Optimal trajectories of the spacecraft with electric propulsion for the Jupiter flight via swing-by in the three-body problem

Аuthors

Konstantinov M. S.^*, Nguyen D. N.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mkonst@bk.ru
**e-mail: bauman252@mail.ru

Abstract

The accuracy analysis of the point gravity method during the design of interplanetary trajectory of the spacecraft with electric propulsion via Earth swing-by.
Development of a method for designing the interplanetary trajectories of the spacecraft with electric propulsion via Earth swing-by using restricted three-body problem for spacecraft motion.
Comparative analysis between use of the point gravity method and use of the restricted three -body problem.
The heliocentric trajectory optimization problem is formulated by using the Pontryagin’s maximum principle.
Motion equations of spacecraft are written with the help of restricted three-body problem.
The continuation method in parameter is used to solve the boundary value problem.
The originality of this article is related to the development of method for the trajectory optimization of the spacecraft with electric propulsion for the Jupiter flight via Earth swing-by in the restricted three-body problem.
The method for the interplanetary trajectory of the spacecraft with electric propulsion for the Jupiter flight via Earth swing-by in the restricted three-body problem is developed.
It is shown that the mass estimation method precision of spacecraft with electric propulsion to explore Jupiter with using Earth swing-by which is formulated on the point gravity method is not more than 1%. This is the confirmation of the correctness of the point gravity method in designing the interplanetary trajectory of the spacecraft.
The comparative analysis of the above two methods is presented.
Space mission to the Jupiter with nuclear electric propulsion.
In this paper the method of interplanetary trajectory of spacecraft with electric propulsion via Earth swing-by using models of spacecraft motion in the restricted three-body problem is proposed. In order to optimize the trajectory of spacecraft Pontryagin’s maximum principle is used. The method can be used to analyze any interplanetary trajectories with nuclear electric propulsion with gravity assist maneuver from any planet.
The comparative analysis of results for using two types of spacecraft motion model (the point gravity method and motion equations written by the restricted three-body problem) is shown. Types of trajectories and structure of switching functions using these two methods are practically coincided, and relative deviation of the required mass of xenon does not exceed one percent.
The comparative analysis has shown the correct usage of the point gravity method in designing spacecraft trajectories with electric propulsion for the Jupiter flight via Earth swing-by.

Keywords:

spacecraft, Jupiter, optimal trajectory, gravity assist trajectory, transversality conditions

References

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