DarinK

It’s all well and good to talk about events at a cosmic scale— galaxies and stars and century-long orbits —but human experience tends to happen within a very local sphere, and that will remain true long after we’ve made our way to other planets, and perhaps even other stars. Worldbuilding isn’t just about building big clockwork mechanisms—it’s also about building experiences.





Physical Characteristics

Once we have our planets placed in orbits and their masses picked out, the obvious place to start in defining their characteristics is determining their size. For a planet of given mass, the radius will depend on the density, and the density depends on composition.





Fortunately, composition itself has a predictable relationship to mass on most exoplanets, because the solid cores tend to all be composed of a similar mix of rock and metal and there’s a good correlation between the mass of the solid core and the mass of the acquired hydrogen atmosphere. Observed exoplanets can be divided into three regimes of mass-radius relationships

: Terrestrial planets up to 2.04 Earth masses with small atmospheres and high densities; “neptunes” between 2.04 Earth masses and 0.414 Jupiter masses with densities that drop rapidly with increasing mass due to larger atmospheres; And “jupiters” above 0.414 Jupiter masses with ever more massive atmospheres but radii slightly decreasing with mass due to greater compression of the atmosphere. We can therefore roughly predict the radius of a planet with any given mass:

m = planet mass (Earth masses)

r = planet radius (Earth radii)





Mass-radius trends (red line) with typical error (shaded regions) from known planets and exoplanets (symbols). Chen and Kipping 2016





However, there’s a decent bit of variation in observed planets from these averages, particular within the “neptunes”, which have differing portions of hydrogen, heavier volatiles, and solid materials. Temperature and age have a significant effect on the radii of gas giants (they cool and contract over time), and hot jupiters especially have greatly inflated radii due to their high temperature, somewhat skewing this trend; Jupiter and Saturn are both about 4/5 the radius predicted by these formulas.





volatiles, as lithophilic or “rocky” materials like silica (SiO 2 ) that tend to form oxides and appear in the mantle and crust, and the siderophilic or “metallic” materials like iron and nickel that tend not to form oxides and instead sink to the core. Some researchers define another category, the chalcophilic materials that tend to bond with sulfur, but they’re a small portion of most planets and fall roughly between lithophiles and siderophiles when speaking of density. But I’m guessing we’re going to be most concerned with terrestrial planets, and there we do see a large variety of densities based on different compositions. Though there are many types of materials that could conceivably form planets, in most cases we can divide them into 3 broad categories: the, as I mentioned before —for small planets water is by far the most common—and two types of refractory materials, theor “” materials like silica (SiO) that tend to form oxides and appear in the mantle and crust, and theor “” materials like iron and nickel that tend not to form oxides and instead sink to the core. Some researchers define another category, thematerials that tend to bond with sulfur, but they’re a small portion of most planets and fall roughly between lithophiles and siderophiles when speaking of density.





Not all metals are siderophiles (I’m using “metals” in the chemical sense now, referring to elements on the left side of the periodic table that can form metallic bonds and tend to make positive ions). Magnesium is a major lithophile in the form of bridgmanite (MgSiO 3 ) and many heavy metals like uranium and thorium are lithophilic.





On the surface, these materials have typical densities of 1, 3.5, and 7.8 g/cm3 respectively, but in the interior of a planet they can be highly compressed. Earth is about 2/3 rocky mantle and crust and 1/3 metallic core (even with large oceans, volatiles only account for about 0.03% of the total mass), giving it an uncompressed density of just under 4.3 g/cm3, but the actual density is 5.5 g/cm3. For a given composition, more massive planets will have higher densities.









For planets less than 0.01 Earth masses, bulk density will be close to uncompressed density. For larger planets, the radius of a planet of given mass can be approximated based on the fraction of water—for a water-rock planet—or fraction of rock—for a rock-metal planet

:

R

= radius (Earth radii)

M = mass (Earth masses)

f w = water mass fraction

f r = rock mass fraction





Predicted mass-radius curves for planets of given composition Fortney et al. 2007





For planets with a mix of water, rock, and metal, the radius can be approximated by finding the uncompressed density of the mixture, and then working backwards to find the water-rock or rock-metal mixture with equivalent density:









ρ = bulk uncompressed density of the total (g/cm3)

f w = mass fraction of water (~0.0003 for Earth)

f r = mass fraction of rock (0.68 for Earth)

f m = mass fraction of metallic core (0.32 for Earth)





This isn’t the most ideal method, but it’s about the best we can do with neat, simple formulas; see some tools for more precise estimates of ice-rock-metal planets here . Waterworlds aren’t too likely to be habitable anyway, for reasons we’ll discuss in the next post, so the Earthlike worlds we’re most concerned with can be modelled as rock-metal planets.





