Patent Document ID: 9031818
Application ID: 13518790
Patent Flag: 1

Claim One:
1. A method for determining a trajectory for a transfer of a spacecraft from a starting space body to a target space body with respect to a given central space body, the determined trajectory being optimal with respect to a given space mission requirement to be met by the transfer of the spacecraft; the method comprising: providing, according to the Pontryagin maximum principle, a physical-mathematical model relating model quantities and physical quantities representing the transfer of the spacecraft with respect to the given central space body, the model quantities comprising a first model vector quantity and a second model vector quantity, the first model vector quantity having a first modulus changing in time and a first space orientation which changes in time and is defined by a first longitude angle changing in time and by a first elevation angle changing in time, the first model vector quantity representing, instant by instant, a respective optimal direction of thrust of the spacecraft with respect to the given space mission requirement, the second model vector quantity having a second modulus changing in time and a second space orientation which changes in time and is defined by a second longitude angle changing in time and by a second elevation angle changing in time, the second model vector quantity representing, instant by instant, a time-evolution of the first model vector quantity; setting, in the physical-mathematical model, starting and final boundary conditions, the starting boundary conditions being such that, at a starting time of the transfer, position and velocity of the spacecraft are close to position and velocity, respectively, of the starting space body, the final boundary conditions being such that, at a final time of the transfer, position and velocity of the spacecraft are close to position and velocity, respectively, of the target space body; setting, in the physical-mathematical model, first conditions such that the second modulus is related to the first modulus through a angular-velocity-related quantity depending on the given central space body; setting, in the physical-mathematical model, second conditions such that a specific longitude angle, between the first longitude angle and the second longitude angle, and a specific elevation angle, between the first elevation angle and the second elevation angle, are independent one from the others; considering first starting times included in a given time range, first longitude values of the specific longitude angle included in a given longitude range, and first elevation values of the specific elevation angle included in a given elevation range; and determining a trajectory for the transfer of the spacecraft on the basis of the physical-mathematical model, of the considered first starting times, of the considered first longitude values, and of the considered first elevation values.