Bodes law revisited

[Richard Mentock]

Ray Tomes wrote:
>
> lb...@aol.com wrote:
>
> >Im Artikel <32c6b6eb...@aklobs.org.nz>, rto...@kcbbs.gen.nz (Ray
> >Tomes) schreibt:
>
> >>>Planet Saturn Uranus Neptune Pluto
> >>>n 1 2 3 4
> >>>n*9.75 au 9.75 19.5 29.25 39.0
> >>>Actual distance 9.5 19.2 30.1 39.4
>
> >>>Planet Mercury Venus Earth Mars
> >>>n 1 2 3 4
> >>>n*0.35 au 0.35 0.7 1.05 1.4
> >>>Actual distance 0.39 0.72 1.00 1.52

Let's try something simpler, with less factors. Kepler's law
says that T^2 = (4 * Pi^2)/(G * M) * r^3, where T is period and
r is radius. If we use astronomical units to measure r, and
years to measure T, then the formula is simply T^2 = r^3.

Or, r = T^(2/3)

Set up the planets so that each planet has twice the period T of
the planet before it. This sets up a nice resonance condition.
In the following table, r is computed as above, whereas R is the
actual planetary orbit radius.

Planet n T r R r/R
Mercury 1 0.25 0.40 0.39 1.03
Venus 2 0.5 0.63 0.72 0.87
Earth 3 1 1.00 1.00 1.00
Mars 4 2 1.59 1.52 1.04
Asteroids 1 5 4
Asteroids 2 6 8
Jupiter 7 16 6.35 5.20 1.22
Saturn 8 32 10.08 9.54 1.06
Uranus 9 64 16.00 19.18 0.83
Neptune 10 128 25.40 30.06 0.84
Pluto 11 256 40.32 39.52 1.02

Not bad, huh? Two asteroid belts, as some astronomers
believe, and the worst ratio is there at Jupiter, which
has probably swept up some of the asteroids and has
moved into that orbit somewhat.

--
D.

men...@mindspring.com
http://www.mindspring.com/~mentock/index.htm