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Research Article | Open Access
Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications
Abstract
This study made use of a shape-based method to analyze the orbital dynamics of a spacecraft subject to a continuous propulsive acceleration acting along the circumferential direction. Under the assumption of a logarithmic spiral trajectory, an exact solution to the equations of motion exists, which allows the spacecraft state variables and flight time to be expressed as a function of the angular coordinate. There is also a case characterized by specific initial conditions in which the time evolution of the state variables may be analytically determined. In this context, the presented solution is used to analyze circle-to-circle trajectories, where the combination of two impulsive maneuvers and a logarithmic spiral path are used to accomplish the transfer. The determined results are then applied to the achievement of the Earth–Mars and the Earth–Venus transfers using actual data from a recent thruster developed by NASA.
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Pages 413-427
Cite this article:
Bassetto M, Quarta AA, Mengali G. Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications. Astrodynamics, 2022, 6(4): 413-427. https://doi.org/10.1007/s42064-022-0135-3
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