Ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems

The current stage of space exploration is characterized by an increased interest in the development, deployment, and operation of low-orbit satellite constellations (LOSC) for Earth and near-Earth space remote sensing for military and civilian purposes and for global and regional satellite communications. Reusable space launch vehicles have significantly reduced the orbital injection cost. As a result, satellite operators are developing and deploying large-scale LOSCs of various orbital structures with a large number of spacecraft. According to current estimates, more than 70% of all the operating satellites operate in low-Earth orbits (LEOs) at altitudes between 160 km and 2,000 km. Since LEO satellites are generally much cheaper than satellites in geostationary orbits, the possibility of their on-orbit servicing (OOS) has not been the focus of research. However, the use of LEO OOS has prospects for growth. Techniques for ballistic planning of LEO OOS missions have been and are being developed. The disadvantages of approximate techniques include the use of simplified flight dynamics models. Most of the existing exact techniques are based on the use of full mathematical models of flight dynamics and the shooting method to solve the boundary value problem of an orbit transfer. Using the shooting method requires a sufficiently accurate initial guess, which is difficult to determine. To obtain a second approximation, use is mainly made of optimization methods, which do not always find a global minimum. In this regard, there is a need to develop new techniques that would be free from the above disadvantages. The goal of the article is to develop a ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems. The technique includes the identification of LEO areas promising for OOS, a mathematical model of the dynamics of perturbed OOS orbit transfers in modified equinoctial orbital elements, and a solution algorithm for the boundary value problem of determining the control parameters of perturbed OOS low-orbit transfers. The problem is solved using methods of statistical analysis, flight dynamics, shooting, genetic optimization, and mathematical simulation. The novelty lies in the identification of LEO areas promising for OOS and the development of a mathematical model of orbit transfer dynamics in modified equinoctial orbital elements and a solution algorithm for determining the control parameters of perturbed OOS low-orbit transfers. The results of the work may be used in the justification and planning of LEO OOS missions and the formulation of requirements for LEO OSS mission propulsion systems.