The dynamics of uncertainty - Measuring orbit knowledge and quality in unstable orbits

Abstract

The dynamics of orbit uncertainty in an unstable orbital environment is discussed with specific application to the orbit determination of a halo orbit about the Earth-Sun LI point. The goal of the paper is to understand the basics of orbit determination and orbit uncertainty dynamics in this environment and to present some basic results. The dynamics model is based on the Hill equations of motion and the orbit determination measurement model is based on the classical Hamilton-Melbourne analysis for the information content of a Doppler pass of data. Results are presented and the major departures from the classic two-body orbital environment are highlighted. These differences include: non-alignment of the direction of the largest orbit uncertainty and the geometrical down-track direction, dominance of the unstable manifold for uncertainty dynamics in the absence of tracking, anti-correlation of unstable and stable manifolds and the direction of largest orbit uncertainty when tracking is present.