Naturally these calculations can be made on my worldbuilding spreadsheet ; if you input a planet mass in the “system builder” tab, it will calculate radius using the simpler 3-regime model by default, but if you input metal and/or water mass fractions, it will use the more detailed model for terrestrial planets.





hydrostatic equilibrium, with the gravitational pressure distributed equally across the whole surface. This is sufficient to cause all bodies with a radius above 250 km (0.05 Earth radii)—corresponding to 0.00005 Earth masses for rocky bodies— Note that linking radius directly to density assumes that all planets are spherical. Fortunately this is a safe assumption because even solid materials behave like fluids at the size of planets and so will tend towards a, with the gravitational pressure distributed equally across the whole surface. This is sufficient to cause all bodies with a radius above 250 km (0.05 Earth radii)—corresponding to 0.00005 Earth masses for rocky bodies— to collapse into spheres (slightly varying with a smaller threshold radius for less dense bodies). True hydrostatic equilibrium isn’t achieved until around 0.00035 Earth masses, but bodies in the transition zone will be rounded by gravity while still molten during formation and then “frozen in” to a spherical shape as they cool. As mentioned, rapidly rotating bodies may also have a flattened or elongated shape due to centrifugal acceleration (e.g. Haumea).





Now that we have the radius, it’s easy enough to determine surface gravity and total surface area through the magic of ratios:









g = surface gravity (Earth gs; 9.81 m/s2)

m = planet mass (Earth masses)

r = planet radius (Earth radii)









A = surface area (Earth areas; 5.10*108 km2)

r = planet radius (Earth radii)









One last subtle effect is the distance to the horizon; the Apollo astronauts were reportedly surprised at how close it appeared on the moon. The exact distance depends on the altitude of the observer, local topography, and atmospheric refraction, but for the approximation of an observer on a perfectly spherical, atmosphereless planet:





d

= distance to horizon (any unit so long as all 3 are the same)

h = height of observer

r = radius of planet





For an observer 2 meters tall, the distance to the horizon is 5.05 km on Earth and 2.64 km on the moon.

Surfaces

Classifying planetary bodies purely by size, while informative in a pinch, is a bit too simplistic. If we want to know what a planet will actually be like to visit and live on, then what we really have to ask is what sort of surface we will encounter—and how many surfaces, for planets with distinct atmospheres, oceans, and landmasses. To some extent this is determined by size as well, but there’s a lot of variation, both observed within our solar system and theorized elsewhere.





The type of surface is determined in large part by the composition, and the composition is determined in large part by the distance of the planet from the star during formation—in particular, the position relative to icelines for water and other volatiles. But planets can migrate and material can be scattered throughout the protoplanetary disk, so the ultimate arbiter of what types of surfaces a planet can have is the surface temperature.





A quick, easy way to get a rough estimate of a planet’s temperature is to model the planet as a blackbody, which means that it will reflect a portion of incoming light based on its albedo—a measure of how reflective the surface is—absorb the rest, and emit it all directly back into space. The rate at which a blackbody radiates heat is tied to surface temperature, and if the amount of heat radiated doesn’t match the amount absorbed then the planet will gain or lose heat until the surface reaches an equilibrium temperature where the heat radiated matches the heat absorbed:

T eq = equilibrium temperature (K)

T = star effective temperature (K)

a = albedo (0.3 for Earth)

R = star radius (any unit so long as D uses the same)

D = planet-star distance





This works decently well for airless, rapidly-rotating bodies, but slow-rotating bodies—such as tidal-locked planets—cool less efficiently, and many planets retain heat better due to the greenhouse effect or have an additional source of internal heat. We’ll discuss these more in the next section, but for now remember that larger planets tend to have more internal heating (and cause more heating for closer-orbiting moons due to internal friction from tidal forces) and thicker atmospheres tend to cause more greenhouse heating (though heavily dependent on composition). As points of reference, Earth is 33 K hotter than its equilibrium temperature due to greenhouse warming and Jupiter is 40 K hotter due to internal heat.





And, of course, these are just average temperatures; a low-obliquity planet will be warmer at the equator and cooler at the poles, allowing for different types of surfaces. For a rapidly-rotating planet with low obliquity (or near to an equinox for a high-obliquity planet) and negligible heat transport due to an atmosphere or ocean, the substellar point—the point on the dayside closest to the sun—should be hotter than the average by a factor of √2, or ~1.41. Slow rotation will tend to increase the temperature difference if there is negligible heat transport, but with a thick atmosphere the effect is a bit more complex so I’ll leave that discussion to next time.





A lot of fictional depictions have a bad habit of depicting single-biome planets that are homogenous across their surfaces. It is feasible for a planet’s surface to be dominated by rock, ice, water, or lava, and to some extent a desert world is possible, but as more complexity is added (atmospheres, oceans, tectonic activity) it will tend to lead to more surface variation. Even Mars, a prototypical desert planet, has rocky highlands, dusty lowlands, ice caps, and various local features formed by volcanoes, glaciers, tectonic forces, and water. I would expect any planet with complex life to have a very diverse surface.





Let’s take a quick tour of some of the more common types of surfaces—solid, liquid, and gaseous—that we might expect to encounter.

