Average number and type of planets orbiting given star types I don't need "exact" numbers, but I'm trying to create an auto-generator for a stellar map to crate stars that are "somewhat" accurate.

I'm looking for numbers on the average number and type of planets around each type of Star, and whether they could be a good source for mining or are they good places for life?

So, like, I need an idea of how what is the average number of planets that are expected around a G class star, how many are expected to be Gas giants or terrestrial and what is the likelihood of them being in the habitable zone and containing life. 

If I base it on Sol I would suspect about 10 planets, 50% terrestrial and 50% gas giants, with 1 to 3 in the habitable zone and a 30% chance of life developing. I'm looking for something similar to this type of information.

I assume this wouldn't be good for across the board or even for G class stars in general.

So I guess I'm looking for estimated planetary statistics based on spectral type? I don't want a list of exoplanet and stars that I have to look through and then make a bad guess at, but a good estimation of these numbers based on known facts.

This Question doesn't have a simple enough answer for me to grab onto to use effectively without just making too much stuff up anyways.

This Question seems to have pieces of information that I'd use to work something out, but it would likely by far more inaccurate than what other people would come up with and there might be better answer than that so I ask my question.
I wrestled with this one a bit, but because there's no real scientific answer to it, your best bet might to look at the 6 or 8 best known other solar-systems and build off that.   There's no right answer, so a base off evidence approach is probably the way to go.

Or, if you want to base it off nonsense, but sound impressive, you could use the Titius-Bode law.   But I think that's a bad idea, unless large gas giant planetary migration is kept to a minimum, because a migrating Jupiter would make mincemeat of that "law".  

The easiest exoplanets to find are planets with short orbits and the easiest stars for us to find planets around are smaller stars.   

With those limitations to your view, given that large planets are easier to see, it's hard to say how many smaller ones are out there or how many distant planets from their star.   There's basically zero information to build on regarding those 2 points.   



A few generalities though, just for fun.

Rocky planets like the 4 inner planets in our solar system form inside the the Frost Line.  These planets are very low water by percentage.    Now, you could look at the Earth and say "there's tons of water on Earth", but there's really not, at least, not in terms of water to silicate ratio.   Much of Earth's water is on the surface, so we see lots of water, but Earth is basically Iron, Nickle and Silicates with less than 1/3 of 1% of water by volume (even less by mass).   By volume, (using the 860 mile diameter sphere pictured below and from this article).  Earth is about 1 part in 800 water by volume.   



There may be as much or more water trapped in Earth's mantle than in the oceans, so the ratio might be closer to 1 part in 400 or there abouts, but the point remains the same.   If Earth is 0.25% water by volume, it's mostly made of stuff that isn't water.

Ceres, by comparison, may be as much as 25% water.  See here and here.  That's 100 times as much water to dry material ratio.   Outside the Frost-line you're going to get very different types of planets.  

Over time, you have to figure atmospheric changes, which planets will lose their atmosphere and which planets will heat up like a greenhouse.   

Now lets take 3 types of stars, one with 1 solar mass like our sun, one with 0.4 solar masses (red dwarf) and one with 2.5 solar masses (very bright star).

Our sun has a lifespan of roughly 10 billion years and a frost-line, currently at about 2.7 astronomical units (roughly Ceres distance from the sun), but when the sun was young and the planets were forming, our sun was some 30% less luminous, so the frost-line would have been (.7)^.5 * 2.7, or about 2.2 AU.   Now different frozen gases have different frost-lines, but this is just an approximation.   The fact that Ceres is about 25% water even though it's losing water to empty space implies that it formed outside the frost-line where frozen water was abundant.   Ceres is just one example.  All the large moons of the outer planets are also ice and rocky composites.  

So, take our 0.4 solar mass red dwarf - a very common type of star.  It's luminosity (0.4)^4th power, is about 1/39th as bright, so it's frost-line would be a bit over six times closer in, less than 0.4 AU.   With less gravitation it might not have a much smaller disk of spiraling matter at the time of formation, so a much larger percentage of the material that forms our red dwarf's solar-system would probably form outside the frost-line, which would imply, fewer 99% dry rocky worlds and more wet (25% water) worlds.   We have many worlds like that in our solar system, but they're all moons or dwarf planets.   Ceres, Ganymede, Europa, Titan, Triton, many others are icy-rocky composites that formed beyond our solar-systems frost-line.   

Many of the Kepler observed exoplanets have densities that suggest "water-worlds", many of them larger than Earth.   This fits with the red-dwarf, closer in frost-line argument.   We have no way of knowing how many rocky worlds smaller stars have, but I think it's a safe bet that they have a lower ratio of 99% or greater dry material worlds like our 4 inner planets simply because of the smaller zone inside the frost-line.

The reverse is true for the 2.5 solar mass star.   It also has a short lifespan of 10 billion / (2.5)^3, or about 640 million years, so there's less time for the planets to form, get past any early bombardments and cool down.    And the frost-line for our 2.5 solar mass star would be about 14 AU when the star is in it's early life, some 6 times further than the frost-line in our solar-system, so that's likely a much greater "dry" region for planet formation.   You probably get a higher percentage of rocky worlds around larger stars, so a star 1.5 or twice as bright as our sun could (in theory) have 6 or 8 rocky worlds of varying sizes ranging from hot to cold.  At least, I think it could, though I'm pretty sure this has never been observed.  

