GURPS Space World Building Issue

[Roh]

I am running into something I seriously can't puzzle out here. On Step eight it says "Finally, for any world type other than Asteroid Belt, multiply the result by the square of the world’s diameter (measured in Earth diameters).".

To me this seems to be saying use the decimal generated based on earth being 1. Squaring a decimal... Would give me a smaller decimal wouldn't it? I'm bad at math but I tried to find something on the web to tell me other wise I couldn't. While if the world had been just 1 then that would make a considerably larger change in the final number but... Still not seeming even remotely correct. Exactly what the hell am I supposed to square? Can anyone clear this one portion up for me?

[David Johnston2]

Originally Posted by Roh

I am running into something I seriously can't puzzle out here. On Step eight it says "Finally, for any world type other than Asteroid Belt, multiply the result by the square of the world’s diameter (measured in Earth diameters).".

To me this seems to be saying use the decimal generated based on earth being 1. Squaring a decimal... Would give me a smaller decimal wouldn't it? e?

Yes it would. Just go ahead and do it.

[Diomedes]

The math is correct. That calculation is essentially modifying the population capacity by accounting for the surface area of the planet, which is proportional to the square of the diameter. So a planet of 0.9 Earth diameters will have only 0.81 times as much surface area as Earth, while a planet of 1.2 Earth diameters will have 1.44 times as much.

Basically, the square means that getting farther away from 1 will have a disproportionate effect.

[Roh]

I must have gotten something very wrong in the math. It was going to have the population cap at under 200 million for a planet that was over 5000 miles in diameter. At tl 10. That just seems... Questionable.

[Humabout]

Originally Posted by Roh

I must have gotten something very wrong in the math. It was going to have the population cap at under 200 million for a planet that was over 5000 miles in diameter. At tl 10. That just seems... Questionable.

We need your numbers. What is the world's affinity, diameter, and TL?

[Roh]

I had actually already gotten rid of them. But... roughly 0.5 diameter, 7 affinity, TL 10, 50% ocean coverage... Aaah. I can't remember most of the other attributes but I plan to start over tomorrow. First thing is I'm going to make that World sheet fillable instead of making ugly text files.

[David Johnston2]

If your affinity is 7 then the base would be 130 million times 20 million or 2.6 billion. After applying the diameter modifier it should have been about 1.2 billion with a 5.000 mile diameter. 5,000 miles isn't .5.

[Myrion]

I wanted to shamelessly plug my Starsystem generator which takes care of all the fiddly maths for you:
http://ultima.vsos.ethz.ch/starsystem-gen/
With the source here:
https://github.com/tschoppi/starsystem-gen/

However, it seems that something broke on the server, which I'll have to fix tonight.

[Roh]

Okay then I was right on track up until 130 million then. I broke down at the squaring the planets diameter(in earth diameters). I'm very bad with math. And from the wording I couldn't see how the instructions weren't going to make the number smaller not larger.

And it seems like I screwed up at the diameter too. Which I did find kind of confusing but I had though I managed to muddle my way through.

[whswhs]

Originally Posted by Roh

Okay then I was right on track up until 130 million then. I broke down at the squaring the planets diameter(in earth diameters). I'm very bad with math. And from the wording I couldn't see how the instructions weren't going to make the number smaller not larger.

Well, they were. Say for example that your population base is 2.6 billion. That's how many people Earth could sustain at its TL and affinity score and so on. But say your planet's diameter was half of Earth's. Then it would have only one-fourth the surface area. With the same number of people per square mile, and one-fourth the square miles, you get one-fourth the number of people. And one-fourth of 2.6 billion is 0.65 billion. That's how it's meant to work.

Suppose, on the other hand, that the planet had 1.5x Earth's diameter. That's 2.25x the area. That would give you 5.825 billion. Having a lot more people on a bigger planet seems right, yes? But if a bigger planet has more a smaller planet should have fewer.