The analysis of combined methods of artificial satellite orbit formation

Dynamics, ballistics, movement control of flying vehicles


Sokolov N. L.

Central Research Institute of Machine Building, 4, Pionerskaya st., Korolev, Moscow region, 141070, Russia


The goal of this work is to conduct a comparative analysis of the known and future spacecraft insertion profiles to the orbits of Mars and Jupiter artificial satellites’. Different modifications of combined profiles are researched which require conducting of propulsive maneuvers with an aerodynamic acceleration of a spacecraft in the atmosphere, as well as the profile consisting in the propulsive orbit formation. The main optimality criteria are the minimum of total energy consumption and the maximum of physically realizable spacecraft reentry corridors.

The task solution of spacecraft optimal control is fulfilled with the use of necessary optimality conditions of Pontryagin’s maximum principle. The areas of rational application of profiles are detected including preliminary aerodynamic braking of a spacecraft in the atmosphere, shared control by aerodynamic and propulsive forces in the atmosphere, multiple passage of upper atmosphere by a spacecraft.

It is shown that the use of a combined profile for orbit-shaping with atmospheric maneuvering is high efficient as the power consumption with its use is 3-3.5 times less in comparison with the propulsive profiles during the insertion into the Mars satellite orbits and 7-10 times less during the insertion into Jupiter satellites.

It is determined that during spacecraft reentry near the lower boundary of the corridor it is reasonable to perform the propulsive trajectory correction maneuver. It allows reducing of total required energy consumption by 1.5-2 times or expanding of physically realizable reentry corridor by 10-15 % in comparison with the profile without a correction impulse. The energy consumption can be more considerably reduced for the profile with a spacecraft’s multiple passage of upper atmosphere. However, with the use of the given profile, the time for satellite orbit-shaping considerably increases.

The obtained results are of practical importance and may be used for deep space missions. The general principles of the methodological approach are adjusted for the solution of other tasks of spacecraft optimal control.


spacecraft, satellite orbits, optimal control, minimum of necessary energy consumption, maximum of reentry corridor width


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