Solid Surfaces

Rock

This is the obvious one, but of course there are all sorts of different kinds of rock. For a system with a composition like ours, rocky material consists mostly of silica (SiO 2 ) mixed with magnesium, calcium, and aluminum, though many other elements appear in varying portions and often some amounts of volatiles and siderophiles as well.









The first rocky material formed would have been chondritic, named for the round chondrules, formed from droplets of material that was briefly molten during accretion, that make up much of their mass. Many asteroids that never melted are still chondritic today. Color varies and albedo of these bodies is typically 0.3-0.6, and density is around 3.5 g/cm3.









Once enough mass has gathered together to form a planet, the heat of formation and internal radioactivity will usually cause the originally chondritic material to melt and differentiate. Once the surface cools, it will form basalt, a grey or black and frankly visually uninteresting rock. Much of the initial basalt surfaces of our solar system have been ground up by impact events, but later tectonic activity can cause lava to flood over the surface, forming flood basalts that are still visible as the dark regions on the Moon and Mars. Earth has some flood basalts, such as in Iceland, and the ocean floors are primarily basaltic. Albedo is low, around 0.1, and density is 3.0 g/cm3 due to differentiation out of some of the metals.





On Earth, tectonic processes cause volatiles to mix with basalt in the upper mantle at subduction zones, and the resulting magma rises up through the crust to form andesite, a mix of rocks that form the bedrock of the continents (note that I’m counting both igneous andesites and metamorphic variants as the same, as their bulk properties are pretty similar). The rocks are even poorer in metals than basalt, lending them a light grey or white color, or reddish due to alkali metals; granite is a typical andesite. Alternative formation pathways are possible; Mars has large regions of andesitic crust, indicating a period of volcanism in the presence of water after the formation of the initial basaltic crust. Albedo is higher than for basalt, around 0.3, and density is lower, 2.5 g/cm3, which causes the continents to “float” higher on the mantle.









sedimentary rocks. Quartz (near-pure silica) will resist erosion longest, and so survive as intact grains that can be compressed together to form white or yellow sandstone. Other materials are dissolved and later deposited as carbonate, sulfate, phosphate, or nitrate minerals, with varying colors, albedos, and densities—though all usually broadly similar to andesite. Evaporation of large bodies of water can leave behind evaporites like halite salt and gypsum that appear mostly white and have And finally, planets with atmospheres experience various weathering processes that break down basalt or andesite rocks and rework the material into. Quartz (near-pure silica) will resist erosion longest, and so survive as intact grains that can be compressed together to form white or yellow. Other materials are dissolved and later deposited as, orminerals, with varying colors, albedos, and densities—though all usually broadly similar to andesite. Evaporation of large bodies of water can leave behindlike halite salt and gypsum that appear mostly white and have albedos as high as 0.7

. Earth and Mars both have large regions of sedimentary rocks, while Venus’s lack of water and frequent volcanic resurfacing seem to largely preclude their formation.





The geometry of rock formations is a big, complicated subject, but very briefly: Volcanic activity will tend to form big masses of homogenous rock (though lava flows will sometimes make pleasant columnar basalts ); sedimentary rocks tend to be deposited in flat, parallel layers (though they can be tilted or even overturned) and deformed rocks (such as from continent collisions) tend to form layers that are broadly parallel but with irregular boundaries and large-scale folds and bends.





Metal

Iron is by far the most abundant metal in the solar system—and the universe—with nickel a distant second. Thus all the solar system planets and many moons have iron-nickel cores (a planet could conceivably lack a core if all its iron is oxidized during formation, causing it to be mixed in with the rocky crust ). Differentiation during planet formation will typically place metals under layers of rock and volatiles, so exposed metal surfaces are rare, but there are a few plausible ways they might develop.





Iron meteorite; the hexagonal crystals form naturally from molten iron in low gravity. Tila Monto, Wikimedia





First, interactions between sunlight and dust particles at the inner edge of a protoplanetary disk may preferentially push silicates outwards and leave iron behind, allowing metal-rich planetesimals to form

. This could be the cause of Mercury’s high metal content of around 70%, as well as the origin for exoplanets that must necessarily have high densities to orbit as close to their stars as they do

vulcanoids, could exist in close orbits of the sun near 0.1 AU, but . Even more metal-enriched bodies, sometimes termed, could exist in close orbits of the sun near 0.1 AU, but none have been observed —though the interference of the sun’s glare makes it hard to rule out the presence of small bodies

.









Alternatively, a body that has differentiated into a metallic core and rocky mantle could lose its exterior and leave the core exposed. A sufficiently powerful impact could do the job, and this is another proposed origin for Mercury m-type asteroids. The largest such asteroid, as well as the metal-rich. The largest such asteroid, Psyche , at 0.000006 Earth masses, is almost pure iron-nickel. However, attaining such high metal content from impacts becomes more difficult for larger bodies, as the higher gravity prevents escape of the ejected material; post-impact metal contents higher than 85% are unrealistic for Earth-mass planets .





