The partial banana mapping: a robust linear method for impact probability estimation

TL;DR

This paper introduces a robust linear impact probability estimation method for near-Earth asteroids, utilizing a curvilinear coordinate system to improve accuracy over traditional target plane methods.

Contribution

The paper develops a modified impact probability estimation method using a curvilinear coordinate system that accounts for the shape of the confidence region, enhancing accuracy and reliability.

Findings

More accurate impact probability estimates than target plane method.

Better handling of the confidence region shape in impact assessment.

Improved robustness in impact probability calculations.

Abstract

This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.