Just The Caffeine Talking

Notes on Worldbuilding Part 9: Moons!

I'm back! Let's talk about moons now.

Most planets have moons, ranging from little chunks of ice or rock to planet-sized bodies like Triton or Titan. Moons can affect their primary planet — and sufficiently large moons of a giant planet in the Goldilocks Zone might be habitable worlds in their own right.

How Big? Studies of the moons of the Solar System suggest that the upper limit for a natural moon's mass might be comparable to that of Mars, or 0.1 Earth — but observations of potential "exomoons" circling planets of other stars (we couldn't write sentences like that back in the 20th Century) suggest that moons could be Earth-sized or even massive "Super-Earth" size. So a "forest moon" like Endor in the Star Wars series is perfectly plausible.

Looking at the moons of the Solar System, it seems as though there's a sharp distinction between the rocky worlds of the inner system and the big gas and ice giants of the outer system. Within the Asteroid Belt, moons are scarce, and only Earth has a really large one. Beyond the asteroids, every planet has at least one big moon, and most have several, accompanied by swarms of tiny moonlets.

(More and more I find it useful to consider the inner Solar System as the Sun's "moons," with the sprawling moon systems of the outer giants as separate entities.)

Anyway, if you want to select randomly, I suggest giving planets in the inner zone just one or two moons each, and those should be small. If you're generating them randomly, roll 1 six-sided die and subtract 3 for the number of moons. For size, roll a 10-sided die: on a 1-6 the moon is a tiny asteroidal moonlet like Phobos or Deimos, with a diameter less than 50 kilometers. On a 7-8 it's a sizeable asteroid with a diameter up to 100 kilometers. On a result of 9 it's a big asteroid, 100 to 200 kilometers across; and on a 10 it's a giant moon. Giant moons have a mass of several percent of the parent planet: roll a 6-sided die and multiply by 1/100 of the planet's mass.

True double planets may exist. So far we haven't really seen any, but there's no reason why they can't happen. Assign a 1 in 100 chance that an inner-system world could be a double planet, in which case just give the planet a companion with a mass equal to a 10-sided die roll times 10 percent of the planet you've already got.

In the Goldilocks zone and beyond, rocky worlds can have more moons. Roll a six-sided die and subtract 2 for the number of moons. Determine size as above.

Ice Giants and Gas Giants all seem to have large families of moons. For either type, roll a 10-sided die for the number of large moons, and a 20-sided die for the number of small ones. If the result is 20, roll two dice and take the sum.

Large moons of giant worlds are basically icy dwarf planets. In the Solar System the outer moons have masses ranging from less than 1/1000 Earths to about 1/50. But it's certainly possible to have much bigger moons.

Determine the mass of a major moon (big enough to treat as a planet for our purposes) using the "exploding die" method employed by some roleplaying games. Most moons have a mass (in Earths) of one 10-sided die times 1/1000 Earth mass; if the die roll is a 10, reroll and multiply by 1/100 Earth mass instead; and if that roll comes up 10, reroll again and multiply by 1/10 Earths. If that roll is also a 10, then roll a six-sided die and divide by 2 to get the mass in Earths.

This is likely to be a long and tedious chore, so only do it if you have a reason to. If you've got a giant planet in the Goldilocks Zone, then obviously it's important to see if any of its moons might be habitable. (And remember: you're creating this star system — you can make them big enough if you want!)

How Far? As to orbital distance around the primary planet, moons can't form at an orbital distance less than about 3 planetary radii from the planet's center. This is due to tidal forces and is called the Roche Limit (https://space.fandom.com/wiki/Roche_limit). Within that limit you don't get a moon, you get a ring system. In the Solar System, most of the big moons huddle fairly close to the primary, typically between about twice the Roche Limit out to a couple of million kilometers away.

Beyond that the giant planets have a mess of small moons the size of asteroids or comets, most of them probably captured bodies. Many have highly tilted orbits, often quite eccentric as well. Jupiter and Saturn each have a family of retrograde moons orbiting clockwise.

If you really want to generate these distances randomly, start at the Roche limit. The first moon will be a six-sided die times the Roche distance. Each additional moon's orbit will be a distance equal to 10 percent times a six-sided die greater than the previous moon.

For a rocky world like Earth, it's simpler to just roll a 100-sided die and multiply by 10,000 kilometers.

Effects: Large moons seem to slow the rotation of the parent planet. For a big world like the giants of the outer Solar System, the effect is negligible. But Earth apparently rotated faster in its early history. If the planet has a big moon, maybe double or triple its day length. And if the moon's mass is bigger than 10 percent of the parent planet's mass, then assume the two worlds are tidally locked, each presenting the same face to each other eternally.

Next time: Weird Worlds.

