System and method for controlling motion of spacecrafts

A method for controlling a motion of an object from a geostationary transit orbit (GTO) of an earth to an orbit of a moon, comprising:

• determining a first trajectory of the motion of the object from an intermediate orbit of an earth to a neighborhood of a stable manifold of a first Lagrange point (L1) as a function of a time of flight;
• determining a second trajectory of the motion of the object from the GTO to the intermediate orbit based on a set of initial conditions of the first trajectory;
• determining a third trajectory of the motion of the object from the neighborhood of the stable manifold to an L1 orbit based on a set of final conditions of the first trajectory;
• determining a fourth trajectory of the motion of the object from an L1 orbit to the orbit of the moon based on a size of the L1 orbit;
• and
• determining a trajectory from the GTO to the orbit of the moon as a combination of the first trajectory, the second trajectory, the third trajectory, and the fourth trajectory, wherein steps of the method are performed by a processor;
• wherein the determining the first trajectory further comprises:
• determining a set of zero-fuel trajectories from a set of orbits of the earth to the neighborhood using an approximate mapping of a perturbation of the motion by a gravity of the moon;
• selecting a zero-fuel trajectory optimizing the time of the trip;
• and
• modifying the zero-fuel trajectory to determine the first trajectory such that the first trajectory satisfies a constraint on the time of flight while optimizing the consumption of the fuel.