Okay, so here's a very basic way of replacing the Bode's Law orbit determination with something that more closely resembles a "realistic" method involving orbital harmonics.
The example system shows only the star and planets. Moons, rings, and other objects orbiting the planets were not included for simplicity's sake.
The table translates a 6D (or 6d6) roll into integer ratios of periods between adjacent orbits. These ratios are converted into decimal multipliers for orbital periods and an orbital radius. Assumptions and knows are listed, a procedure is spelled out, and an example system is given.
Code:
6D: Prat: Pmux: Rmux:
6 10:9 1.111 1.073
7 9:8 1.125 1.082
8 8:7 1.143 1.093
9 7:6 1.167 1.108
10 6:5 1.200 1.129
11 5:4 1.250 1.160
12 9:7 1.286 1.183
13 4:3 1.333 1.211
14 7:5 1.400 1.251
15 10:7 1.429 1.269
16 3:2 1.500 1.310
17 8:5 1.600 1.368
18 5:3 1.667 1.406
19 7:4 1.750 1.452
20 9:5 1.800 1.480
21 2:1 2.000 1.587
22 9:4 2.250 1.717
23 7:3 2.333 1.759
24 5:2 2.500 1.842
25 8:3 2.667 1.923
26 3:1 3.000 2.080
27 10:3 3.333 2.231
28 7:2 3.500 2.305
29 4:1 4.000 2.520
30 9:2 4.500 2.726
31 5:1 5.000 2.924
32 6:1 6.000 3.302
33 7:1 7.000 3.659
34 8:1 8.000 4.000
35 9:1 9.000 4.327
36 10:1 10.000 4.642
o "Prat" is the ratio between the periods of two adjacent orbits (Outer:Inner).
o "Pmux" is the multiplier applied to the period inner orbit to determine the period of the outer orbit
o "Rmux" is the multiplier applied to Orbit 0 to determine the radius of Orbit 1. This is the only time this column is used.
Assumptions & Knowns:
• P^2 = R^3
• R = (P^2)^(1/3)
• P = (R^3)^(1/2)
o Unavailable (UA) orbits are subject to intense heat from the central star and have temperatures of greater thsn 2000 degrees. The "Rock Line" orbit is the outermost Unavailable orbit.
o Inner Zone (IZ) orbits expose worlds to too much stellar radiation; such worlds are hot, dry, and generally inhospitable.
o Habitable Zone (HZ) orbits are in a temperate region where stellar rsdiation is neither too much nor too little. If other factors are right, llfe may exist on worlds in this region.
o Outer Zone (OZ) orbits do not provide enough stellar radiation for worlds; such worlds are cold and inhospitable.
o One "standard" day is 24 hours long.
• Or 1,440 minutes long.
• Or 86,400 seconds long.
o One "standard" year is 365.2421875 days long.
• 365 and 31/128 days long.
• 365 days, 5 hours, 48 minutes, 45 seconds long (365:05:48:45).
• Also called the "Mean Solar Year" or the "Mean Tropical Year".
• This is a real-world value.
o Single-star stellar system.
• Needs work-up for multi-star systems.
o Spectral Class of star is known
• For this discussion, use "G2".
• If Spectral Class is M0 through M9, Size DM for all planets is -2.
o Luminosity, relative to Sol, is known
• For this discussion, use "1"
o "Rock Line" orbit is known (0.300AU)
• A planet in this orbit would be vaporized and dissipated.
• Part of Inner Zone (IZ).
• This orbit cannot be occupied by a planet.
o Inner Zone (IZ) is known (>0.300AU to <0.707AU)
• DM for SIZ is -2 per orbit inward from HZ.
• For all IZ orbits, DM for ATM is -2.
• For all IZ orbits, HYD is 0 (e.g., "Desert World").
• For all IZ orbits, DM for POP is -5.
o Habitable Zone is known (0.707AU to 1.414AU)
• If ATM is 0, 1, or A+, then DM for HYD is -4.
o Outer Zone is known (>1.414AU)
• For all OZ orbits, planetary DM for ATM is -4.
• If orbit is OZ+2 or more, roll 2D for 12 for ATM to be A (e.g., "Exotic").
• If ATM is not 0, 5, 6, or 8, then DM for POP is -2.
• For all OZ orbits, DM for HYD is -2.
• For all OZ orbits, DM for POP is -3.
• If ATM is 0, 1, or A+, then DM for HYD is -4.
o "Frost Line" orbit is known (3.000AU)
• "Frost Line" orbit is part of Outer Zone (OZ).
• Beyond this orbit, there be Gas Giants (GGs).
• Roll 2D for 5+ for each orbit beyond the "Frost Line" to have a Gas Giant.
Procedure:
A) Position orbits around central star.
1) Roll 2D to determine number of planets orbiting central star.
o If star Spectral Class is M0 through M9, apply a DM of -4.
o If star Spectral Class is K0 through K9, apply a DM of -2.
2) Determine radius of "Orbit 0 / Rock Line" in AU from Luminosity of star (1).
o 0.300AU = Radius of "Orbit 0" for G2-V star.
• Note: This orbit is "Unavailable, and therefore empty.
3) Determine period of "Orbit 0" in years from radius of "Orbit 0".
o (0.300^3)^(1/2) = 0.164yr (59.90 days) = Period of "Orbit 0"
• Note: This orbit is "Unavailable, and therefore empty.
4) Roll 6D to determine period multiplier (Pmux) of next orbit outward.
o Example: 6D --> 21
• Note: This example yields 2.000 for Pmux.
5) Multiply period of "Orbit 0" by Pmux to obtain period of "Orbit 1"
o 0.164yr x 2.000 = 0.328yr = 119.8 days.
6) Determine radius of "Orbit 1" from period of "Orbit 1"
o (0.328^2)^(1/3) = 0.476AU.
• Note: This example of Orbit 1 is in the Inner Zone (HZ).
7) Roll 6D to determine period multiplier (Pmux) of next orbit outward.
o Example: 6D --> 28
• Note: This example yields 3.500 for Pmux.
8) Multiply period of "Orbit 1" by Pmux to obtain period of "Orbit 2"
o 0.328yr x 3.500 = 1.148yr = 419.3 days.
9) Determine radius of "Orbit 2" from period of "Orbit 2"
o (1.148^2)^(1/3) = 1.096AU.
• Note: This example of Orbit 2 is in the Habitable Zone (HZ).
10) Repeat steps 6, 7, and 8, for each subsequent orbit.
o Pmux rolls: 21, 28, 19, 26, 18, 24, 20, 20, 24, and 19.
• Prat results: 2:1, 7:2, 7:4, 3:1, 5:3, 5:2, 9:5, 9:5, 5:2, and 7:4.
(continued)