Not Lost in the Cosmos

For the next couple of weeks I'm going to be conducting a science fiction writing workshop for the Smith College summer Precollege Program. This means blogging will be very slow, and may not resume until the course is over. I haven't forgotten about the worldbuilding project. Have patience!

Notes on Worldbuilding, Part 8: Planetary Characteristics

This is where we figure out the details that actually determine what it's like on the planet. Some of these can be figured pretty precisely, others are up to the creator. (For gamers I've included random generators.)

Size: We know the mass (in Earths), and we've determined the density relative to Earth. Mass divided by density gives us volume (in Earths), and the cube root of volume gives us the planet's radius in Earths. Multiply that by 6,400 to get the planet's radius in kilometers. (Double the radius to get the diameter.)

Some comparisons: Mars's radius is 3400 kilometers, and Venus's is 6000 km. Note that even a "mega-Earth" with a mass of 10 times Earth's own mass would be only about twice Earth's diameter.   

Gravity: This is pretty straightforward. Relative mass (in Earths) divided by the square of radius (in Earth equivalents) gives you the surface gravity in Earth "gees" (often abbreviated g). Multiply that by 9.8 meters per second squared for the actual force, but keeping it in multiples of Earth gravity is probably more useful.

Mars's surface gravity is 0.38 g, Venus's is 0.9, and that hypothetical mega-Earth would have a crushing 2.8 gsurface gravity — about the same as at the cloud tops of Jupiter.

Escape Velocity: This is how fast you have to be going to get off the planet. It's useful to figure out how practical space travel is from that world, and for the atmospheric composition (see below). The simplest way to figure it is to divide the planet's mass (in Earths) by its radius (in Earth radii), take the square root of that, and multiply the result by Earth's escape velocity of 11 kilometers per second. 

Rotation: Planetary rotation is anyone's guess, really. Close to the Sun, tidal forces slow a planet's rotation. Mercury's rotation is locked into a 3:2 resonance with its orbital period (which fooled astronomers on Earth for years into thinking the planet kept one face permanently to the Sun). And there seems to be some vague connection between mass and spin rate: Jupiter's day is only 10 hours long, and Saturn's is about the same. But . . . Earth is ten times the size of Mars and yet they have almost identical day lengths. Meanwhile Venus takes 243 days to turn on its axis, and does it backwards, to boot.

So you can basically pick whatever day length you want. The absolute minimum would be somewhere around 3 or 4 hours for an Earthlike world, which would create a perceptible reduction of surface gravity at the equator due to centrifugal force effects. Slow the rotation in close orbits to some small multiple of the orbital period, and if the planet has a big moon you should aim for something in the 20-30 hour range. (In the case of an actual double planet, or the moon of a bigger planet, rotation and orbital period will be the same. We'll cover that later.)

If  you want to generate rotation randomly, I suggest simply rolling two 20-sided dice to get the day length in hours for an Earth-sized or larger rocky planet. If either die comes up 20, multiply by 10, and if both come up 10, re-roll and multiply the new result by 100.

Axial Tilt: This is another wild card. Most planets have their axis of rotation aligned with their axis of revolution around the Sun, within twenty or thirty degrees, at least. Except . . . Uranus's axis is deflected 90 degrees so it's lying on its side, and Venus seems to be entirely flipped over. Astronomers make vague noises about giant impacts during planet formation, but nobody really knows for sure why these weird exceptions exist.

So for "normal" planets pick an axial tilt in the range of about 20 to 30 degrees. To determine randomly roll a 20-sided die plus 10 degrees. If the die comes up 20, roll two 20-sided dice and multiply the sum by 10 for the tilt in degrees.

Atmosphere: The atmosphere composition depends on gravity, temperature and whether or not life exists on the planet. For now, assume that life is Earth-type life and can only exist in the Goldilocks zone.

I started to work out an enormous overcomplicated spreadsheet to provide data for different gases at different temperatures, but in the course of researching it I found this diagram showing what gases can exist at a given combination of temperature and escape velocity: https://en.wikipedia.org/wiki/File:Solar_system_escape_velocity_vs_surface_temperature.svg#file.

There are a few gases I would add to the list. Hydrogen cyanide (HCN) has approximately the same molar mass as nitrogen, and hydrogen sulfide (H2S) is close to oxygen.

Find the point on the chart where your planet's temperature and escape velocity meet. Any gases above that on the chart will be lost to space.

At low temperatures some gases condense and freeze out. Water freezes at 273 Kelvins, hydrogen cyanide at 260 Kelvins, ammonia at 195, carbon dioxide at 194, hydrogen sulfide at 191, xenon at 160, methane at 90, nitrogen at 63, oxygen at 54, and hydrogen at 14. Higher atmosphere pressures can make this happen at warmer temperatures, but you'll have to work that out on your own. I'm already at the limits of my chemistry knowledge.

