Transfers in the central Newtonian field from high-elliptical orbits to geostationary one of a spacecraft with low thrust, which becomes zero in the Earth shadow, are considered. To find such trajectories so called 'non-completed' two-point boundary value problem that do not include a condition of optimal crossing the shadow boundary is solved. It's shown that when a longitude of ascending node Ω₀ is equal to 180⁰ expenditures of working substance are not much more than for a basic transfer (without switching the low thrust off). If Ω₀ is chosen the best and the duration of flight is half-year or smaller then expenditures are less than for a basic transfer.

multi-orbital trajectories, spacecraft, low thrust, geostationary orbit, Earth shadow, two-boundary problem

Theoretical and applied problems of mechanics

Akhmetshin Rauf Zulfarovich,  axmetro@yandex.ru,  KIAM RAS