Finally, a planet or moon that passes inside its Roche limit may have its outer layers stripped away . The remaining metal-rich body is not likely to be particularly long-lived.





However they form, metal-rich planets will be very dense, around 8 g/cm3, and have greyish exteriors with albedos around 0.1 to 0.2.





Regolith

This is a broad term describing any loose material over the solid surface. So it applies to soil and sand on Earth, the ultrafine dust of Mars, and the surface material of the moon (in principle it applies to snow as well). On Earth and Mars it’s produced by the weathering of solid rock by wind and water, but on airless bodies it can be produced by the continuous bombardment of micrometeorites grinding up the surface; even many asteroids are covered in regolith.





Left to right: Earth soil (HolgerK, Wikimedia), Lunar regolith (NASA), Martian regolith (NASA/JPL-Caltech/MSSS)



The moon Titan also appears to have regolith formed of tholins (a mix of molecules formed by combinations of nitrogen and hydrocarbons) that form in the atmosphere, deposit on the surface, and then are eroded by methane rains.





Regolith types can be broadly defined by composition and size of the average grain , but our grain size types are calibrated for Earth, where moisture will tend to bind small grains into larger ones; on drier bodies the regolith can continue to break down into ever-smaller grains, which could be a health and mechanical hazard for any future settlers of the moon or Mars. A typical sand grain in a desert on Earth has around 100 times the diameter of a grain of Martian soil, putting the latter in the range of “clay”, though it is much less cohesive than Earth’s clay. In spite of the difference, dunes have been observed on Earth, Mars, and Titan, indicating that under the influence of similar forces all types of regolith tend to form similar structures regardless of composition.





Regolith is produced all across Earth, but most is either washed out to the oceans by water or held in place by vegetation. Sandy deserts are caused by an absence of moisture, which leads to an absence of vegetation, and a lack of static surface material also exposes more bedrock for weathering. Because this sand is, as mentioned, primarily silica, the albedo can be as high as 0.4 in dry conditions. Martian iron oxide dust has an albedo around 0.3, and lunar regolith is close to basalt, around 0.12. Broadly speaking all regoliths should be lighter colored than their source rocks.





Ice

Water ice is the typical surface material for small bodies in the outer system, but past their respective ice lines ammonia, methane, nitrogen, and carbon monoxide ice can form as well. Both Mars and Earth have ice caps inside the iceline thanks to their atmospheres, and other bodies may have ice in permanently shaded craters or valleys near their poles. Any tidal-locked world is likely to have ice covering its nightside, and for cool atmospheric worlds this may extend into the dayside, forming an “eyeball world”.









2 ) and ammonia (NH 3 ) it’s somewhere inside Saturn’s orbit at 9 AU, for methane (CH 4 ) it’s inside Uranus’s orbit at 18 AU The ice line for water is estimated to be around 2.7 AU primordially and 5 AU currently in our solar system, but for other compounds it’s harder to pin down: For nitrogen (N) and ammonia (NH) it’s somewhere inside Saturn’s orbit at 9 AU, for methane (CH) it’s inside Uranus’s orbit at 18 AU , and for carbon monoxide (CO) it’s around 30 AU . Water is the dominant component of all known icy bodies, but Triton and Pluto are both tinted pink by methane.





Ice has a lower compressive strength than rock, so it cannot form steep mountains. Once more than a couple 100 meters of ice piles up (given Earthlike gravity) it will form a glacier and flow outwards in all directions unless channeled by rocky features. Glaciers can be 10s of kilometers thick in their centers, but have very shallow slopes. If the ice layer is relatively thin (less than 100s of kilometers) and is underlain by a liquid ocean, the surface will be even smoother because any topographical features are unsupported.





cryovolcanism, where heat from the body’s interior causes water to burst through the overlaying ice just as lava burst through the crust on Earth. Repeated warming and cooling of the ice can also causes sections of the surface to rift apart and slide past each other. On Europa these rifts It’s easy to think of an ice-covered world as frozen and dead, but they can be remarkably dynamic. Many of the icy worlds of our solar system show evidence of, where heat from the body’s interior causes water to burst through the overlaying ice just as lava burst through the crust on Earth. Repeated warming and cooling of the ice can also causes sections of the surface to rift apart and slide past each other. On Europa these rifts may even divide into tectonic plates that subduct under each other, just as rocky plates do on Earth .





Triton, Neptune’s largest moon, has a surface layer of transparent nitrogen ice that causes a sort of “solid greenhouse effect” under sunlight, heating darker subsurface ice until it melts and bursts through the surface to form geysers that could last over a year and shoot up plumes of material 8 km high cryolava of water and liquid ammonia, analogous to the flood basalts of inner system bodies . Triton also shows evidence of cryovolcanism and tectonic rifting, and some flat plains appear to have been formed by floods ofof water and liquid ammonia, analogous to the flood basalts of inner system bodies .





