Study of time-free transfers into libration point orbits with multiple constraints

Preliminary designs of time-free transfers connecting a low Earth orbit with a halo orbit around the sun-Earth L₁ point are developed with impulse maneuver and multiple orbital element constraints. As a practical application, the constraints, including orbital altitude, inclination, right ascension of ascending node, and flight-path angle, are considered to describe the circular Earth parking orbit. The problem is then solved directly by a differential correction, using the constraint partial derivatives relative to state vector and Julian day. To reduce the sensitivity of the initial condition for differential correction, initial value functions are constructed based on the relationship of free variables and constraints.Numerical results show that Δv for halo orbit insertion ranges fromafew meters per second to hundreds ofmeters per second, depending on the specific inclination and right ascension of as cending node of Earth parking orbit, and demonstrate that the method for designing transfer trajectories with multiple constraints is feasible.