Planets Galore
This is a lot of fun, so I downloaded the extrasolar data and found several systems with four or more known planets in them. Here are the plots of planet period vs $n$, as in $n = 1,2,3,4$. 
posted by Kea | 9:02 PM
6 Comments:
Regarding 55 CNC (Cancri), it's perhaps interesting that the Titius-Bode law for the solar system has been applied to the distances of planetary orbits in System 55 CNC") on your post:
Arcadio Poveda and Patricia Lara, The Exo-Planetary System of 55 Cancri and the Titius-Bode Law, Revista Mexicana de Astronomia y Astrofisica, v44, pp243-246 (2008)
Although Ivan Kotliarov strongly objects to reviving that law for 55 CNC. I wonder if the other examples support the hypothesis or not?
Thanks for the link, Nigel. I couldn't remember who had looked at this.
Actually, these planets (b,c,e,f) for 55 Cnc line up quite well with n=1,2,3,9.
Nige, thanks for the reference to the 55 Cancri paper about the Titius-Bode Law, which is roughly equivalent to the extension of Kepler's Polyhedral approach that I like (see my web page at
tony5m17h.net/ConformalKepler.html
and the more detailed paper to which it links).
Obviously, I am happy to see that the first Exo-Planetary system to be studied (55 Cancri) has similar structure.
As to the objections by Ivan Kotliarov, I note that the substance of his technical objections seem to be directed at the detailed form of the Titius-Bode formula, which is NOT a valid objection to Kepler's nested polyhedron approach or my extension of it.
Further, there is a more recent paper at arXiv 0903.1732 by Pankovic and Radakovic that provides further physical basis for such results.
Tony Smith
Hi Tony,
Thank you very much for the reference to the paper by Vladan Pankovic and Aleksandar-Meda Radakovic on the relationship between Kepler's 3rd law and the Titius-Bode law. I like the analogy between the Bohr atom and the planetary orbit radii.
Thanks also for the reference to your page http://tony5m17h.net/ConformalKepler.html, the comparison of polyhedral solids is interesting, although it looks headed for Platonic mathematical beauty rather than mechanistic physics that increasing understanding of the dynamic causal processes behind the planetary orbital radii. Presumably in the early solar system there must have been swirling gas and dust clouds around the star which condensed into the planets, a process supposedly set off by the arrival of the debris shock front from a relatively nearby supernova 4,540 million years ago, which delivered heavy elements like iron. It would be nice if there was a theory of the how dust containing different elements at different radii created the planets of different compositions which are now found at those radii. I suppose that secondary fractionation is also important, with the heat from the sun boiling light elements off the nearby small planets (with low gravity) over millions of years, while bigger planets with stronger surface gravity that are further from the sun and less severely heated will lose less light elements. So the mainly soild planets near the sun may initially have had a lot of light elements, which soon evaporated with molecular escape velocity due to the heat, leaving only the heavier rocks as a residue. I wonder if it is possible to model all the processes in a computer simulation?
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