Fresh snow has a very high albedo of 0.8, but partially melted and refrozen ice will typically be closer to 0.6, and “dirty ice” mixed with regolith can be as low as 0.2. These values will all be lower for planets orbiting redder stars. Micrometeorite impacts should tend to gradually coat a planet’s surface with a dusty layer, lowering the albedo, but cryovolcanism and related resurfacing processes can keep the surface covered in fresh ice.





Carbon

oxide chemistry: a silicate and metal oxide mantle, water seas, and what little carbon there is mostly forming carbonate minerals and CO 2 . This is because early in a system’s development, carbon and oxygen form carbon monoxide, a volatile that is largely driven out of the inner system by solar wind. Our solar system has a C/O ratio of 0.5—which Most of what I’ve said so far has assumed a primarilychemistry: a silicate and metal oxide mantle, water seas, and what little carbon there is mostly forming carbonate minerals and CO. This is because early in a system’s development, carbon and oxygen form carbon monoxide, a volatile that is largely driven out of the inner system by solar wind. Our solar system has aof 0.5—which should be typical of most nearby systems —so most of the carbon was lost from the inner system and large amounts of oxygen remain. But a system with a C/O ratio above 0.8 could retain much more carbon, causing the formation of carbon planets. Individual carbon planets could also conceivably form in primarily oxide systems due to local variations in the protoplanetary disk.





carbide chemisty: silica carbide and diamond interior, graphite surface, and hydrocarbon seas Such a planet would be dominated bychemisty: silica carbide and diamond interior, graphite surface, and hydrocarbon seas . Tectonic processes could bring some of the mantle material to the surface, meaning these planets could have literal mountains of diamond. However, carbides and diamond are poorer insulators than oxides and likely mix less with heat-producing radioactive materials, so these planets will cool faster and probably be tectonically inactive for most of their lives.





It’s hard to judge what the exterior appearance of such a planet would be (formal research tends not to project too far beyond current observation for these sorts of exotic planets), and really it could be as diverse as for oxide planets. Graphite is very dark grey or black with an albedo of 0.04, but diamond can have a range of colors and much higher albedo (I can’t seem to find a specific number because most people have, for understandable reasons, never considered the possibility of extensive regions of diamond on a planet’s surface, but I’d expect it to at least be comparable to quartz).





Sulfur

Sulfur is a bit of an odd element; more volatile than silicate rock and more refractory than water, but not quite common enough to dominate the chemistry of the protoplanetary disk like O, C, Si, and Fe do. On Earth the vast majority of the initial sulfur content sank towards the core and has remained there, leaving the crust depleted of it, and much the same is true of most other solid bodies. The exception is in volcanic regions where sulfur dioxide (SO 2 ) is released into the atmosphere and concentrated deposits of elemental sulfur can form. If these minerals aren’t soon buried, they will be weathered by water and form sulfide or sulfate minerals downstream, in effect diluting the sulfur in the silicate crust.





2 ice, with an average albedo of 0.63 On Io, however, constant widespread volcanism releases huge amounts of sulfur and there is no water to weather it. As such, Io is covered by broad expanses of yellow and red elemental sulfur and white SOice, with an average albedo of 0.63 . Any world with an Earthlike composition that experienced similar rates of volcanism for an extended period (which would require high internal heat, probably only possible from tidal heating by a star or planet in most cases) could expect similar results.





Vegetation

Obviously I can only speak with confidence about Earth’s vegetation, but it might be broadly similar for other worlds. Contrary to many fictional depictions, it’s not realistic for a planet to be entirely covered in thick forest. Vegetation requires water, and a planet with enough water to support widespread forests will also likely have large oceans. Perhaps we could posit floating vegetation spreading onto and eventually dominating the sea, but that raises questions about nutrient supply and tolerance of extreme ocean storms. A flat “swamp world” with global but shallow water coverage isn’t realistic either: For one, there would be no nutrient-rich mountains or major river systems to supply these forests; for another, such a world would have to be tectonically dead, which doesn’t bode well for its long-term habitability. At any rate, any habitable planet is going to have global weather systems that lead to wetter and drier regions, and so forest cover should at least have some regional variation.





But where vegetation occurs, it should be abundant. It’s easy to forget that the temperate regions of Earth that are now dominated by urban areas and agriculture had near-total forest coverage before human activity, and this has been the case most of the time since the Carboniferous Era.





On Earth, the albedo of vegetation is around 0.15, lower for thick forests and higher for grassland. It’s hard to say what it might be like for other planets, but broadly speaking we might expect to see some correlation with spectrum and intensity of sunlight: redder and dimmer light should encourage darker plants to absorb more of the available light, and bluer and hotter light should encourage more reflective plants to protect the delicate photosynthetic molecules. Any number of colors are conceivable—even on Earth today there are red and purple varieties of photosynthetic algae that likely dominated more of the surface in the past—but that’s a subject I’ll dig deeper into at another time.

