Orbit-State Model Selection for Solar-Sailing Mission Optimization

The numerical performance of orbital state models may be in uenced by how much physical information is directly re ected by the di erential equations of motion. Traditionally, Cartesian coordinates are commonly used in astrodynamics applications, because the orthogonality of the system results in simple equations with attractive numerical properties. Alternative formulations that take the shape of the orbit into account are the uni ed state model (USM) and the modi ed equinoctial elements (MEE), which have shown a superior numerical performance. These three models are compared in a mission analysis of a solar sail going to the Sun to observe the poles. This is a long-duration, low-thrust mission that would bene t from any gain in computational speed. Integrating the three state models in an evolutionary optimization framework, where the optimal solution is obtained after only a very large number of function evaluations, it was found that the convergence of the nal solution is comparable for all three state models. On average the Cartesian model requires about 3.5 times more function evaluations than the other two, with the USM being superior to the MEE. In a multi-objective framework, the quality of the Pareto front in terms of convergence is also comparable for all three state models, with possibly a slight favor for the USM and MEE as being progressed a bit more. In terms of number of Pareto individuals the Cartesian model is a clear winner with a larger number of individuals quite well spread over the Pareto front, although the USM and MEE do not actually perform poorly in this area.