Highlights of Astronomy, Volume 16 XXVIIIth IAU General Assembly, August 2012 T. Montmerle, ed. c  International Astronomical Union 2015 doi:10.1017/S1743921314005109 The Possible Interrelation of TNO and Long-Period Comets by MOID Distribution A. S. Guliyev 1 , Sh. A. Nabiyev 1,2 , R. A. Guliyev 1 and A. S. Dadashov 1 1 Shamakhy Astrophysical Observatory NAS, Azerbaijan, email: ayyub54@yahoo.com, 2 Qafqaz University, Azerbaijan, email: snebiyev@qu.edu.az The study objects of our work were 91 TNO with diameters greater than 200 km. On the other hand, the paper used the data for 1048 and comets with aphelion and perihelion distances Q> 30 AU and q> 0.1AU, respectively, were observed until 2012. Short-perihelion comets (sporadic and concentrated in separate groups) were excluded from the analysis. If some comet split into several parties, we have taken data for only one fragment, which is marked with the letter A. Data for comets are taken from the catalog [4] and the individual Circulars International Astronomical Union, issued in period after 2008. The data for TNO, mostly borrowed from the website [5], as well as the issues of the same circulars. Research methodology is the same as in [1]. By number of comet passes from traffic zone selected TNO is compared to the modeled 67 zones. That differs from it only on the parameters Ω (longitude of the ascending node) and I (inclination). The Ω ranges from 0 0 to 330 0 in increments of 30 0 and I - from 0 0 to 90 0 with such steps to pole the planes were equidistant from each other ([2] and[3]). Ultimately, defines the following values: N - number of comet passes in traffic zone selected TNO; n, σ, t and α - average comet passes for 67 zones, normalized difference (t =(N − n)/σ), the variance a confidence interval of t, respectively. As a validation of the values t and α appropriate use the one-sample t-test, which leads to values of 1.67 and 0.95, respectively. To calculate the value of r (i.e. MOID) used the following formula: r 2 =  R 2 (dn)+  q(1 + e) 1+ e cos ν  2 − 2R(dn)(q(1 + e)) 1+ e cos ν  1 − sin 2 i × sin 2 (ω − ν )  Here R(dn) is the distance TNO in a direction of the ascending nodecomet’s orbit, q and e-non-variant elements comet’s orbits, i and ω angular elements of the comets orbitsrelatively to moving plane of selected TNO, ν - true anomaly of the comet. Naturally, the formula contains some inaccuracies, because the distance of the planet towards remote host comets orbits might differ slightly from the true direction, where the distance between TNO and comet is minimal. However, for this issue, and its ulti- mate objective, such inaccuracy does not play a significant role. Anyway, it is extremely improbable, that redundancy of comet passes to zones of interesting us can be results of such discrepancy, most likely to the contrary, the result could be more significant when taking into account the exact distance of the planet. Thus, at the first stage of our calculations for 91 TNO and 1048 comets are calculated values r (only 95368 values). It is difficult to assess what law should obey their distribu- tion, but it whenever a selected should cover the intervals from TNO 0 to Q (aphelion distance of a planetary body). In a preliminary study of the set of values of r especially noteworthy existence of a large number of small values. It is possible that a more rigorous 154 https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1743921314005109 Downloaded from https://www.cambridge.org/core. IP address: 54.70.40.11, on 22 May 2019 at 07:46:41, subject to the Cambridge Core terms of use, available at