The relative abundance of the gases in an atmosphere can vary quite a bit, based on the composition of the stellar nebula when the planet was forming. The simplest rule of thumb is to take the abundance of the elements in the universe as your guide: hydrogen is the most abundant, followed by helium, carbon, nitrogen, oxygen, neon, sulfur, and argon.

Oxygen won't occur as a free gas without life. It's rocket fuel and wants to burn the universe. On a lifeless world it will be locked up in water, carbon dioxide, and in the rocks of the crust.

Effects of Life: If a planet has plants (or plant-like organisms) doing photosynthesis, they may produce oxygen from carbon dioxide and water. As noted above, oxygen plays all too well with others: a planet with oxygen in its atmosphere won't have more than trace amounts of methane, ammonia, hydrogen sulfide, or hydrogen cyanide.

Atmospheric Pressure: There's an important concept in chemistry called "partial pressure." This is the percentage of a given gas in an atmosphere, multiplied by the atmospheric pressure. Earth's atmospheric pressure at sea level is 1 bar (by definition), or 1000 millibars. The atmosphere is 20 percent oxygen, so the partial pressure of oxygen at sea level is 200 millibars. Humans seem to need about 160 millibars of oxygen for normal metabolism. This means we could survive in a lower-pressure atmosphere if its oxygen content was higher, so that the partial pressure comes out the same — or conversely in a higher-pressure environment with a low oxygen concentration.

Pressure is a function of the atmosphere's actual mass, times the planet's surface gravity. The actual quantity of atmosphere around a planet can vary widely — Venus has a much more massive atmosphere than Earth does, even though it's hotter and has little magnetic protection, so its surface pressure is nearly 100 times what you and I are breathing. For rocky planets it does seem to be an all-or-nothing situation: small bodies have no pressure to speak of, Earth has 1 bar, and Venus has 100 bars.

To generate atmosphere pressure for rocky worlds randomly, roll a 6-sided die: 1 means vacuum, 2 means a trace atmosphere, 3 means a thin atmosphere, 4 means a medium atmosphere like Earth, 5 means dense, and 6 means massive. Pressure for a trace atmosphere is 1-10 millibars (use a 10-sided die to determine randomly) times the surface gravity (in Earth gravities). For a thin atmosphere it's 1-100 millibars (use percentile dice) times gravity. For a medium atmosphere, it's 100-1000 millibars times gravity (use a 10-sided die and multiply by 100). For a dense atmosphere it's 1000-10,000 millibars times gravity (roll a 10-sided die times 1000). And for a massive atmosphere it's 10 to 200 bars (roll a 20-sided die and multiply by 10 bars). 

If there's oxygen in the atmosphere, calculate the partial pressure to see if it can support humans and Earthly animal life. Presumably any native species are evolved to fit the local conditions. Note that since pressure drops off at high altitudes, a world with pressures too high at sea level might still have high plateaus with bearable conditions for humans. This involves a concept called "scale height" which is explained here: https://en.wikipedia.org/wiki/Scale_height. Pressure drops logarithmically as you increase altitude (that's the natural log, not log-10).

Next time: Moons!

Notes on Worldbuilding, Part 7: Temperature and Composition

From here on out I'm going to concentrate on solid planets which might be home to life we can interact with. These are bodies with a mass in the range of 0.1 Earth to 10 Earths, though I will include occasional nods to "Mega-Earth" type worlds even bigger than that. My plan is to work my way up the temperature scale to give some ideas about composition, density, and what atmospheric gases the world can retain.

Very Cold: These are planets with a temperature less than 100 Kelvins. They may have a little internal heat if they're big enough, but get almost no energy from the parent star. If they're small — a mass less than 0.1 Earths — they're likely low-density agglomerations of rock and ice. The very small ones may not even be differentiated inside (i.e. no distinct core, mantle, or crust). Density for those little ones will be low, from 0.2 times that of Earth (which is to say, about the density of ice) to perhaps 0.75 Earth (like Mars). Atmosphere will be very thin, a wisp of hydrogen and nitrogen with perhaps some helium.

Bigger worlds comparable to Earth (0.1 to 2 Earths) in that cold region can generate enough internal heat to have a distinct core and interior layers. I'm going to assume they are primarily rock and metal, so density will be close to that of Earth, 0.75 to 1. However, at the big end one might see "baby ice giants" which have swept up a lot of lighter elements and so have a low density of 0.3 or 0.4. Either way, the atmosphere will be mostly hydrogen with significant amounts of helium and nitrogen.

"Super-Earth" sized planets at those low temperatures are simply small ice giants like Uranus and Neptune. Density of 0.3 times that of Earth, with a massive atmosphere of hydrogen and helium, seas of liquid hydrogen, ice below that, then rock, then metal at the very center.

