Conplanet/Space/Solar System

Our solar system has, err.... 11, no..... 9..... ah! 8 planets, a Sun and plenty of asteroids and moons.

Distance approximation formulas

You have 2 to choose from. Take your pick.

Titius-Bode law

Wikipedia Article

Refers the distance of the planets from the sun.

$R_{i}=0.4+0.3\times 2^{i-2}$

with the exception of $i=1$, where $R_{1}=0.4$

The distance of the i-th planet is given by this formula.

Relative to our solar system:

Planet	$2^{i-2}$	T-B rule distance	Real distance
Mercury	0	0.4	0.39
Venus	1	0.7	0.72
w:Earth	2	1.0	1.00
Mars	4	1.6	1.52
w:Ceres (Dwarf Planet) + w:Asteroid field	8	2.8	2.77
Jupiter	16	5.2	5.20
Saturn	32	10.0	9.54
Uranus	64	19.6	19.2
Neptune. Pluto (Dwarf Planet) exists at this point, though.	128	38.8	30.06
Pluto (Dwarf Planet)	256	77.2	39.44

The law works on the fact that planets settle in relative ratios to each other, however, the problem with Neptune has discredited this formula.

Dermott's Law

The little-known Dermott's Law. I can only quote Wikipedia, one of the few web references on the subject (all other references are essensially repetitions of the same text):

Wikipedia Entry on Dermott's Law, accessed on 24th Feb 2007

Dermott's Law is an empirical formula for the sidereal period of major satellites orbiting planets in the solar system. It was identified by the celestial mechanics researcher Stanley Dermott in the 1960s and takes the form:

T(n) = T(0).Cⁿ

where T(n) is the sidereal period of the n^th satellite, T(0) is of the order 0.46 and C is a constant of the planetary system. Specific values are:

• Jovian system:     T(0) = 0.444; C = 2.03
• Saturnian system: T(0) = 0.462; C = 1.59
• Uranian system:    T(0) = 0.488; C = 2.24

Such power-laws may be a consequence of collapsing-cloud models of planetary and satellite systems possessing various symmetries; see Titius-Bode Law. They may also reflect the effect of w:resonance-driven commensurabilities in the various systems.

Orbital period

One option.

Kepler's third law

T² ∝ R³

Basically: Period is proportional to distance from sun to the power of 1.5, or:

$Period\propto {\sqrt {Distance^{3}}}$

Tweaking to make more physics-compatible

Okay, so you have your basic numbers now. Tweakin' time!

Preventing Orbital Disturbance

First off, we'll need to prevent one planet's orbit from disturbing another planet's orbit (so it'll remain stable for more than a few years after its birth).

This means that ...

Section is U/C.

External links

• http://www.reference.com/browse/wiki/Orbital_resonance : A very good page on ratios between planets - use these in your solar system!
• w:Titius-Bode law
• w:Dermott's Law : Hardly any information, includes 4 useful ratios for 4 systems (including our own) though.
• Non-titius but regular spacing of moons: http://www.floridastars.org/9605cohe.html
• w:Orbital period : Skim through this, you'll pick something up.