The Table of Kracht Group Comet

Introduction

The Kracht group is discovered and is hereby named after the famous German amateur astronomer Rainer Kracht. Despite being members of sungrazers like the Kreutz group, observations prove that many of them survive perihelion thanks to their relatively larger perihelion distances ($q \approx 8 R_{Sun} - 12 R_{Sun} $). Scientific studies reveal that the Kracht group, along with the Marsden group, 96P/Machholz 1, the Daytime Arietids, and the Southern δ Aquarids are related to each other as part of the larger Machholz Complex (Ohtsuka et al. 2003; Sekanina and Chodas 2005). It is thought that a progenitor comet has split and thus formed these various components of the complex ahead of 950 CE or thereabouts. It is Jupiter that accounts for the current divergence among the orbits as the major perturber after subsequent close encounters. It will be interesting to show their Tisserand's parameters with respect to Jupiter, $T_J$. If the hypothesis is sound, $T_J$ should be strongly correlated.

Before moving on to the table below, we need to derive the heliocentric position of perihelion for the sungrazers.

Let $ i $ be the inclination of a sungrazer's orbital plane with respect to the ecliptic, $\omega $ the argument of perihelion, and $\Omega $ the longitude of ascending node. With knowledge from Euclidean solid geometry, one will not be baffled to compute the heliocentric longitude and latitude of perihelion, denoted as $L$ and $B$ respectively. We obtain

$ L = \Omega + \arctan(\cos i \cdot\tan \omega) $

$ B = \arcsin(\sin i \cdot \sin \omega) $

For less workload I wrote two short routines in IDL to specially perform the computation for me.

 

Data

Orbital elements of the Kracht group comets. Please note that owing to poor precision of LASCO images during astrometry, some of the following linkages are uncertified, and therefore alternative linakges are still possible.

Comparison with 96P/Machholz:

Epoch	P	$q$	$\omega$	$\Omega$	$i$	$L$	$B$	$T_J$	Source
2454205.5	5.24	0.124617662286515	14.61824824802251	94.55063039982306	59.9551168902691	101.99062	12.61898	1.9418219	JPL

Discussion

We can learn that despite the great differences in $q$, $\omega$, $\Omega$ and $i$, the similarities in $L$, $B$, and $T_J$, the Tisserand Parameter with respect to Jupiter, can clearly be noticed, which indicates that the Kracht group comets should be closely related to comet 96P/Machholz. Curiously, Matthew Knight (2008) has analyzed six of the published Kracht group linkages, moreover, 14 Marsden group linkages, each with an elliptical solution and concluded that their Tisserand Parameters range from 1.80 - 1.99 bracketing the value of 96P/Machholz. Whilst $T_J < 2$ suggests an Oort origin, $T_J > 2$ suggests a Jupiter family origin. In the table that lists the Kracht group comets, many of the Tisserand Parameters are less than 2. However, there are significantly some whose Tisserand Parameters are larger than 2, wherefore no definitive conclusion can be drawn that whether or not the Kracht group comets belong to the comets of Oort origin or of Jupiter family origin.

Copyright © Man-To Hui on 2011/11/02

Top

Back... -- Zurück...

Home