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

Davide Farnocchia; Siegfried Eggl; Paul W. Chodas; Jon D. Giorgini; Steven R. Chesley

doi:10.1007/s10569-019-9914-4

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

Davide Farnocchia, Siegfried Eggl, Paul W. Chodas, Jon D. Giorgini, Steven R. Chesley

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	36
Journal	CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
Volume	131
Issue number	8
DOIs	https://doi.org/10.1007/s10569-019-9914-4
State	Published - Aug 1 2019
Externally published	Yes

Keywords

Impact hazard
Orbital dynamics
Planetary encounters

ASJC Scopus subject areas

Modeling and Simulation
Mathematical Physics
Astronomy and Astrophysics
Space and Planetary Science
Computational Mathematics
Applied Mathematics

Online availability

10.1007/s10569-019-9914-4

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AU - Chesley, Steven R.

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N2 - 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.

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

Abstract

Keywords

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