The significance of the Titius-Bode law and the peculiar location of the Earth's orbit

Abstract

Using the Lynch method, we continue the discussion on the statistical significance of agreement between planetary distributions and a power law. The Lynch method determines the probability that a power law (e.g. the Titius-Bode law) will agree by chance, at the observed level, with a given sequence of planetary distances. We find interesting results by assuming not only that the mean asteroid-belt distance should be considered as a regular planetary distance, but also that the current distance of the Earth should be regarded as peculiar and omitted from the Titius-Bode law. We examine these assumptions under two cases: (a) where no physical limitations are imposed and (b) where relatively close planetary orbits are excluded. We find that the corresponding sequence of distances matches the power law by chance with a probability of only 0.3 per cent for case (a) and 3 per cent for (b). These values are in direct contrast to those corresponding to the traditional Titius-Bode law as well as those corresponding to some common alternative assumptions. These range from 29 to 100 per cent for (a) and 95 to 100 per cent for (b).

Astrophysics in 2004

“…The Titius-Bode law fits better if you (a) count the asteroid belt as a planet and (b) leave out the Earth (Neslusan 2004). I guess we must agree with (b), since Earth gets a separate section, but if anyone insists on (a) we will quote Abraham Lincoln's question, "How many legs does a horse have if you call its tail a leg?"…”

The meteor-shower complex of comet C/1917 F1 (Mellish)

“…To study the theoretical stream of comet C/1917 F1, we utilize the procedure suggested by Neslušan (1999), which was slightly modified and described in more detail by Tomko & Neslušan (2012). Below, we recall the basic steps of the procedure and their application to the case of the parent comet under study.…”

“…The alternation of the initial orbital corridor can be revealed by modeling the stream and studying its dynamical evolution for a suitably long period. In the past, the meteoroid streams of several parent bodies were studied with help of various stream models (e.g., Williams & Wu 1994;Wu & Williams 1995;Brown & Jones 1998;Asher 1999;Asher et al 1999a,b;Neslušan 1999;Beech 2001;Asher & Emel'yanenko 2002;Lyytinen & Jenniskens 2003;Asher 2005;Vaubaillon et al 2005a,b;Wiegert et al 2005;Kaňuchová & Neslušan 2007;Vaubaillon & Jenniskens 2007;Asher 2008;Babadzhanov et al 2008;Jenniskens & Vaubaillon 2010;Vereš et al 2011;Tomko & Neslušan 2012;Babadzhanov et al 2013;Jopek et al 2013;Neslušan et al 2013a,b;Sekhar & Asher 2013, 2014a.…”

The meteor-shower complex of 96P/Machholz revisited

“…To study the orbital evolution of test particles in the modeled, theoretical stream, we follow the procedure suggested by Neslušan (1999). The procedure, with some improvements, has recently been described in more detail in the paper by Tomko & Neslušan (2010).…”

“…The dynamical evolution of the meteoroid stream of comet 96P/1986 J2 (Machholz 1) is studied within our series of studies of comets in orbits that are situated relatively far from the orbit of the Earth (Neslušan 1999;Tomko & Neslušan 2010). We have already studied the part of the 96P stream related to the Quadrantid meteor shower (Kaňuchová & Neslušan 2007).…”