Probability of coincidental similarity among the orbits of small bodies – I. Pairing

Abstract

Probability of coincidental clustering among the orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups of 2,3,4, ... members. Probability of coincidental clustering is assessed by the numerical simulation, therefore, it depends also on the method used for the synthetic orbits generation.We tested the impact of some of these factors. For a given size of the orbital sample we have assessed probability of random pairing among several orbital populations of different sizes. We have found how these probabilities vary with the size of the orbital samples.Finally, keeping fixed size of the orbital sample we have shown that the probability of random pairing can be significantly different for the orbital samples obtained by different observation techniques. Also for the user convenience we have obtained several formulae which, for given size of the orbital sample, one can use to calculate the similarity threshold corresponding to the small value of the probability of coincidental similarity among two orbits.

Generating realistic synthetic meteoroid orbits

“…The figure shows that the differences are minor, except an apparent dearth of orbits around ω ≈ 180°. Otherwise, the results are similar to those obtained by the Jopek and Bronikowska (2016)…”

“…a function which maps a real number x to the least integer greater than or equal to x. The samples were drawn following method E of Jopek and Bronikowska (2016). The results are shown in Figures 1 to 6.…”

“…The data exhibit a distinct structure with two main branches, of which Figure 2: Comparison of the perihelion distance histogram of the synthetic orbits with the observed dataset. The synthetic orbits were generated by method E given in Jopek and Bronikowska (2016). the central one that peaks at ω ≈ 180°is further divided into a high and a low q branch of high density.…”

“…Although the Earth orbit intersection condition (Equation 1) was used to estimate the perihelion distance in Jopek and Bronikowska (2016), it was not utilized as a part of this methodq was directly estimated from the density model. The main reason for not using this equation is the loss of correlation in the perihelion distance with other orbital elements.…”

“…For example, if it is assumed that the meteoroid's heliocentric distance at the moment of collision with Earth is fixed at 1 AU at all positions in the orbit, the real range of orbits is not covered, as the Earth's distance to the Sun slightly changes with time. Moreover, Jopek and Bronikowska (2016) method E uniformly distributes the e cos ω signs, not taking into account any correlations in the orbits other than the ecliptic latitude ratio. This option was tested and it was found that more consistent results were obtained when q was retained as one of the estimated parameters.…”