Design-and-Ballistic Optimization of the Earth-to-Jupiter Mission for a Spacecraft with the Electric Propulsion Unit

Аuthors

^*, Starinova O. L.^**

Samara National Research University, Moskovskoe shosse, 34, Samara, Russia

*e-mail: lykkk99kk@163.com
**e-mail: starinova@ssau.ru

Abstract

Design-and-ballistic optimization process of a mission of the spacecraft (SC) with the electric propulsion system (EPS)  mission requires multiple solutions of variation problems for the Earth-to-destination planet transfers at various design parameters. Storage and processing of the previously obtained results allows their application both for solving variation problems with various parameter values and design-based mission optimization with analytical dependencies. This approach was previously successfully applied for the design-and-ballistic optimization of the Earth–Mars–Earth mission, including one with a gravity assist maneuver near Venus during direct or return transfer. Approximate relationships were obtained for the ballistic parameters of transfers between the Earth, Mars, and Venus, depending on the design parameters of the SC and EPS. This article describes the results of this methodology applying to a mission to the Jupiter system. The study validated the above said method effectiveness through specific case studies:
1. A Single-Point Verification: arbitrary design parameters were selected. Initial guesses (including flight time and initial values of adjoint variables) were quickly obtained by the approximate equations. With these guesses as a starting point, iterative optimization was performed to obtain an accurate optimization solution.
2. Comparison of the Results: Comparison demonstrated that the differences between the pre-optimization and optimization initial values of conjugated variables were minimal. Errors in the final orbital parameters (heliocentric radius, velocity components) were very small as well. This indicates the fact that the approximate equations ensure high-quality initial guesses, converging to a highly accurate solution within a few iterations.
3. Global Testing: Systematic testing was conducted across the entire design parameter space. The results reveal that although direct application of the approximate equations may introduce a certain error due to the non-uniform parameter variations, iterative computation commencing from these initial values always converge quickly. The convergence error, computational time, and number of iterations were recorded during testing, which proves the method ability to consistently and efficiently provide feasible solutions throughout the computational domain.
The study allows making a conclusion that the approximate equations derived from the optimized database can provide excellent initial values for the optimization model of the Earth–Jupiter low-thrust transfer trajectories. This approach ensures that iterative computations always achieve convergent solutions and significantly reduces the time required to obtain a feasible solution. This achievement lays a formidable foundation for subsequent applications of more complex optimization methods (e.g., neural networks), offering a fast and reliable starting point.

Keywords:

Earth–to-Jupiter flight, low-thrust trajectory optimization, maximum principle of Pontryagin, two-point boundary value problem, parameter continuation method, polynomial regression

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