[seqfan] Re: Another planetary sequence

[Jonathan Post]

I had some related OEIS submissions to these rejected:
.
Bode's law: A003461*, A061654

On Sun, Sep 11, 2016 at 1:44 PM, Rick Shepherd <rlshepherd2 at gmail.com>
wrote:

> That probably effectively describes one such simplification. (Disclaimers
> before this goes far: I'm neither a combinatorialist nor graph theorist --
> although I audited *part* of a graduate combinatorics course once (not the
> related graph theory course)).
>
> I would like as general as possible (too): Really n bodies; e.g., not
> necessarily just one "star". One body could be orbiting multiple bodies. A
> second body could be orbiting multiple other bodies. Maybe both groups are
> orbiting another group of "stars". Also, would like not to restrict moons
> of moons of... other than by n.
> (not really necessarily caring (yet) which are gravitationally stable or
> not)
>
> There seem to me to be several possible sequences here.
>
> Thanks for your reply.
>
> Rick
> On Sep 11, 2016 4:20 PM, "Olivier Gerard" <olivier.gerard at gmail.com>
> wrote:
>
> > 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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> >
>
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