Planetary encounter analysis on the B-plane: a comprehensive formulation

The B-plane is a fundamental tool to analyze planetary encounters of small bodies and spacecraft flybys. In this paper, we review the B-plane formulation with a full derivation of its coordinates and their partial derivatives, which allow the mapping of orbital uncertainties onto the B-plane. We find that this mapping can be sensitive to variations in the inbound asymptote, especially for low-velocity encounters, and to non-Keplerian dynamics for distant encounters. Under linearity assumptions, we show how to derive close approach boundaries and impact probabilities from the orbital uncertainty mapped onto the B-plane.