Orbit-Phasing Based Transfer Trajectory to Inclined Heliocentric Orbit around Sun-Earth L4

This study presents the design and validation of an orbit-phasing based transfer trajectory to achieve a heliocentric, inclined, near-circular orbit around the Sun-Earth L4 point. The method assumes a spacecraft initially in a low Earth parking orbit and employs two principal impulsive maneuvers. The first burn, performed at perigee, provides Earth escape while simultaneously shaping a heliocentric phasing orbit with reduced semi-major axis and desired inclination, thereby allowing the spacecraft to lead Earth in orbital phase. Upon achieving a 60° phase separation, the second burn circularizes the orbit at 1 AU, establishing the mission orbit around L4. Analytical derivations identify a continuous set of feasible parking orbit elements and burn vectors, with the phasing orbit defined by the number of revolutions required for rendezvous. To validate the approach, high-fidelity numerical simulations were conducted using the General Mission Analysis Tool (GMAT), incorporating planetary perturbations, non-spherical Earth gravity, and solar radiation pressure. Results confirm that numerically optimized burn magnitudes closely match analytically driven solutions, with overshoots below 1% for both insertion and circularization burns. Additional midcourse correction and station-keeping maneuvers were introduced to ensure convergence and long-term stability, with required velocities on the order of 0.11-0.16 km/s for corrections and only a few meters per second for station-keeping. Over decadal propagation, the spacecraft maintained proximity to L4 with minimal phase drift, demonstrating the robustness of the trajectory design. The findings establish that two-body analytical approximations are sufficient for deriving optimal transfer conditions and that the proposed orbit-phasing strategy provides a practical and efficient means of accessing inclined mission orbits around Sun-Earth L4. The methodology enables mission designers to select among a family of valid initial conditions that can be tailored to constraints such as launch site geometry or target inclination, thereby enhancing flexibility for future heliophysics or communications relay missions.