Fooling around with world formulas

[robject]

Anyone who's compulsive enough to tidy up other peoples' messes know what it feels like to find piles of finicky equations, and to suspect there are easier ways of getting at the same results. That's me and world building.

Just seeing what orders of magnitude are needed; what range of results comes out of the data given.

Density (benchmark) = [1 + Siz + Atm + Flux - Orbit Number]

0 or less: Hunk of ice
1 to 5: Rocky core
6+: Metallic core (perhaps partly molten?)

Gravity (in Gs) = Density x Siz / 100

 

[BytePro]

Note, IIRC, world size of 8 is ~ earth size... so Density of 12.5 for 1 G would be required in the above. But note also that earth has a solid (perhaps crystal) mostly iron core.

From a game standpoint surface gravity would be the most relevant.

Mass and density can then be derived if at all relevant.

Exoplanets four times the density of Earth to mere fractions the density of Jupiter have been observed (who knows, maybe hollow planets even!).

 

[robject]

I wonder if core is a tricky situation, then. Outer core molten, inner core solid... wonder if it matters much at that point? Icy, Rocky, Metallic. Starting to sound like an asteroid.

 

[BytePro]

Really, unless you have a planetary geologist in the party, or plan an 'inner world' campaign, interior layout and composition is just flavor... and density is really only of use in determining mass and gravity.

As surface gravity is the most relevant play stat - that is what I would aim to come up with a simple 'generation' rule based on a roll with size, atmo and hydro exceptions/DMs in the flavor of the other generation rules.

This could also help accommodate atmo types that would otherwise be exceptional since one can base this reasoning on gravity (in RL we have seen some really exceptional densities already...).


Note, when desired, the rest can derive from it and the UWP size code ala the simple formula in CT LBB 2 for planetary templates...
For world sizes 1 thru A, and given:
- D = world size code
- Gs = surface gravity in Standard g's
We can obtain...
- R = radius in 100s of km is 8*D
- K = density in Standard densities based on 8*Gs / D
- M = mass in Standard masses of K(D/8)^3
where Standard densities is based on a world size of 8 yielding a Standard g (which for game purposes I would make 10 m/s^2) for a Standard mass.

 

[shaunhilburn]

Anyone who's compulsive enough to tidy up other peoples' messes know what it feels like to find piles of finicky equations, and to suspect there are easier ways of getting at the same results. That's me and world building.

Just seeing what orders of magnitude are needed; what range of results comes out of the data given.

Density (benchmark) = [1 + Siz + Atm + Flux - Orbit Number]

For nickle-iron terrestrial planets, the mean density is logarithmic in proportion to size.

Let r = radius and d = density (relative to earth), then

ln(2d) = ln(2) × r and 2d = 2^r ............. so d = 2^r / 2

The results are approximate; there will be slight variations IRL depending on core size.
For the moon, r=0.273, d = 0.604 = 3.33 g/cc, and for Mars, r=0.533, d = 0.723 = 3.99 g /cc. A super-earth with r=1.5 has d=1.414 = 7.8 g/cc.

Watery/icy bodies (icy moons, failed cores, oceanic superterrestrials) have 1/3 to 1/6 of the indicated density value.

 

[robject]

My next demi-conquest is Temperature. This one is fiddly compared to gravity, and I'm still struggling.

Far as I can tell, the most I can dumb it down still requires knowing star Luminosity (L). I can't get around that, and since Luminosity is google-able, well, I can't shrug it off.

Orbital "Factor" creates a small but fairly straightforward side equation, along the lines of:
F = 1060 / [sqrt(2)^On]

And the last bit, Energy Absorption and the Greenhouse Effect, are some evil combination of Atmosphere and Hydrographics which still eludes me, but apparently results in a value ranging from 0.5 to 1.0 for normal atmospheres, and 0.6 to 1.6 for exotics.

 

[shaunhilburn]

My next demi-conquest is Temperature. This one is fiddly compared to gravity, and I'm still struggling.

Far as I can tell, the most I can dumb it down still requires knowing star Luminosity (L). I can't get around that, and since Luminosity is google-able, well, I can't shrug it off.

Planet temperature isn't something easily 'dumbed-down'.

A star's luminosity, and distance from the star are the main variables determining planet temperature. There's no getting around it.
Googling 'luminosity' will only confuse things, because it can mean either 'visible output' or 'total output' depending on the source.

A star's bolometric luminosity (total energy output, Sol=1) Lb = R^2 × T^4
R = stellar radius (Sol=1)
T = effective Kelvin temperature / 5778 (Sol=1)

Orbital "Factor" creates a small but fairly straightforward side equation, along the lines of:
F = 1060 / [sqrt(2)^On]

That's grossly oversimplifying it.

And the last bit, Energy Absorption and the Greenhouse Effect, are some evil combination of Atmosphere and Hydrographics which still eludes me, but apparently results in a value ranging from 0.5 to 1.0 for normal atmospheres, and 0.6 to 1.6 for exotics.

Lb = bolometric luminosity R^2 × T^4 (total energy output, Sol=1)
Ab = planet's bond albedo (reflectivity at all wavelengths; 0 to 1, Lifebearing worlds 0.27 - 0.32, modern Earth = 0.3)
a = planet's distance in AU
Tg = greenhouse temp (~10K for Snowball Earth, 33K for modern Earth, ~45K for Late Cretaceous Thermal Optimum)

Ignoring internal heat, a planet's temperature (in Kelvin degrees) is:

T ~ 254.5 × (Lb / 0.695 × (1-Ab)/a²) ^0.25 + Tg

Even this is a bit of over-simplification.

