Mutual Tidelocking of planets and moons

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Mutual Tidelocking of planets and moons

Postby Crucis on Mon 05 Oct 2009 21:21

"Mutual Tidelocking" (MTL) is the situation where the planet AND moon are tidelocked to each other.

In ISF, the chance of MTL is 6%. And in Ultra, chance of MTL is 7% (+1% per extra moon).

HOWEVER, the situation where Mutual Tidelocking is of most serious importance is when a potential Type T planet is tidelocked by its star. In ISF, you simply need to be MTL'd. However, in Ultra, you need to be MTL'd to a "large moon". The problem with Ultra's requirement is that to be MTL'd in the first place, the moon needs to be either fairly large and/or very close to the planet. (This is what the tidelocking formula indicates, not simply an opinion.) You do NOT need some huge "twin planet" to properly MTL a star-planet TL'd potential Type T to force it to back into rotating. If the planet is mutually tidelocked, then it is mutually tidelocked. Period. A planet can be MTL'd with a relatively small moon, if that moon is close enough.

However before this is taken as a total criticism of Ultra, I should also point out that even the 6% number used in ISF (and the 7% number in Ultra) for MTL's is also quite low, from a certain point of view. Let me explain.

In our Solar System, there are 15 "major" moons, i.e. moons having a radius of 500 km or more. And if you compare that to the number of moons that Starfire should produce, it's in the right ball park. Thus, it appears that defining moons in Starfire as "major" (500+ km radius) moons is a respectable definition. (If you were to start reducing the minimum size of moons for Starfire's definition, you would start to greatly increase the number of moons that Starfire's sysgen rules should be producing. And I don't think that that is a good idea.)

But what does this have to do with Mutual Tidelocking? Let me explain. I've done the math using the proper tidelocking formulas using the sizes and masses of the 15 major moons in our Solar system vs. Earth, and came to some very interesting conclusions.

At 5 tac hexes, 1/3 of the Solar System's major moons would mutually tidelock with Earth. And at 1 tac hex, all 15 major moons would MTL with Earth ... all 100% of them. Over the range of 1 to 5 tac hexes, the weighted average comes out to about 55%. Not 6%, not 7%. 55%. (Well, actually 54.6%.)

Here are a rough table of what MTL chances could look like for each range between 1 and 5 tH, based on the mass distribution of the 15 major moons in our Solar System vs the mass of Earth.

Moon Orbit: MTL chance
1 tH: 100%
2 tH: 60%
3 tH: 50%
4 tH: 40%
5 tH: 30%

These numbers are rounded to a comfortable round number (usable against 1d10) from the actual numbers. The reason for the big drop in the % chance between 1 and 2 tH is that roughly 50% of the major moons in our SS are between 500-800 km in radius, with the remaining 50% being dispersed between about 1300 and 2600 km in radius. This chart represents the decreasing likelihood of the moon in questioning being sufficiently large to MTL as range increases.

Clearly, the chance of mutually tidelocking should be MUCH greater if the definition of "moon" in Starfire requires them to be major moons with radii of 500 km or greater.

On the flip side, if the defined size of a moon was locked to a set MTL% that was much lower, you'd end up with much smaller moons, which should a) be much more numerous and b) should have much lower population limits. (Smaller radii mean much smaller surface areas and hence lower population limits.)

Personally, I think that sticking with the definition of Moons as "major" 500+ km moons, and just increasing the MTL chance is the better option since it's a much simpler solution with fewer secondary effects that I can see. I'm not terribly interested in having to worry about comparative surface areas of different sizes of planets and moons and the effect on population limits. It's just a lot simpler to use the current abstracted population differentiation of planets vs. moons.
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Re: Mutual Tidelocking of planets and moons

Postby Cralis on Tue 06 Oct 2009 00:28

For the record, the research Fred did for this section has "newer" information then what Ed and I had for the work done on my SFMV "complex sysgen" research. The change is significant enough that even though we disagree on a few nagging details (such as relative sizes), the fact is that his work is going to force a redo the SFMV moon section.

In other words, Fred has done such a great job I'm stripping a good portion of my moon section out and replacing it with the information from his research. IMHO Fred has done the best job of double-checking the complex sysgen material out of anyone and has the distinction of actually finding something that has changed so significantly that I'm abandoning one of the sections.

I'd support this for COSMIC, guys! His simplifications are spot on and his research is top notch.
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