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Re: Stable and unstable orbits and the Titius-Bode law
Piper R.W. Hollier schrieb:
> 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.
Hello Piper and List,
1766
Titius von Wittenburg formulated what has become known as the
Titius-Bode law of planetary distances (r = 0.4 + 0.3 x 2n). The
discovery of Uranus, by Herschel in 1781, further kindled the belief
that there was a missing planet near 2.8 AU.
1794
Chladni inferred an extraterrestrial origin of meteorites. By 1803
Olbers proposed that the meteorites come from an asteroidal exploded
planet.
1801
Piazzi at Palermo discovered asteroid 1 Ceres.
1944
O.J. Schmidt postulated the start of formation of a planet near 2.8 AU,
by accumulation of particles and planetesimals, which was, however,
interrupted by Jupiter's perturbations so that the asteroids resulted
instead.
The Titius-Bode Law in action:
Distance from the Sun Planet Real solar distance
00.0 + 0.4 = 00.4 AU Mercury 00.39 AU
00.3 + 0.4 = 00.7 AU Venus 00.72 AU
00.6 + 0.4 = 01.0 AU Earth 01.00 AU
01.2 + 0.4 = 01.6 AU Mars 01.52 AU
02.4 + 0.4 = 02.8 AU CERES 02.77 AU
04.8 + 0.4 = 05.2 AU Jupiter 05.20 AU
09.6 + 0.4 = 10.0 AU Saturn 09.55 AU
19.2 + 0.4 = 19.6 AU Uranus 19.21 AU
------------------------Neptune-----------------
38.4 + 0.4 = 38.8 AU Pluto 39.52 AU
Well, as you can see, the T-B law doesn't provide any room for Neptune
and becomes relatively inaccurate with regard to Pluto's orbit. But,
alas, we all know that Neptune and Pluto are quite exotic in several
respects.
Best wishes from sunny Germany from Bernd who is now going to switch off
his computer to go and work in the garden :-)
Bernd
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