 

[robject]

Right! And I'm aiming for an even grosser over-simplification, to wit: when the players hit the dirt, I want to say what is causing them discomfort, and how discomfortable it is.

In other words, I don't need to know temperature so much as effect. That's much easier to wild-ass estimate using the star's luminosity, the world's orbit "number" (from Traveller, and itself a gross simplification; AU is okay too if it's too rough), and the world's Atm and Hyd digits.

The results will be significantly gross.

But the facts is, we have more detailed rules already. Nobody needs me to do it again. And let's face it, nobody would want me to try.

 

[BytePro]

What ruleset are you starting from, btw?

Bk6 is really pretty simplistic, I mean at the level of detail being discussed...

As for temp - Bk6 Habitable zone should be a good starting point, and the Criteria for Orbits defines several useful ranges including a start point for the extremes (i.e. +50/-20 C).

From an ingame perspective, the 'ave' temp of a planet is almost meaningless - at a base minimum, high and low temps might have some limited value. To be useful as a 'calculated' value would necessitate knowing planetary location with respect to such attributes as rotation (tidal locking), orbital inclination and orbital position (time of 'year').

Look at Earth's temps -> ave. ~ 15 C with extremes from ~ +60 to -90 C.

So, unless you intend using a computer, ditch calculating - simply provide a table for base temp relating Atmo/Hydro and orbital zone which references a temperature table. Then use rolls against the indicated table to determine current temp based on season and climate zone (defined for the world map latitude and day/night). A weather table might be in order as well (i.e. rainy, windy).

 

[rancke]

I would start such a table of revised rules something in this vein:

These tables do not provide stars in the proportions current (2012) astrophysicists believe prevail in the universe. They are skewed to provide stars suitable for worlds where humans can thrive and adventures abound.

Roll 2D:

2 <type>
3 <type>
4 <type>
5 <type>
6 Type FV
7 Type GV
8 Type KV
9 Type MV
10 <Type>
11 <Type>
12 <type>

Worlds in the life zone of a Class FV star orbits outside the solar jump limit. [Consequences for jump to and from].

Worlds in the life zone of a Class GV star orbits just outside or just inside the solar jump limit. [Consequences].

Worlds in the life zone of a Class KV star orbits days inside the solar jump limit, but are far enough from the star to not be tidelocked. [Consequences].

Worlds in the life zone of a Class MV star are so and so many days inside the solar jump limit and are tide locked. [Consequences].​

And so on with the more extreme variations.

For temperature, I might use something like this:

2 Frozen
3 Very cold
4 Cold
5 Chilly
6 Cool
7 Earth-normal
8 Warm
9 Tropical
10 Hot
11 Very hot
12 Scorching

And then explain how to calculate the orbital distance that gives that temperature, assuming a baseline albedo and a ditto greenhouse effect.


Hans

 

[BytePro]

I loved Bk 6 - have to say its my favorite book beyond Bks 1-3. But, practically speaking, very few systems were actually ever given Bk 6 treatment in officialdom - and probably not very many by most folks who owned Bk 6.

I might have done 2 or 3 systems total by hand. Then I automated my own version - because the RAW is incomplete for such - which is the only real way to approach system generation. At least one which draws from RW layman science...

Which is where Bk 6 deviated a bit from the other books.

I love formula based approaches - they are great when programming design systems (particularly for spaceship creation). However, for true pen and paper, a much different, story orientated approach, arguably would have been more useful. And made things less prone to becoming readily dated along with avoiding any pretense of being 'realistic'. Which makes things more 'believable' - at least in the sense of suspension of disbelief as opposed to having full knowledge of blatant falsehoods.

Ex: Fictional classifications ala Star Trek worlds ala 'Class M planet' for Earth like planets...

Desciptive details, like density and world composition can just be made up or selected from tables - blatant fantasy, but such is on par with everything else (jump drives, 2D space maps, psionics, etc, etc.). Traveller's mistake with system gen was trying to base it too closely on reality, instead of on story telling and ingame support.

 

[Fritz_Brown]

- M = mass in Standard masses of K(D/8)^3
where Standard densities is based on a world size of 8 yielding a Standard g (which for game purposes I would make 10 m/s^2) for a Standard mass.

But, since K = 8*Gs / D, this works out to
M = Gs(D/8)^2

 

[robject]

I love formula based approaches - they are great when programming design systems (particularly for spaceship creation). However, for true pen and paper, a much different, story orientated approach, arguably would have been more useful. And made things less prone to becoming readily dated along with avoiding any pretense of being 'realistic'. Which makes things more 'believable' - at least in the sense of suspension of disbelief as opposed to having full knowledge of blatant falsehoods.

I think this is sort of where I'm coming from, too.

 

[rancke]

I love formula based approaches - they are great when programming design systems (particularly for spaceship creation). However, for true pen and paper, a much different, story orientated approach, arguably would have been more useful. And made things less prone to becoming readily dated along with avoiding any pretense of being 'realistic'. Which makes things more 'believable' - at least in the sense of suspension of disbelief as opposed to having full knowledge of blatant falsehoods.

I think this is sort of where I'm coming from, too.

That was more or less what I was trying to get at with my post. The one-line comments would actually be about a paragraph or two each, guiding the user of the tables towards whatever kind of world he was looking for as a setting for his adventure(s).


Hans

 

[robject]

That was more or less what I was trying to get at with my post. The one-line comments would actually be about a paragraph or two each, guiding the user of the tables towards whatever kind of world he was looking for as a setting for his adventure(s).

I pretty much agree with that, Hans.

Obviously, I'm not a world builder in the DGP sense.