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.
Refers the distance of the planets from the sun.
with the exception of , where
The distance of the i-th planet is given by this formula.
Relative to our solar system:
|Planet||T-B rule distance||Real distance|
|w:Ceres (Dwarf Planet) + w:Asteroid field||8||2.8||2.77|
|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.
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 nth 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.
Kepler's third law
T2 ∝ R3
Basically: Period is proportional to distance from sun to the power of 1.5, or:
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.
- 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.