Cold: This is the temperature range from 100 to 200 Kelvins. Tiny planets less than 0.1 Earths are similar to their Very Cold counterparts — rock and ice, low density. The main difference is that methane and carbon dioxide become important atmosphere gases. Rocky worlds in the 0.1 to 2 Earth size can have hydrocarbon atmospheres like Saturn's moon Titan. Densities range from 0.6 to 1 for those worlds. The slightly warmer temperature makes "baby ice giant" planets less likely at this size.

Big "super-Earth" rocky planets in the 2 to 10 Earth size range may exist, with thick atmospheres and deep oceans of liquid methane. They might also have liquid water deep under the surface, melted by heat from the planet's core. Density would be 1 to 1.3 times that of Earth for these giant rocky planets. More likely, however, is that these massive worlds are ice giants with a density more like 0.3.

Chilly: Planets outside the Goldilocks Zone but with temperatures above 200 Kelvins. Ice is still a rock, but atmospheres of carbon dioxide, methane and ammonia are possible. Densities are about the same as above, but there's more options for atmospheric gases — and some of those are decent greenhouse gases so there's the possibility that a planet Earth-sized or larger in this region might be able to claw its way up to the melting point of water, at least some of the time. At the upper end of the size scale they would simply be "warm Neptune" planets with low density.

Goldilocks Zone: When water isn't a rock, planetary density changes abruptly. Having liquid water on a planet means two things. Yes, you might have life. But it also puts the planet at risk of losing its hydrogen. See, water molecules in the upper atmosphere can get broken into their constituent atoms by energetic particles from space. Some fraction of the free hydrogen can then escape the planet into space before it oxidizes again. Over geological time scales this can allow a planet to lose all its hydrogen. That means no water, and it also has knock-on effects on things like continental plate movement and vulcanism. It seems to have happened to Venus, and on Mars until that world lost so much atmosphere it got too cold for liquid water to exist on the surface. A powerful magnetic field like Earth's keeps the energetic particles at bay.

We don't have a very good understanding of how planetary magnetic fields work, but they seem to be generated in the dense metal core. Bigger planets are more likely to have a dense molten core, but it isn't universal. Venus seems like it ought to have a molten core but it doesn't generate much of a magnetic field at all. This may be related to Venus's weird slow rotation. As always, when science isn't sure, that means writers can indulge themselves. Choose or flip a coin to decide if your planet has a magnetic field as powerful as Earth's.

For small rocky bodies less than 0.1 Earths, the Goldilocks zone means no more water. All of it melted and got blown away. In the 0.1 to 1 Earth range, it all depends on how good a magnetic field the planet has. No planetary magnetic field means no water. Hydrogen might remain in heavy molecules like sulfuric acid. A working magnetic field means at least some surface water if the planet's big enough (more on that later). This does mean a higher density: Mercury's density is about the same as Earth's — 25 percent higher than Mars's density even though Mars has twice Mercury's mass. So simply assume all rocky inner-system bodies with a mass of 0.1 Earth or more have about Earth's density.

Bigger bodies, "super-Earth" and even "mega-Earth" sized can almost certainly hang on to their water even without magnetic protection, as their escape velocity is high enough to retain lighter atoms. For them the danger is runaway greenhouse effect due to all that atmosphere.

Hot: Within the inner edge of the Goldilocks zone, small worlds have all their water and volatiles cooked away, and big planets suffer a runaway greenhouse effect as water vapor is a major greenhouse gas. Expect a lot of airless Mercury-type worlds and a lot of Venusian and "super-Venus" planets, all with Earth-type density.

Above about 400 Kelvins, sulfur is a liquid. It's a reasonably common element, so some hot planets might have molten sulfur seas, especially if they have no hydrogen to bond with the sulfur and turn it into sulfuric acid. This raises some interesting possibilities for complex molecules of carbon, silicon and sulfur in a liquid sulfur medium.

A giant "super-Earth" type in the inner zone might be what's known as a Chthonian planet — the inner core of a gas giant which migrated inward but had all its lighter elements boiled away. Some exoplanets are thought to be this category, but we don't know for sure. A Chthonian world can be extremely dense, up to 1.5 times the Earth's density.

Molten: Above about 1000 Kelvins, rocks start to get gooey and planets basically don't have a solid surface any more. At those temperatures all the lighter elements can escape from any world smaller than a brown dwarf. Assume all bodies in that temperature range are made of dense heavy rock and metal with a density up to 1.5 times that of Earth.

Whew! It took a lot more space than I expected just to get the planetary density. Next time we'll really start putting it all together and figure out size, gravity, and maybe take a swing at atmosphere.