The use of particle distributions in Solar system small body dynamics

ABSTRACT The extraterrestrial material, called meteoroids, that constantly enters the Earth’s atmosphere gives us a unique opportunity to examine the motion and population of small bodies in the Solar system. This exploration requires simulating the motion of these particles. Currently, only the timing of meteoroids encountering the Earth is well predicted by such simulations, while other parameters are uncertain. This can be remedied by proper stochastic representation and estimation using a sufficient number of samples. We propose methods to both represent simulations in a stochastic manner and to improve sampling using Importance Sampling. We also demonstrate these methods practically with a test model. Using the test model resulted in an error reduction by a factor of 3 without increase in computation time. Thus, we validated that these techniques can be implemented on and are compatible with Solar system small body dynamics models. Based on these results we predict that when properly implemented on a larger and more complex model, Importance Sampling can improve sampling numbers by several orders of magnitude without increasing computation time, depending on the simulation in question. The methods presented here bring advantages such as; greatly reduced estimation errors, fitting models without re-running simulations, model comparisons without sample variations, circumventing unknown properties using invariant measures, representing large particle numbers without additional errors. This methodology has wide application possibility and will enable larger, more reliable and reusable simulations of dynamical astronomy.

DIVISION A COMMISSION 7: CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY

In order to mark a distinction with the traditional triennial reports, for this legacy issue we have asked our present and past OC members, as well as a few other outstanding members of the Celestial Mechanics community, to write a short essay on “recent highlights and the future of Celestial Mechanics”. Below we collect the contributions of the people who responded to our invitation. As it is natural, each of them interpreted their task differently. Some produced a dissertation on broad and general aspects, others focused on a specific topic of their interest. Some considered that their role was to provide a detailed review, with a list of key references, others preferred to mention the topics for which progress has been significant but without quoting any references, implicitly considering that this progress was possible thanks to the collective efforts of many scientists, and not just a few. This is great, as we appreciate the diversity of attitudes and opinions.

DIVISION I: COMMISSION 7: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

President of Commission 7 Zoran Knežević opened the business meeting at 18:40 and proposed the agenda which was accepted without change.