Development of an Improved Spherical Shaping Method for High-Inclination Trajectories

Over the past years, numerous missions for spacecraft with low-thrust propulsion have been planned to include large orbital plane changes. In order efficiently generate and evaluate orbits for such missions, use can be made of the spherical shaping method proposed by Novak. When inclinations larger than 15 degrees are present however, the error in the ΔV found by this method increases significantly. It was found that the spherical shaping method’s applicability and accuracy at high orbital inclinations can be improved through the development of a more accurate elevation shaping function. The purpose of this MSc thesis was therefore to do research on the development and implementation of such a function.Using a number of test cases, three potential methods to obtaining a more accurate elevation shaping function were evaluated. These methods included the usage of spherical triangles, Fourier series and an alternative function that was obtained during the development. By evaluating the ability of various functions to describe the unperturbed and perturbed orbits included in the test cases, a new elevation shaping function was found. This shaping function was based on the aforementioned alternative function obtained during the development.The accuracy of the new elevation shaping function was tested using a number of cases. It was observed that the new elevation shaping function significantly increased the spherical shaping method’s accuracy at high orbital inclinations; at an inclination of 20 degrees, the error in the ΔV found was decreased to less than 1 percent. However, this error did increase as the inclination became larger.The spherical shaping method was furthermore applied together with the new elevation shaping function to the design of two missions. These missions included rendezvous trajectories to the dwarf planet Makemake and to the comet 2003 EH1. It was found that the new elevation shaping function enabled the spherical shaping method to produce smooth trajectories with attainable ΔVs to both targets, even though the inclination of 2003 EH1 is approximately 70 degrees. Aerospace Engineerin