities required from the Earth-centered parking orbit and the insertion velocities at the halo orbits. These computations enable us to generate detailed velocity profiles and assess the propulsive demands of different transfer durations. Additionally, we investigate the influence of the out-of-plane amplitude \(\:{A}_{z}\) of the halo orbits on maneuver costs. We consider five halo orbits with varying values of \(\:{A}_{z}\) (\(\:1.1\times\:{10}^{5},\:\:\:2.0\times\:{10}^{5},\:\:3.0\times\:{10}^{5},\:\:4.0\times\:{10}^{5}\:\text{a}\text{n}\text{d}\:5.0\times\:{10}^{5}\:\text{k}\text{m})\:\)to analyze how the size and shape of the halo orbit affect the required velocity changes (ΔV). The study quantifies the total velocity magnitude necessary for the spacecraft's insertion onto the transfer path. We also implement the coordinate transformation of the state vector of spacecraft from the Sun-Earth barycentric rotating frame to the Earth-centered inertial J2000 frame.