The Changes of the Orbital Elements and Estimation of the Initial Velocities of Stream Meteoroids Ejected from Comets and Asteroids

The values of the initial velocity of the meteoroids ejected from the parent bodies are small and as a result, the most of the young meteoroid streams have similar orbits to their parent bodies. Assuming that the members of the observed meteor stream evolved under the influence of gravitational perturbations mostly, Pittich 1991, Proceedings of the Conference on Dynamic of Small Bodies of the Solar System, Polish-Slovak Conference, Warsaw, October 25–28, 1988, pp. 55-61], Williams 1996, Earth, Moon, Planets 72, 321–326; 2001, Proceedings of the Meteoroids 2001 conference, Kiruna, Sweden, August 6–10, 2001, pp. 33–42] estimated the ejection velocities of the stream meteoroids. Equation relating the ejection velocity Δυ and the change Δa of the semi-major axis, Williams (2001), was applied with two slightly different variations. In the first one (M1) as Δa the difference between the mean orbit of the stream and the orbit of the parent body was substituted, in the second one (M2), as Δa the dispersion of semi-major axes around the mean orbit of the stream was used. The results obtained by these two methods are not free from discrepancies, partly explained by the particular orbital structure of the stream. Kresak 1992, Contrib. Astron. Obs. Skalnate Pleso 22, 123–130] strongly criticized the attempts to determine the initial velocities of the stream using the statistics of the meteor orbits. He argued that this is essentially impossible, because the dispersion of the initial velocities are masked by much larger measuring errors and by the accumulated effects of planetary perturbations. In our paper, we study the reliability of M1 and M2 methods. We made a numerical experiment consisting of formation of several meteor streams and their dynamical evolution over 5000 years. We ejected meteoroids particles from the comets: 1P/Halley, 2P/Encke, 55P/Tempel-Tuttle, 109P/Swift-Tuttle and from minor planets (3200) Phaethon and 2002 SY₅₀. During the integration, the ejection velocities were estimated using both M1 and M2 methods. The results show that the velocities obtained by M1 method are unstable: too high or too low, when compared with the known ejection velocities at the time of the stream formation. On the other hand, the velocities obtained using M2 method are too small, mostly. In principle, M2 estimates the dispersion of the distribution of the ejection velocities around the mean value, not the mean value itself. Applying more accurate Equation relating Δυ and Δa we decreased the bias of the results, but not their variation observed during the evolution of the streams and the parent bodies. We have found that the variability of the estimated ejection velocities was caused mainly by the gravitational changes of the semi-major axis and eccentricity of the parent body. In brief, we have found that the reliability of the results obtained by M1 or M2 method are low, and have to be used with great care.