The two defining features for a planet are its mass and its temperature. Those data can pretty much predict its likely size, composition, and how suitable it is for life.
Temperature is a function of the world's distance from its primary star, and how bright that star is. By "bright" I mean the star's luminosity, which is a measure of how much energy it puts out. That is distinct from its visual magnitude, which describes how bright it looks as seen from Earth.
I'm not going to re-type data you can find elsewhere, so if you're using a real star, look up its luminosity. If you're making up a star system, look up the type of star you've got — F3, K9, whatever — and pick a value from the known range of luminosity for that kind of star.
To figure the temperature for each orbit around that star, you can do it the easy way or the hard way.
The hard way is to actually compute the black-body temperature based on the incoming energy flux. Read about it here: https://en.wikipedia.org/wiki/Planetary_equilibrium_temperature.
The easy way is to just compare the values for your fictional star system to the Solar System. Divide the star's luminosity (measured in multiples of the Sun's value) by the distance in AU squared. That gives you a value of how much energy the planet gets compared to Earth. Take the fourth root of that (hit the square root button twice) and multiply by 287, which is Earth's average temperature in degrees Kelvin. Then convert back into Celsius by subtracting 273 from the result. (You have to go through the Kelvin degrees step or it won't work properly.)
Note that this is the average temperature across the entire surface, and assumes that the planet reflects about as much energy as Earth does, retains as much heat as Earth does, and has a rotation rate that's roughly comparable. But it's good enough to make rough estimates of things like whether water can exist.
The Goldilocks Zone: Because water is not just important for life but a whole lot of other things, and because it's so common in the Universe, it's important to figure out the "climate zones" in a star system.
The inner zone is the space around the star where a planet's average temperature is too hot for liquid water to exist. Worlds orbiting in that zone won't have oceans, won't have ice, and unless they are very massive they won't have any atmospheric gases containing hydrogen (no hydrogen, no methane, no ammonia, etc.). Since gas giants and brown dwarfs are basically nothing but hydrogen, you're unlikely to have them in the inner zone — unless there's a "hot Jupiter" situation where a giant planet formed in the outer system and migrated inward over time.
I'm going to define the boundary of the inner zone as the distance at which a planet's temperature is 373 Kelvin — the boiling point of water at 1 atmosphere of pressure. A more dense atmosphere with higher pressure might keep water from boiling off — but such an atmosphere will also have a higher greenhouse effect and retain more heat, so I'm just going to let those factors cancel each other out.
Compute the boundary distance using the equation D (distance in AU) = the square root of (Star luminosity divided by 2.85). Orbits within that boundary can only have rocky worlds, except as noted above.
The "Goldilocks Zone" (or in astro-speak the Circumstellar Habitable Zone) is the belt with temperatures between boiling and freezing. We've already figured the inner boundary, but the outer edge is a bit more fuzzy. A small world like Mars might be too cold at its current distance from the Sun, but if Mars was bigger and had a more dense atmosphere it might retain enough heat for liquid water. And we've seen that moons like Io and Europa orbiting a giant planet can get heat from tidal forces even if they're far from the Sun. So I'm going to figure the outer edge as the distance at which an Earthlike world would be below freezing, but keep in mind that there may be exceptions.
Compute the outer edge of the Goldilocks Zone using the equation D = square root of (Star luminosity divided by 0.82). Planets orbiting beyond that distance may have plenty of water, but most of it will be solid ice.
Mass: The other critical feature for planets is mass. Again I'm going to use Earth equivalents rather than kilograms, because the numbers are a lot handier.
We don't exactly know what determines how much mass a planet can gather up during early formation. Obviously, if you're using a real star system, just use the estimates for planetary mass that professional planetary scientists have worked so hard to come up with for you.
