Sir Chaos wrote:
So... sorry. I´m pretty sure working with orbital resonances as you originally suggested would create great (and quite possibly more realistic) planetary systems than what I settled on, but the complexity of the math involved puts it beyond the scope of what I want to do.
It needn't be too bad, though whether it meets your criteria is a matter of how good the user is at mental arithmetic. Two digit by three digit multiplications ought to be good enough.
Start at the innermost planet and work outward, or at the outermost and work inward, or at the most important one and work both ways. Roll dice. Consult at table, which will tell you what resonance is next and give you an orbital radius factor. Multiply the current orbit's radius by the factor off the table to get the radius of the next orbit, rounding up. Very like what GURPS Space 4th ed. does (Step 22, pp108–109), except that having radius factors of 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, and 2.0 you have factors corresponding two the 2/3 power of common small-integer ratios: 1.21 (4:3 resonance), 1.31 (3:2 resonance), 1.37 (8:5 resonance), 1.41 (5:3 resonance), 1.45 (7:4 resonance), 1.48 (9:5 resonance), 1.59 (2:1 resonance), 1.76 (7:3 resonance), 1,84 (5:2 resonance), 2.08 (3:1 resonance).
You can master a lot of difficult calculations with table look-ups.
I don´t have linear radius factors in the current line of thought - I have logarithmic ones, currently leaning towards calling them "orbital shells": Shell 0 is at 1/128 AU, a bit less than 1.2 million km, and Shell 70 is 1 AU. A distance of 10 shells doubles radius. So with 1d6+4 shells between two occupied orbits, we´d be at 1.41, 1.52, 1.62, 1.74, 1.87 and 2.0 approximately.
The advantage I see in these is that, with luminosity and black body temperature also abstract values on a logarithmic scale, and the change of energy received over distance subject to the inverse square law, black body temperature decrease from shell to shell is nicely linear: -1 per shell.
On the other hand, using the ratios you supplied, calculating black body temperature change from one occupied orbit to the next is going to awkward. At the distance for a 2:1 orbital resonance, the difference in black body temperature would be about -6.69 on the logarithmic scale, or about -60.4% energy received.
Although... we could always call those radii approximate numbers. A shell isn´t really a narrow circle with an exact radius, it´s a region of space extending about 3.6% in either direction (each shell is about 7.2% further out from the star than the previous one).
Let´s say you roll 1d6 and check the result on a table:
1 - 3 shells (factor 1.23 - close to the 4:3 resonance)
2 - 4 shells (factor 1.31 - 3:2 resonance)
3 - 5 shells (factor 1.41 - 5:3 resonance)
4 - 7 shells (factor 1.62 - close to the 2:1 resonance)
5 - 8 shells (factor 1.74 - close to the 7:3 resonance)
6 - 9 shells (factor 1.87 - close to the 5:2 resonance)
This way, I can continue to use my shells, (abstract) black body temperature continues to be easy to determine, and the orbits are close enough to being scientifically justified for a layman´s work.