Planar Problem of an Optimal Transfer of a Low-Thrust Spacecraft from High-Elliptic to Geosynchronous Orbit

Low-thrust flights from high-elliptic orbits are of considerable interest, since they allow one to decrease (compared to high-thrust flights) the propulsion consumption and to reduce the flight duration. At the same time, in comparison with the spiral unwinding flights from low near-circular orbits, this scheme minimizes the harmful effect of the radiation belts. Based on the maximum principle, the problem of optimization is reduced to a two-point boundary value problem, which is solved numerically using the modified Newton method. A method is suggested to obtain the initial approximation for solving the boundary value problem. The method takes advantage of the idea of transition from an approximately optimal trajectory to the optimal one. Two problems, which have different low-thrust models, are considered: one with permanently acting low thrust and the other with the possibility of turning it on/off. In both cases no restrictions are imposed on the thrust direction. A comparison of these problems is made. We investigated (i) what gain in the final mass can be attained when passing from the first to the second problem, (ii) at the cost of what loss in flight duration this can be achieved, and (iii) what changes in the optimal program of control must be done in this case.     

On the asteroid hazard

The concept of “space patrol” is considered, aimed at discovering and cataloging the majority of celestial bodies that constitute a menace for the Earth [1, 2]. The scheme of “optical barrier” formed by telescopes of the space patrol is analyzed, requirements to the observation system are formulated, and some schemes of sighting the optical barrier region are suggested (for reliable detection of the celestial bodies approaching the Earth and for determination of their orbits). A comparison is made of capabilities of electro-jet engines and traditional chemical engines for arrangement of patrol spacecraft constellation in the Earth’s orbit.     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

Space patrol: Variants of the optical barrier scheme

Different variants of the space patrol system to be designed for discovering and cataloging space objects hazardous for the Earth have been investigated. The basic idea of this system is to create an optical barrier using the telescopes deployed in a heliocentric orbit. Difficulties (as well as ways of overcoming them) of this program are analyzed, associated with form and position of the orbit of a space object relative to the patrol spacecraft, determination of orbit parameters, and mutual motion of space objects and the telescopes on spacecraft. The barrier’s schemes with scanning vertical or horizontal belts are considered. Some examples of observational conditions are presented for space objects crossing the barrier region: angular positions, velocities, distances, and numbers of days during which they are observed in the barrier region. The barrier’s characteristics are given for telescopes deployed in the orbits of the Earth and Venus.