Semilinear impact monitoring

Partial-banana mapping: Search for impactors

¹ LTE, Observatoire de Paris, Univ. PSL, Sorbonne Univ., Univ. Lille, LNE, CNRS, Paris, France
² Institute of Applied Astronomy, Russian Academy of Sciences, Kutuzova emb. 10, St. Petersburg, Russia

^★ Corresponding authors: dmitrii.vavilov@obspm.fr; daniel.hestroffer@obspm.fr;vavilov@iaaras.ru

Received: 22 January 2024
Accepted: 19 May 2025

Abstract

Context. Near-Earth asteroids that orbit in the vicinity of the Earth have regular close approaches with our planet, and some of the asteroids can even collide with it. Several methods exist to compute an impact probability (IP). They include linear methods that can promptly give an estimate, but only provide reliable results when the two-body formalism is not strongly perturbed. Nonlinear methods are more robust, but several thousand asteroid orbit clones have to be integrated for a reliable result.

Aims. We developed a semilinear method that is reliable for IP computations and is fast enough. On one hand, it is robust and can handle perturbations from close encounters with planets, and on the other hand, it only requires the numerical integration of several orbits.

Methods. We modified the partial-banana mapping (PBM) method (which we developed in earlier work), which uses a special curvilinear coordinate system to approximate the curved shape of the uncertainty region in physical 3D space. As in PBM, at the time of the possible collision, we determine the closest point to the Earth along the main axis of the uncertainty region. Based on this, we determine the initial condition in orbital space at the epoch of observations that leads to this point, integrate this orbit, and finally, compute the impact probability. The scheme can be iterated until the procedure converges. This approach allowed us to take gravitational perturbations into account.

Results. The method was applied on 16 test cases and showed that virtual impactors were determined for 15 cases in the first run (without iterations). The computed impact probabilities agreed with the Monte Carlo results that were taken as reference, and they were more accurate than the results of linear methods for a similar computing time. The method worked even for the possible collision of (99942) Apophis in 2036 and successfully handled the close approach in 2029 (the Apophis orbit in the test was obtained from observations in 2004–2006). For one of the 16 cases, the collisional orbit was too far from the nominal orbit, and the impact probability was zero (which agrees with the Monte Carlo result), while the estimates from the linear methods for the impact probability were about 5%.

Conclusions. The method we developed successfully fills in the gap between fast linear methods with a numerical integration of the nominal orbit alone, which are of limited usage for an almost pure two-body problem, and time-consuming nonlinear methods that sample the uncertainty region with a numerical integration of several thousand orbits.