The influence of jump conditions in conjugate variables on the multiorbit spacecraft transfers with switching the low thrust off in the earth's shadow

Transfers in the central Newtonian field to the geostationary orbit are considered under the assumption that low thrust becomes zero when spacecraft with solar panels enters the Earth’s shadow. Using the maximum principle, the two-point boundary value problem is formed. It includes the conditions for optimal intersection of the shadow boundaries, the so called jump conditions in conjugate variables. Then the influence of jump conditions on the two-point boundary value problem solutions is investigated. Calculations for the flights of spacecraft with initial mass 5550 kg and thrust 0.55 N (initial acceleration 0.1 mm/s²) from the initial orbit with inclination 13° and the height of perigee 9.2 Mm and of apogee 76.8 Mm were done. They showed that if the argument of pericenter is equal to 0° and the longitude of the ascending node Ω₀ = 180°, the difference in the propellant cost for two trajectories – with or without taking into account the jump conditions – does not exceed 0.15 % (in comparison with “nominal” trajectories, i.e., transfers without zeroing the thrust), and may be less than 0.01 % for some values of initial time. For other values of Ω₀, the difference may be greater than 30 %. It was discovered also that the two-point boundary value problem may have several solutions. They differ from each other by the set of orbits crossing the Earth’s shadow.