Gas giants are fairly simple in nature.   All a gas giant needs to form is sufficient gravity to retain it's hydrogen and helium and a source of hydrogen and helium to collect.   A gas giant is more likely to form outside the frost line, but there's no reason why a gas giant couldn't form inside the frost-line.  You'd need about 8 earth masses of a rocky world at Earth temperatures to have a sufficiently high escape velocity that it could retain hydrogen and Helium and in theory, grow into a gas giant, but further away from the star where there's less solar heating, the amount of mass needed goes down with cooler surface temperatures, and with the additinoal mass of ices outside the frost line, it's probably far easier for gas giants to form outside the frostline than inside.  

The next thing to consider is Planetary Migration.  

Take our Solar-system for example.  There's a theory that Neptune and Uranus may have formed formed inside Jupiter and Saturn, but Jupiter and Saturn pulled them outwards as they drew inwards, perhaps because in the early solar-system there was a period when Jupiter and Saturn were in resonance.  

It's also possible that there were 3 large gas giant planets in our solar-system initially.   (not counting Neptune and Uranus as "large" gas giants).   The 3 gas giant model helps explain the formation and water content of the 4 inner planets.

And it's also thought that Jupiter migrated inwards towards the sun, then back outwards.   If Jupiter had kept migrating inwards, which may be the case for several hot Jupiter planets that have been observed, then there's no telling what would have happened to the inner planets, perhaps scattered every which way, some out of the solar-system, pushed too close to the sun or swallowed by the migrating hot Jupiter.  A migrating hot Jupiter would wreck havoc with smaller inner planets as they crossed orbits.   

As it is, our own Jupiter may have tossed a large gas giant planet completely out of the solar-system and perhaps made Neptune and Uranus switch places.    (all this is just numerical model based hypothesis, but several articles have been written about these ideas).

Here's a very cool video, if you have some time that runs models on planet formation on "sol" like systems, estimating planet size, location and including how much water the inner planets are likely to get from comets.   Earth, it's thought, got most of it's water from comets and asteroids, largely thanks to Jupiter's migrations.

If you skip forward to about 20 minutes 40 seconds in, you'll see he's computer modeled several different scenarios on planet formation with different gas giant combinations.   The chart shows eccentricity on the y-axis and distance from the star on the x-axis.  As eccentricity goes to one (top of the y-axis), the object is either sent outside the solar-system or close enough to the sun to get vaporized, so basically the dots you see flying up and out of the chart are leaving the solar-system one way or another.

There are, ofcourse other factors, mostly unknowns, like how much material is likley to be available for planet formation when a cloud of matter forms into a solar-system.   Our sun, for example, is something like 99.8% of the mass of the solar system with just 0.2% making up all the other stuff, but I don't know and I don't think anybody knows if that 0.2% is standard, higher than average or lower, and how larger stars might have different ratios than smaller onces, or how much of the material that gets blown off a star in it's young life gets captured by it's orbiting, forming planets.   

It's entirely possible that more planetary material can lead to larger but fewer planets as larger planets tend to sweep out a bigger area where less planetary material over the same area might actually give you more smaller planets, but how many planets are likely to form in an average star system, based on size of the star, I don't think anyone knows.   But predictions can be modeled on what happens after the planets form.

What Kepler can tell us:

Most red dwarf stars have planets and at least 25% have planets in their habitable zone.   Source.   (Red Dwarfs are the easiest planets to look at and look for stars).

From the article:   


  The new finds imply that virtually all red dwarfs throughout the Milky
  Way have planets, and at least 25 percent of these stars in the sun's
  own neighborhood host habitable-zone "super-Earths," researchers said.


A simple (2-5 inner, 3-5 outer) won't cut it if you're looking for accuracy, but you might be able to run some models, based on how much you (randomly) decide that the gas giants move around and how much material you randomly give the planets.   Heavier planets would need more space around them.   

As for mining.  Venus would be a nightmare - too acidic.   Water worlds I would think would be terrible.   No solid platform to build on.   Ice worlds also not great.  Planets with past volcanic activity would be ideal and smaller planets are probably best, as most of the energy with mining probably goes into lifting the material into space, not actually the mining part.   Smaller planets could more easily build a space elevator.   Mars (volcanoes), maybe Mercury would probably be the best mining planets in our solar-system, unless you're mining for 3-HE, in which case, I'd look at the gas giants.   The moon is (I think), a terrible place to mine 3-HE, it's got so little of it, but the Moon's advantage is that it's close. 

All that said, I'd just look up 6 or 8 fairly well studied solar systems and build based on those, add some common sense, like a hot Jupiter would remove half the smaller planets, and go with that, because there is no real knowledge on what the most likely scenarios and probabilities are.

Too long? / too many guesses?.  I think about exoplanets a lot.  It's one of my favorite subjects.  I'm very much looking forward to the James Webb Telescope's launch.