Atmospheres

Every planet has at least some thin gas near its surface, but here I’m concerned mostly with thick atmospheres that can significantly impact the chemistry of the solid surface and allow for liquid oceans. Atmospheres may be primary, meaning they formed with the planet from gasses in the protoplanetary disk or volatiles liberated from solid material during formation, or secondary, meaning they formed after the primary atmosphere was lost from volatiles stored in the interior and later outgassed by volcanic activity.





Atmospheres can be lost in various ways, but in most cases the most important mechanism will be thermal escape. Any gas in an atmosphere will have some average velocity based on its molar mass (a measure of the relative mass of different types of molecules) and temperature:









v therm = typical thermal velocity (m/s)

R = gas constant; 8,314.4598 g m2 s-2 K-1 mol-1

T = temperature (K)

m mol = molar mass (g/mol)





hydrodynamic escape, where the gas simply flows off the planet like a continuous wind. Escaping lighter gasses can carry away heavier gasses with them, removing the entire atmosphere. This appears to be happening to hot jupiters in other systems, and Earth and Venus If the average thermal velocity actually exceeds escape velocity—which, recall, is determined by the planet’s mass and radius—then the planet experiences, where the gas simply flows off the planet like a continuous wind. Escaping lighter gasses can carry away heavier gasses with them, removing the entire atmosphere. This appears to be happening to hot jupiters in other systems, and Earth and Venus may have lost their primary hydrogen-rich atmospheres this way .





Jean’s escape But even where the average velocity is below escape velocity, random collisions will cause some gas particles to exceed the average, and so all atmospheres experience some loss due to . As a rule of thumb, when the average velocity of a gas reaches 1/6 the escape velocity, then the rate at which it escapes will be great enough that the atmosphere could become depleted of that gas in less than billions of years.





Rough chart of gasses that can be retained under given escape velocity and temperature. Cmglee, Wikimedia





So for a planet with a composition similar to Earth and a temperature of, let’s say, 300 K, this leads us to a naïve estimate for the minimum mass of a planet necessary to retain a Nitrogen-dominated atmosphere of 0.03 Earth masses. However, heating of Earth’s upper atmosphere by solar radiation can push it to 1500 K, and similar heating should occur for any nitrogen-dominated atmosphere with similar insolation. This gives us a more conservative estimate of 0.32 Earth masses for the minimum mass. There’s not a lot of published literature regarding this question of minimum mass for an earthlike atmosphere, but I’ve found at least one more detailed model predicting a critical value of 0.07 Earth masses for a nitrogen atmosphere to last over 4.5 billion years, so my simple model is probably missing some important factors regarding the structure of the atmosphere.





It’s a rough, simplified model, but it does generally match what we observe in our own solar system: massive, cold giant planets in the outer system with thick hydrogen atmospheres; Earth-mass planets like Earth and Venus or smaller but colder bodies like Titan with little hydrogen but thick atmospheres of heavier gasses; sub-Earths and dwarf planets like Mars and Pluto with thin atmospheres; and small dwarf planets and minor bodies with no more than trace atmospheres.





non-thermal escape. Massive impacts can toss superheated plumes of gas into space, and frequent impacts during formation or the Late Heavy Bombardment may have removed the primary atmospheres of all the terrestrial planets. Planets without a strong magnetic field can also lose gasses due to the impacts of solar wind particles, a process called sputtering, but the importance of this escape mechanism is often overstated; Venus’s thick atmosphere manages fine without a substantial magnetic field, and overall it appears that while a magnetic field can help, it is Atmospheres can also be lost due to. Massive impacts can toss superheated plumes of gas into space, and frequent impacts during formation or the Late Heavy Bombardment may have removed the primary atmospheres of all the terrestrial planets. Planets without a strong magnetic field can also lose gasses due to the impacts of solar wind particles, a process called, but the importance of this escape mechanism is often overstated; Venus’s thick atmosphere manages fine without a substantial magnetic field, and overall it appears that while a magnetic field can help, it is neither sufficient nor necessary for a thick atmosphere .





And finally, atmospheric gasses can be lost without escaping to space if they’re sequestered in the crust by chemical reactions with surface materials. Earth’s oxygen is being continuously lost this way, but it is replenished by biological activity. Sequestered volatiles can also be returned to the atmosphere by outgassing from volcanoes.





Altogether this means that a planet with higher gravity and lower temperature at the surface will generally have a thicker atmosphere, but it’s by no means a strict relation. Formation histories of individual planets can vary immensely, and even gas giants can lose their atmospheres completely to become rocky chthonian planets.





For a planet with a given surface pressure, pressure will fall more quickly with altitude for planets with higher surface gravity and average molar mass. More precisely:









p = pressure (atm)

p 0 = pressure at 0 altitude (atm)

e ≈ 2.71

g = surface gravity (Earth gs)

h = altitude (meters)

m = gas average molar mass (g/mol)





There is no sharp boundary for the top of an atmosphere; the density of gasses continuously drops until it reaches that of the interplanetary medium. Rough boundaries can be marked where the chemistry and behavior of that thin medium is dominated by the planet rather than the star, but this boundary lies far beyond the point where life could exist or orbiting objects would stop experiencing significant drag. By convention the boundary of Earth’s atmosphere is often set at the “Karman line” at 100 km altitude, where the pressure is roughly 0.000001 atm.





