“Not full” two-boundary problem for finding multi-orbital transfers with zero low thrust in the shadow
A lot of calculations of multi-orbital transfers from elliptical orbit (with perigee distance ≈ 15.6 and apogee distance ≈ 83.2 thousand km, and inclination 13°) to geostationary orbit of spacecraft with low thrust, which becomes zero in the Earth shadow, is done. To find such trajectories so called 'not full' two-boundary problem that do not include a condition of optimal crossing the shadow line is solved. That's why trajectories are not optimal, but in many cases expenditure of working substance is not much more than on a trajectory without switching off the low thrust. For longitude of ascending node equal to 180° and different start dates the difference is later than 1%. The peculiarity of two-boundary problem is that in some cases more than one solution may exist.