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!
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