KEPLERIAN DISTRIBUTION...
And I well thought I wouldn't come back to the BUILDING BLOCKS section, ha, I was pretty wrong I guess.
SO, last time we scratched a talk about placing planets in their orbits (PART 4), we saw what I now call 'Keplerian Distribution', in short, you set a base number, usually 0, and build up a progressive sequence with some sum or subtraction over it, and there are your planetary orbits.
If we take a look at our solar system, we will notice how planets are spaced.Mercury - 0,38 AUVenus - 0,73 AUEarth - 1,00 AUMars - 1,52 AUJupiter - 5,2 AUSaturn - 9,5 AU- -Johannes Kepler when measuring the Solar System, noticed that if we begin a sequence at 0, 3, 6, 12, 24, 48, 96... and so on, added 4 and divided by 10.4, 7, 10, 16, 28, 52, 100... /10 = 0,4 AU, 0,7 AU, 1 AU, 1,6 AU, 2,8 AU, 5,2 AU, 10 AU...
Of course this kinda works well because stable orbits form from orbital resonances, and those really have a progressive mathematical relationship.
The original Keplerian Distribution falls like:
A = ([0, 3, 6...] + 4) / 10
Repeat the procedure for every planet you have to put in place.
Keep in mind that although I stated C is any given value between 0 and 10, that is not quite a rule, but also, your orbits that fall outside the outer boundary of a star system (forty times the host star mass in AU) must be excluded if so.
I've made a Keplerian Distribution Graph in case you having any problems in visualizing what's going on.
- M.O. Valent, 28/06/2019
Hello! This entire blog has been incredibly fascinating to go through and enlightening in a lot of ways. Thank you and your group so much for sharing this wonderful process with the internet, it's also been incredibly helpful with my own projects in regards of understanding some difficult bits.
ReplyDeleteBut the reason I'm commenting in this page in specific rather than the more recent ones is because I have a question.
As I've been double checking some orbits, I decided to give your Keplerian Distribution a go for the funsies, using Vol's System as a check to confirm if I got the formula done right in my spreadsheet.
That's when I stumbled into something weird. According to this post, you utilized 6 orbits and gave each a celestial body of sorts (Veek at 0.31, Hool at 0.58, Paart at 1.11, the Comet at 2.15, Seey at 4.2, and Lahaart at 8.26), but as I replicated the formula, Paart's and forward objects' orbits didn't line up.
In my spreadsheet, Paart's Orbit was at *0.83* instead of the closest approximate 1.34. Even with the general differential margins, that one felt too much unless there was space for a hidden unaccounted orbit. ( https://i.imgur.com/saWMVCU.png )
So my question is: Was this Hidden Orbit intentional or just me replicating this entire formula wrong?
Thank you again for your time and progress with your system!
Hello there - thank you for your support.
DeleteI now understand I wasn't clear enough with that section (I were way less experienced in writing). So you somewhat replicated it wrong in a way.
It said
"For the Vol System, I came up with 0, 2,5, 5, 10, 20, 40.
For the first, I added 3.
For the others, I added +0.1 point according to each position after the star, and sum the previous orbit value.
And divided everyone by 10.
0+3+0.1, 2,5+0.2, 5+0.3, 10+0.4, 20+0.5, 40+0.6.
/10"
So I understand that anyone would have followed like:
(5+0,3) + (2,5+0,2) = 0,8
among other ways to mix and match these numbers
However what I actually meant and did was to pick the number, add 0,1 according to the place (so the 2nd receives +0,2, the 3rd +0,3 etc).
With the exception that the 1st one receives 3 + 0,1.
All of these numbers are then divided by 10.
And the sum with the previous orbits.
So Veek doesn't sum any because it's the first.
Hool sums the orbit of Veek.
Paart sums the orbit of Hool and Veek... and so on
below is the table I've done to reproduce that, since I have lost my original sketches.
(https://imgur.com/a/Q00VhEe)