2024-07-10 –, While Loop (4.2)
One of the main problems in the computation of orbital predictions, is the propagation of the orbital uncertainty. This problem is relevant in a wide range of scenarios, from the design of interplanetary spacecraft trajectories, to the assessment of the hazard posed by an asteroid impacting the Earth. In this talk, we present a technique to propagate large sets of initial conditions in TaylorIntegration.jl via a technique called Automatic Domain Splitting (ADS).
One of the main problems in the computation of orbital predictions, is the propagation of the orbital uncertainty. This problem is relevant in a wide range of scenarios in astrodynamics, from the assessment of the hazard posed by an asteroid impacting the Earth, to the design of interplanetary spacecraft trajectories. A first possibility to tackle this problem, is to solve a given initial value problem (IVP) in terms of Taylor expansions with respect to time and small deviations around a given reference initial condition, a technique known as jet transport (JT). This technique allows to solve IVPs for small neighborhoods around a given reference initial condition. Nevertheless, although our implementation of JT in TaylorIntegration.jl controls the error with respect to time, so far it does not control the error on the Taylor expansions around these small deviations with respect to the reference initial conditions, which under some circumstances can break the accuracy of the IVP solution. In this talk, we present a technique to mitigate this issue. We are implementing in TaylorIntegration.jl a technique called Automatic Domain Splitting (ADS), as introduced by Wittig, et. al. (2015). The idea is simple: we begin with a domain where we can trust JT initially works. As we propagate, whenever an error metric exceeds a tolerance, the current polynomial splits into two JT integrations, each representing half of the original domain. This process is iterated for each new sub-domain throughout an integration, so that the solution for the set of initial conditions is returned as a binary tree of JT solutions. We discuss applications of this technique to modelling of planetary fly-bys by small bodies (asteroids, comets, spacecraft, etc.).
I currently work as a Flight Dynamics Engineer at the European Space Operations Center in Darmstadt, Germany. As part of my PhD research at Mexico National Autonomous University, I developed TaylorIntegration.jl, in collaboration with Dr. Luis Benet. I enjoy researching asteroid and comet dynamics, high-accuracy orbit determination, astrodynamics and Taylor-mode automatic differentiation.