Atmospheres can warm a planet due to the greenhouse effect, but thick atmospheres can reflect away most sunlight before it reaches the surface. Very broadly, an atmosphere with Earth’s surface pressure should lead to higher surface temperatures than one with a pressure 100 times higher or lower, but there are plenty of exceptions.





Hydrogen

2 /He) atmospheres, but smaller planets will tend to lose them early on to hydrodynamic escape. Hydrogen can continue to be outgassed from the interior, and because hydrogen can act as a greenhouse gas in the presence of nitrogen this The default for giant planets, likely common for super-Earths, and even possibly occurring for cold Earth-mass planets. In fact, essentially all planets are expected to form with primary hydrogen/helium (H/He) atmospheres, but smaller planets will tend to lose them early on to hydrodynamic escape. Hydrogen can continue to be outgassed from the interior, and because hydrogen can act as a greenhouse gas in the presence of nitrogen this may have helped warm the early Earth , but for Earthlike temperatures and surface gravity this gas will continuously escape and eventually the interior will be depleted of it. Even if it does survive a while, it cannot coexist with atmospheric oxygen. But as mentioned, exoplanets past roughly 2 Earth masses seem to have generally lower densities, indicating that many have retained their primary H 2 /He atmospheres—some thick enough to be classified as mini-Neptunes.





Within a gas giant, most of the hydrogen does not exist as a gas. Using Jupiter as a model, the visible surface is 50-kilometer-thick region of clouds, blocking most light from reaching the interior. Below that the pressure and temperature gradually increases, reaching levels so high that there’s no sharp distinction between gas and liquid; the hydrogen exists as a supercritical fluid, with a mix of gas-like and liquid-like properties and becoming more liquid-like with increasing depth and pressure. Around 15,000 kilometers down—1/5 of the radius—the hydrogen is expected to behave as a metal, though still not a solid. A rock and ice core may exist, but even that may not have a clear solid surface.









Ice giants have outer layers of hydrogen gas and supercritical fluid, but unlike gas giants their interiors probably lack metallic hydrogen and are instead dominated by supercritical phases of the other volatiles that make up the bulk of their mass.





2 /He atmosphere will depend on the temperature, which affects the formation of clouds of other trace gasses If thick enough to obscure the solid surface, then the outward appearance of an H/He atmosphere will depend on the temperature, which affects the formation of clouds of other trace gasses Modelling of giants with elemental compositions similar to that of our solar system predicts 5 distinct classes :





Class I , less than 150 K, have ammonia clouds with traces of carbon and sulfur compounds that result in the yellow-brown color seen on Jupiter and Saturn. Near the upper end of insolation for this class bands of red, orange, and gold are likely due to production of unstable trace gasses by sunlight. Albedo is around 0.4.









Class II

, from 150 to 350 K, have water clouds like Earth that are predominantly white with some regions of blue tinge due to scattering of light by upper atmosphere gasses. Albedo can be as high as 0.8. However, in some cases at above 200K a sulfur haze may form, turning the planet orange with an albedo of 0.6

.









Class III , from 350 to 900 K, form no clouds and so appear blue for much the same reason a clear sky on Earth is blue. This is also why Uranus and Neptune are blue, because they are too cold to form even methane clouds, but for whatever reason they don’t get a class in this system. Albedo is around 0.12. Again, sulfur hazes may form to as high as 700 K.





Class IV

, from 900 to 1500 K, form clouds of alkali metals like sodium and potassium, which form a very dark haze that cause the planet to appear black or dark brown, perhaps with a reddish glow due to the incandescence of the hotter lower atmosphere. Albedo is very low, about 0.03.









Class V

, above 1500 K, form silicate and iron clouds above the alkali haze, which might give them a grey or greenish color. They may also have a blue halo of lighter gasses escaping to space, and in extreme cases even a comet-like tail. Albedo is higher, about 0.3.





There will probably be more than a few planets that fall outside this scheme due to some subtle variation in composition, so treat it as a general baseline.



Late Breaking Note: The folks over at : The folks over at Orion's Arm have been working on assembling a more detailed breakdown of gas giant colors accounting for different hazes and clouds; it's pretty speculative, but lines up fairly well with this scheme and what I've seen elsewhere.)





Helium

Under the right conditions , a Neptune-like gas giant in a close orbit of its star may lose most of its initial hydrogen atmosphere but retain its helium. The resulting planet will have a whitish color and high albedo.









