Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 67, p. 50-56 (2023)

PRECISING METEOR VELOCITY AS A RANDOM VALUE BY THEORETICAL CALCULATION OF ITS PROBABILITY DENSITY FUNCTION

Pavlo KOZAK, Ph.D (Phys. & Math.), Senior Researcher
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine


Abstract

When processing the results of simultaneous double-station video observations of meteors and subsequent cataloging of their kinematic parameters, the accuracy of the obtained results, that is, the error of each parameter, is important. The most important characteristic of a meteor is its velocity, because it affects the accuracy of determining the semi-major axis and the eccentricity of the heliocentric orbit of the meteoroid – on the one hand, and on the physics of the meteor motion in the atmosphere – on the other. Since after calculating the velocity vector direction, the velocity vector sizes can be searched “independently” (the results will be partially correlated) for each of the points, it is suggested to use these two values ​​to precize the velocity of the meteor, for example, finding its weighted average value. Earlier, we proposed to search all meteor kinematic parameters as random variables by Monte Carlo method, obtaining probability density distributions for each parameter. Since when calculating the meteor velocity in this way, we get two distributions for each of the observation points, it is suggested to find their section as a product of two input distributions with further normalization of its area by one.

At first, a scheme for multiplying histograms was implemented, which was not very convenient because it gave a large scatter of the points of the resulting distribution. In this work, it is proposed to use the fact that both input velocity distributions are of  normal type with high probability (probability 0.998 within three standard deviations) and to use the multiplication of analytical functions of the normal distribution, the result of which will also be a Gaussian function. Appropriate theoretical calculations were made, and this approach was tested on an individual meteor. It is shown that the scheme is mathematically and physically justified and gives effective results.

Key words
Meteor, meteor kinematic parameters, meteor velocity calculation error, Monte Carlo method, probability density functions product.

References

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