• close encounters
• impact monitoring
• Near-Earth Objects
• scattering encounters

The current asteroid Impact Monitoring systems propagate numerically the Virtual Asteroids (VAs) for an arbitrary time in the future (usually 100 years or more) that does not depend on the asteroid. However, the numerical propagation and close encounter analysis of thousands of solutions for 100 years is very computationally expensive, and we believe it would be much better to have a propagation time tailored to each asteroid, depending on the uncertainty of its orbit and the type of close encounters it undergoes. For example, after a scattering encounter (Tommei and Valsecchi, 2024), subsequent close encounter analysis would be quite uninformative.

The thesis starts with a review of the main ideas and results in the so called extended Öpik's theory, and then proceeds with an overview of the basic theory of Orbit Determination, with particular attention to its applications to the Impact Monitoring of NEOs.
The first actual result of this thesis work is to propose a more operative definition of scattering encounter, for which we can give a sufficient condition for an encounter to be scattering through explicit formulas.
We then propose some algorithms to compute approximations of those quantities, either using only the values obtained from the standard propagation procedure using the LOV method, or adding appropriate new samples via LOV densification, or even going outside of the LOV, in the direction suggested by the analytic theory of close encounters. Proof of the effectiveness of the algorithms, in the simplified setup of the analytic theory, will be given to motivate the choices made. Lastly, the results of the algorithms will be presented on a variety of asteroids.