Talk:Color Spray Nebula

Anyone know how far this thing is from the sun? I want to put it on a map for my campaign. ~ Lhynard (talk) 22:31, March 10, 2018 (UTC)


 * Unfortunately, not only is this information not present in Realmspace, but the planets in the Torilian system do not obey Kepler's third law (no reason why they should anyway), so we cannot use it to estimate the distance based on the orbit duration (4000 months). However, the planetary orbits in Realmspace do seem to follow some pattern, which may allow us to derive an unofficial distance:


 * By performing linear regression on the orbital periods as a function of distance, they seem to follow pretty well the following expression:


 * $$r = e^a P^b$$


 * where P is the orbital period, r is the distance from the sun, and a and b are the parameters to be fitted. With a pretty good ($$\chi^2 = 0.97$$) accuracy, one finds the parameters to be $$a = 2.4$$ and $$b = 0.46$$, which would put both nebulae at a distance of approximately 2,500 million miles from the sun. &mdash; Sirwhiteout (talk) 00:48, March 11, 2018 (UTC)


 * The only problem with that is that the crystal sphere of Realmspace only has a 3.2-billion-mile radius. That much is clearly stated in Realmspace. ~ Lhynard (talk) 01:36, March 11, 2018 (UTC)


 * Thanks for pointing that out. I actually meant "million" on my previous comment (and fixed it). So the nebulae would be at 2.5 billion miles, well within the sphere's boundaries. &mdash; Sirwhiteout (talk) 02:50, March 11, 2018 (UTC)


 * Ha ha, that makes a lot more sense. I'll probably use that value for my campaign. ~ Lhynard (talk) 06:01, March 11, 2018 (UTC)


 * Sorry about that, I made this calculation in a hurry (it's been terribly busy here these days). I also corrected the equation above (I had exchanged period and radius when writing the expression here, but the result still holds). I'll see if I can refine that result into something simpler if I have time. It seems highly likely that this is no coincidence, but why not follow Kepler's law? Maybe this new law has a name?


 * I also added K'Thoutek to the analysis this morning. It still follows the same pattern, but only if you consider its aphelion distance instead of its semi-major axis. So, if you want to place a new comet in the sphere, you can still use that equation. :) &mdash; Sirwhiteout (talk) 13:02, March 11, 2018 (UTC)


 * I &hearts; Sirwhiteout. &mdash;Moviesign (talk) 14:34, March 11, 2018 (UTC)