Solution of the Problem of Optimal Spacecraft Launching into Orbit Using Reactive Acceleration and Solar Sail in Kustaanheimo–Stiefel Variables

Abstract

Using the Pontryagin maximum principle and the Kustaanheimo–Stiefel variables, the spatial problem of optimal launching into a given orbit of a spacecraft (SC) controlled by a solar sail and limited or impulsive reactive acceleration of the SC’s center of mass has been solved. The minimized functional is a linear combination with weight factors of two criteria: time and the integral sum of the values of the reactive acceleration impulses of the SC’s center of mass spent on the control process. The first integrals of the equations of the problem and formulas for determining the increments of the phase and conjugate variables under the action of the imparted impulse of reactive acceleration are given. Numerical solutions of the problem are obtained for limited or impulsive acceleration with or without a solar sail. An assessment of the influence of the presence of a solar sail on the duration of the process, on the total impulse of the reactive acceleration value and on the value of the minimized functional is given. Cases of orbit correction and cases when the elements of the new orbit differ significantly from the elements of the initial spacecraft orbit are considered. The optimality of the reactive acceleration, orthogonal to the plane of the osculating orbit of the spacecraft, for the considered small values of the angular element deviations of the orbit from their initial values, i.e., the optimality of such acceleration in the considered examples of the problem of correcting the angular elements of the SC orbit.