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Stable and unstable orbits and the Titius-Bode law

Hello Julia, Ron, Bernd, and list,

At 21:21 25-05-99 -0400, Julia wrote:

> [snip]
>And now that the technicalities have been resolved somewhat, I can see alot
>of room for questions.  Anyone?  I plan to save mine for a rainy day:-)

OK Julia, I will take the bait...

In 1766 Titius van Wittenburg derived a formula which expresses with
considerable accuracy the pattern in the spacings between the planets:

   r = 0.4 + (0.3 x 2**n)

This formula has become known as the Titius-Bode law, honoring both Titius
and J.E. Bode, who gained widespread publicity for this formula by arguing
that it indicated that a planet was "missing" between Mars and Jupiter --
this was several decades before the discovery of the asteroid belt.

Practically every mention I have ever seen of the Titius-Bode law in
astronomy texts has added a disclaimer reading more or less: "This
relationship has intrigued astronomers for centuries, but they now attach
little significance to it: it may just represent the closest possible
spacing of stable planetary orbits." (from Robert T. Dodd's "Thunderstones
and Shooting Stars").

Does anyone know whether recent advances in computer modeling or other
theoretical developments have determined that this systematic spacing of
the planets can somehow be derived from fundamental principles of physics
c.q. orbital mechanics?

Best wishes to all,

Piper

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