A Spacecraft Interplanetary Trajectory Optimizing with the Sequence of Gravity-Assist Maneuvers near the Earth and Venus

Aeronautical and Space-Rocket Engineering


Аuthors

Shevchenko V. V.

Corporation Moscow Institute for Heat Technology, 10, Beryozovaya alleya St., Moscow, 127273, Russia

e-mail: vv.shevchenko5894@gmail.com

Abstract

Potential of scientific space exploration is increased significantly by the gravity-assist maneuvers application. This method, which was successfully tested on the “Pioneer-11”, “Voyager-1,2”, “Vega-1,2” and “Galileo” missions, has consistently led to the key flight parameters improvement. It allowed achieving either significant energy costs reduction, or duration shortening of the transport mission, or simultaneous improvements in both indicators compared to the flights along the direct interplanetary trajectories.
This article solves the problem of designing optimal interplanetary trajectories of a spacecraft (SC) with a combined propulsion system (chemical propulsion system and electrojet propulsion system) for studying the inner heliosphere of the Sun from non-ecliptic positions. The SC flight patterns are being analyzed herewith, in which it is able to perform a sequence of gravity-assist maneuvers at the same point or at the opposite points of the planet orbit. The angular range between two consecutive resonant gravity-assist maneuvers herewith can be either 2pk or p(2k–1), where k = 1, 2, …, K; KÎR. In the first case, the heliocentric orbit is called a resonant one with a whole resonance order, while in the second case it is a π-resonant orbit.
It is assumed that the first impulse, which ensures the movement along the hyperbola of departure from the Earth, is given by the chemical upper stage “Fregat”. The SC is equipped with an electric jet propulsion system with the single “SPE-140D” stationary plasma engine. The interplanetary SC flight scheme characteristics were derived from the solution of the boundary value problem of the Pontryagin maximum principle. Mass of the SC placed into the target heliocentric orbit was being considered as optimality criterion. The SC heliocentric orbit with 30° inclination to the Sun equator plane was assumed as a target heliocentric orbit.
The optimized characteristics of the seven-point boundary value problem are:
- The launch date of the SC from the low-earth orbit (LEO);
- The “Frigate” upper stage running time;
- The hyperbolic excess velocity vector magnitude and direction during the launch from the Earth;
- The electric jet propulsion system “on/off” program on all heliocentric sections of the flight;
- The thrust vector orientation program in the SC active flight sections;
- The dates of gravity-assist maneuvers near Earth and Venus, as well as the gravity-assist maneuvers parameters being selected.
The results of the design-and-ballistic analysis of the end-to-end optimization problem under consideration are the two SC trajectories for the SC putting on the target heliocentric orbit, including a single non-resonant gravity-assisted maneuver near the Earth and a sequence of resonant gravity-assisted maneuvers near Venus:
•    1 : 1 Þ 4 : 3 Þ 3 : 2 – the gravity-assist maneuvers were performed at the same point of the planet orbit, the angular range of a separate heliocentric Venus–Venus flight is 2pk, where k = 1, 2, …, K; KÎR (the first flight pattern).
•    1 : 1 Þ 1,5 : 1,5 Þ 1 : 1 – the gravity-assist maneuvers are performed at the opposite points of the planet orbit (the second flight pattern).
The results of the numerical analysis were as follows. With the same launch date of the SC from the reference low-Earth orbit, the sections of optimal trajectories before the first gravity-assist maneuver near Venus of the analyzed flight patterns were rather similar in all characteristics. The SC mass at the first approach to Venus differs by only 4.1 kg (0.26%). The magnitude of the hyperbolic excess velocity during a gravity-assist maneuver near the Earth differs slightly more (though slightly as well): by 61.5 m/s (about 0.82%). The magnitude of the hyperbolic velocity excess during the first gravity-assist maneuver near Venus differs by 83.9 m/s (about 0.54%). The optimal trajectories characteristics of the flight schemes being considered differ significantly, beginning from the second gravity-assist maneuver near Venus. Application of the π-resonant heliocentric orbit allowed reducing the resonance order on the last heliocentric flight to Venus, and selecting it equal to 1:1. Due to this, duration of the SC staying in resonant heliocentric orbits for the trajectory of the second flight pattern appeared two times less than that of the first flight pattern trajectory without significant  SC mass decrease (decreased by 4 kg) in the target heliocentric orbit.

Keywords:

spacecraft, combined propulsion system, gravity-assist maneuver, maximum principle

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