Eccentric Anomaly Synchronism and Regularised Dynamics for Continuum Interplanetary Orbital Uncertainty Propagation

Uncertainty propagation features many of modern orbital dynamics-related engineering analyses. A solid understanding of how inaccurate measurements affect the subsequent phases of a mission is a crucial task to ensure its safety and success. Typical techniques to assess how uncertain phenomena impact the development of a mission all rely on Monte Carlo-based approaches for the interplanetary space and make use of a Cartesian formulation of the dynamics, so that high-fidelity models can be straightforwardly used. The proposed work studies how the regularisation of the dynamics' formulation, and in particular the choices made for the independent variable in the numerical integration, allow to drastically reduce the chaotic nature of the orbital motion for uncertainty propagation. A simple regularisation approach, commonly known as Kustaanheimo-Stiefel, uses an eccentric anomaly-like independent integration variable. A sample-based study on clouds of initial conditions propagated with this formulation is proposed, which immediately introduces strong evidence of a statistical continuum-like non-chaotic behaviour of the propagated cloud. The scattering effect of close approaches on the propagated uncertainty can also be modelled in a more predictable way, where exponential divergence replaces the apparent chaos that characterises the Cartesian dynamics and, more in general, any orbital description centred on the concept of physical time.