Calculation of the mean orbit of a meteoroid stream

Abstract

The traditional approach used for averaging the parameters of a meteoroid gives results that are biased by several conceptual defects: among others things, the mean orbital elements do not satisfy the laws of celestial mechanics. The Voloshchuk & Kashcheev method in the domain of geocentric parameters removes all of these defects except one: the epoch corresponding to the mean geocentric values, which is critical for the calculation of the mean heliocentric orbital elements from the mean geocentric radiant coordinates and velocity. We propose a new approach: our solution gives the mean orbital elements and the geocentric radiant parameters of the meteor stream, free from all conceptual faults. Instead of the Keplerian orbital elements, we average the heliocentric vectorial elements, and the solution is obtained by the leastsquares method completed by placing two constraints on the mean vectorial elements. One may calculate the corresponding geocentric parameters using the theoretical radiant approach. However, to obtain mutually numerically consistent helioparameters and geoparameters, all members of the stream should be pre-integrated into a common epoch of time. Our approach, due to simultaneous averaging of seven variables, is limited to the streams of seven or more members only. We give the results of the numerical example, which shows that the mean values obtained by our approach differ slightly from those obtained by the traditional averaging. However, for some streams and for some particular orbital elements, the differences can exceeds 2 au in the semimajor axes or 0. 5 in the angular orbital elements.