But for an imaginary star system, you're basically free to assign any value you want. The lower end is around the mass of Pluto (0.002 Earth mass), while the upper end is somewhere in the range of brown dwarf ojects (3000 to 16,000 Earth masses). Above that it's a star. Looking at actual exoplanet data, the biggest known exoplanet is a brown dwarf about 30 times more massive than Jupiter, or about 10,000 Earths.
Among planets, as among stars, it's a good rule of thumb to assume that there are a few big massive ones, a larger number of medium-sized ones, and a whole lot of small ones. If we look at the known multiplanetary systems (courtesy of Wikipedia: https://en.wikipedia.org/wiki/List_of_multiplanetary_systems), one can see that this is pretty accurate — although keep in mind that most of these systems probably have long-period planets we don't know about.
I'm going to lump planets into classes based on mass, and you can put them into your fictional star system as you like. Remember that massive worlds may interdict nearby orbits (see "Failed Planets" in the previous post).
Brown Dwarfs: Really big planets, with a mass above 1000 times that of the Earth. I doubt there will be more than one of these per star system, and they don't appear to be very common. If you're generating the system randomly, generate a random number from 1 to 10, subtract 9, and the result is the number of brown dwarf-sized bodies orbiting the star. The mass is a 10-sided die roll times 1000 Earths.
Gas Giants: Big planets like Jupiter or Saturn, with a mass from about 50 to 1000 times that of the Earth. Our own Solar System has two. If you're randomly generating a star system, I suggest rolling a 6-sided die and subtracting 2 to get the number of gas giants in a star system. Put them beyond the outer edge of the Goldilocks Zone (unless you want a Hot Jupiter, in which case put it close to the star and eliminate all the planets between its orbit and the outer Goldilocks edge).
Generate the mass of a gas giant by rolling a 10-sided die and multiplying the result by 50 to get the mass of the planet in Earth masses. If the die result is 10, reroll the die and multiply the new result by 100 Earths instead. This method means most gas giants will be between 50 and 450 Earths, with a small number of really big ones.
Remember to check for "failed planets" in orbits near your gas giant worlds.
Ice Giants: This is what we now call planets like Uranus and Neptune, with several times the mass of the Earth but low density. I'm giving them a mass from 5 to 50 times Earth. This seems to be a pretty common planetary type, so just roll a 6-sided die to find how many to put in your planetary system. Put them anywhere in the star sytems — astronomers have identified several "hot Neptunes" orbiting other stars. Generate the mass of an Ice Giant by rolling a 6-sided die and multiplying the result by 5 Earths; if the result is a 6 then re-roll and multiply by 10 Earths instead.
Super-Earths: This class of planet has no representatives in the Solar System, unless perhaps Earth itself qualifies as a smalle example. It refers to dense worlds of rock or metal with a mass of 2 to 10 times that of Earth. There may exist "Mega-Earths" with masses of 10 or more Earths, but the observations are in dispute. To get the mass of a Super-Earth generate a result from 1 to 100 using percentile dice or a random number generator, and divide that by 10 (because we're getting into the regime where small differences in mass matter). If you want to allow for Mega-Earths, re-roll any resuilt of 100 and divide by 5 instead.
Rocky Worlds: This is the category that the four inner worlds of the Solar System fit into. Their masses range from 0.1 Earth (Mars) to 1 (Earth, obviously). Use them to fill up any remaining orbits in your star system.
I'm going to assume that rocky worlds can actually meet the lower bound of Super-Earths, so we're actually looking at a range of 0.1 to 2, but it seems likely that the majority of rocky worlds will be small. Generate mass for a rocky world by rolling a 12-sided die and dividing the result by 10. If you roll a 12, re-roll two dice and divide the result by 10.
Dwarf Planets: If you really, really want to spend a lot of time, you can generate dwarf planets for your star system. They have a mass of less than 1/100 Earth, and you can stick them into "failed planet" orbits along with a lot of asteroids, or beyond the outermost planetary orbit in the star's Kuiper Belt.
Next Time: Planetary Composition!
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