Physical Planetography: Orbital Parameters

Introduction

The first stage of any physical planetbuilding is to figure out where the planet is, and the best way to do that is to build up the system.  This post will mostly be regarding a small bit of research I’ve been reading on spacing between planets and gas giant moons in the Solar System. Moons orbiting gas giants seem to be spaced in a manner analogous to the spacing between planets in a solar system.

Now the real first step for this process would be to figure out the parameters for your star. I don’t really want to deal with stellar population distribution in this post(this is taking long enough to write as it is), but I will supply some data to help folks get a start.

Step 1: Star selection

“>World-Building

Stellar Data
Spectral Class Temperature(K) Luminosity(Sols) Radius(Sols) Mass(Sols) Lifetime(years)
Data selected from Gillett,S., <a href="http://www.amazon.com/gp/product/158297134X?ie=UTF8&tag=astrographer-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=158297134X
O5 40,000 810,000 18.7 35.9 440,000
B5 16,000 810 3.7 5.8 72,000,000
A5 8,600 19 1.94 2.16 1.2 billion
F0 7,300 8.5 1.82 1.75 2.1 billion
F5 6,600 3.9 1.50 1.43 3.7 billion
F7 6,300 2.4 1.31 1.27 5.2 billion
G0 6,000 1.4 1.10 1.09 7.8 billion
G2 5,770 1.07 1.03 1.02 9.5 billion
G5 5,600 0.81 0.95 0.95 12 billion
G8 5,400 0.61 0.89 0.88 14 billion
K0 5,200 0.41 0.78 0.79 19 billion
K2 4,800 0.29 0.78 0.72 25 billion
K5 4,400 0.19 0.74 0.64 35 billion
K7 4,200 0.11 0.62 0.55 52 billion
M0 3,900 0.061 0.54 0.48 78 billion
M2 3,500 0.039 0.53 0.42 110 billion
M4 3,200 0.024 0.51 0.38 150 billion
M6 2,900 0.013 0.45 0.32 250 billion
M8 2,500 0.0015 0.21 0.18 1.2 trillion(10^9)

Solar radius = 696,265 km

Solar mass = 1.9891 x 10^30 kg

Solar luminosity = 3.88 x 10^26 W

Solar temperature = 5,770 K

For now, let’s just pick a star class from the list. Eventually, my goal is to put together a fully developed world-building sequence. We’re not there yet…

Step 2: Initial orbit

I’ve seen the distribution of planetary orbits done in a number of ways in several science-fictional RPGs. In MegaTraveller(the ’80s were truly the glorious heyday of oBnoXioUs capitalization) they used a straight, rigid unvaryingly dull Titius-Bode rule. Yawn. In Gurps Space and GURPS Traveller First-In, they used a modified, slightly randomized version of the Titius-Bode rule. This added some interest, but lacked realism and was still a bit rigid. If you know the orbital distance of the first and second planets, you knew the whole system. Ross Smith’s otherwise respectable Planet Generation System dealt with orbital distances in a far more abstract manner(though, you can make an educated guess as to star mass from its known class and use the orbital period in section 4.1 to figure it out. No guarantees that what you get will work for a habitable planet, but hey…). I still steal ideas from him from time to time, though. The well-known Accrete program uses a more sophisticated(by 1960s standards. Hey, they could send a man to the moon back then, can we do any better?) system, but it might be a bit cumbersome for paper-and-pencil applications. Traveller:2300 and the closely-related 2300AD, used a different system, with a randomly selected initial orbit and then randomly selected multiples of each previous orbit as you moved outward. This system was also used by the latest version of GURPS Space(with some kind of modification due to pre-generation of gas giant planets. I haven’t used it yet, but I’m intrigued), and Tyge Sjöstrand’s marvelous, but still incomplete World Generation pdf (if anyone knows how to contact Mr. Sjöstrand, let him know I am interested in helping him complete that thing).

Anyway, for initial orbit, I figure I will use that given in First-In, namely:

The larger value of

R = 0.2 x Mstar/MSol or

R = 0.0088 x Sqrt(Lstar/LSol),

Where: Mstar = mass of the star ; MSol = mass of the Sun

Lstar = luminosity of the star ; LSol = luminosity of the Sun

Mstar/MSol = mass of the star relative to the Sun’s mass

Lstar/LSol = luminosity of the star relative to the Sun’s luminosity

Step 3: Additional Orbits

For my own purposes, I used a list of the ratio of semimajor axes(q_n = a_[n+1]/a_n) of all NINE planets and a selection of gas giant moons given on pages 16-20 of Evolution of the Solar System by Hannes Alfvén and Gustaf Arrhenius(1976, NASA). After I ran the list through a statistical analysis routine in my calculator(HP-48GX, cost $200.00 back in, like 1994. Probably less capable than an iPhone with Mathematica). I have a Java program that can generate pseudo-random numbers on a normal distribution, which is good, because it would take awhile for me to figure out how to approximate this with die rolls.

Mean = 1.82 ; Standard Deviation = 0.9998 ; Variance = 0.9996 ; Maximum = 6.12 ; Minimum = 1.02 ; Median = 1.545.

Looking at the maximum and minimum, here, you can see how this might be hard to generate with less than percentile dice. Those long tails matter. I reroll any result less than 1.02. Doesn’t happen too often, but a normal distribution should have infinite range to either side of the mean(in practice, the computer program has a large but finite tail length). Maybe I should use an exponential distribution?

Suddenly, I realize that I can create a table from a histogram analysis of my list. That would make me a bit less tied to the computer.

With this information, you should be able to get as far on the orbital parameters of your own conworld as I have on Sadwillow, although I generated orbits in Sadwillow’s system some time ago, using the modified Titius-Bode method from First-In.

Thank you for your attention,

Colin

 

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One Response to Physical Planetography: Orbital Parameters

  1. Pingback: Developing a Workflow – Part III: Orbital Positions | Astrographer

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