[seqfan] Re: Another planetary sequence
Olivier Gerard
olivier.gerard at gmail.com
Sun Sep 11 22:19:47 CEST 2016
On Sun, Sep 11, 2016 at 9:12 PM, Rick Shepherd <rlshepherd2 at gmail.com>
wrote:
>
> A category of planet-related sequences of interest (in general to me, and
> combinatorially) is number of types of planetary/star/moon orbital systems,
> probably under various simplifying assumptions (the 3-body problem having
> not been solved yet).
>
> [...]
>
> For simplicity, maybe start with counting all orbital situations that can
> occur with all orbits elliptical and coplanar... Moons can have moons, etc.
> Include rotations or not. Retrograde orbits or not. Well-defining
> equivalence classes of orbital systems may be a bit tricky still.
>
> (I'm deliberately ignoring Figure-8 orbits and such for now.)
>
>
What you describe looks to me essentially like rooted planar trees of
height at most 2
(if we discard moons of moons):
The star as the root, the planets as nodes of depth 1, the moons as leaves,
...
The order of the planet is fixed by the planarity and a reading order
convention.
Including retrograde orbits is just like adding binary coloring to the
edges,
including rotation is binary coloring of the nodes while chosing arbitrarily
one of the colours for the root.
Am I missing something ?
Regards,
Olivier
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