Nitrogen

3 ) ices. N 2 is relatively inert compared to most other atmospheric gasses—the two nitrogen atoms are joined by a strong triple bond—and while The main component of Earth’s atmosphere (78% by volume) as well as that of Titan (98%) and a major component of Venus’s atmosphere (3.5%), probably initially delivered to all in the form of ammonia (NH) ices. Nis relatively inert compared to most other atmospheric gasses—the two nitrogen atoms are joined by a strong triple bond—and while it does appear to cycle into the interior over long periods , it isn’t often incorporated into surface minerals like Oxygen, CO 2 , and water often are. This also means it can exist in stable mixes with many other gasses.









Though atmospheric nitrogen doesn’t interact directly with most life, it has 2 important roles in maintaining Earth’s habitability: First, it creates a cold trap in the atmosphere that causes rising water vapor to condense and rain back down, keeping it from the upper atmosphere where it might escape; Second, nitrogen gas can be “fixed” by lightning or microbes into vital nutrients like ammonium (NH 4 +) and nitrate (NO 3 -). It’s hard to say if this makes nitrogen necessary for life, but at any rate it certainly appears helpful—and, given that it’s a major component in the 3 thickest terrestrial planet atmospheres in our system, it’s also easy enough to come by.





Though Earth is blue primarily due to its oceans, nitrogen contributes as well. Any “colorless” gas will tend to appear blue in thick atmospheres, due to scattering of the light. Even icy or desert worlds may appear blue if they have thick nitrogen atmospheres . The exact color will depend on the pressure and spectrum of solar light; this chart does a decent job of showing the effect of these variations.





Oxygen

2 ) rarity is due to its highly reactive nature, and on Earth it’s only sustained by the action of photosynthetic life. But though oxygenic photosynthesis evolved around 3 billion years ago, consistently high oxygen levels A major component of Earth’s atmosphere (21%) but absent from other atmospheres in the solar system save for the very thin, transient atmospheres of some icy moons (due to photolysis of water). Free oxygen’s (O) rarity is due to its highly reactive nature, and on Earth it’s only sustained by the action of photosynthetic life. But though oxygenic photosynthesis evolved around 3 billion years ago, consistently high oxygen levels have only existed for the last 800 million years . Before then, excess oxygen was mostly sequestered by reactions with surface materials to create oxide rocks, and save for a brief period around 2.3 to 2 billion years ago, concentration was below 1/100 of current values.





As mentioned in Part II, photolysis of water could produce oxygen even in the absence of life, and photolysis in the early atmospheres of Venus, Earth, and Mars appears to be responsible for their oxide-rich exteriors today (That’s why Venus and Mars are both red), but it’s unlikely that oxygen ever built up to significant levels at that time. In any nitrogen-rich atmosphere, the cold trap should limit photolysis to rates too low to overcome sequestration. But an otherwise Earthlike world without nitrogen (or a similar gas like argon (Ar)) would build up oxygen from photolysis until the oxygen itself formed a cold trap, which should occur at roughly 0.15 atm of oxygen—slightly less if there is some small amount of nitrogen or argon . Such a world would be losing roughly 1/4 of Earth’s oceans in water every billion years, which is high enough to be problematic but still low enough that complex life could conceivably evolve before such a world was completely dry.





Thick, oxygen-rich atmospheres could also be caused by photolysis due to the high XUV output of a young red dwarf star even with nitrogen present, and may remain even after the star quiets down if the surface is too saturated with oxides to sequester any more. CO 2 can also be split to produce oxygen around red dwarfs, with or without water present.





Scenarios for production of O 2 -rich atmospheres. Meadows et al. 2017

ozone (O 3 ) layer in the upper atmosphere that can reflect away harmful UV radiation, and it will allow aerobic (O 2 -consuming) life to develop into more complex and energy-intensive forms. If complex life does evolve and vegetation becomes a major feature of that surface, the flammability of that vegetation 2 levels thereafter; on Earth, fires become near impossible below 16% atmospheric oxygen, allowing levels to rise unhindered, and near inevitable above 22%, consuming excess oxygen and bringing levels back down Once oxygen does reach high levels, it will produce an(O) layer in the upper atmosphere that can reflect away harmful UV radiation, and it will allow(O-consuming) life to develop into more complex and energy-intensive forms. If complex life does evolve and vegetation becomes a major feature of that surface, the flammability of that vegetation may control levels thereafter; on Earth, fires become near impossible below 16% atmospheric oxygen, allowing levels to rise unhindered, and near inevitable above 22%, consuming excess oxygen and bringing levels back down (though the greater diversity of vegetation in nature than was used in this study and likely evolution of fire resistance in response to oxygen levels may widen these bounds). Perhaps for this reason, oxygen levels have remained fairly close to 20% (~15-30%) since the appearance of widespread forests 350 million years ago.





Like nitrogen, oxygen should appear blue in thick atmospheres.





Carbon Dioxide

The primary component of Venus’s (96.5%) and Mars’s (95%) atmospheres. On Earth it’s a minor gas (0.04% and rising) but it is the primary gas responsible for the surface temperature, due to the greenhouse effect. Given its profound role in habitability, we’ll leave discussion of the greenhouse effect and the processes controlling Earth’s CO 2 concentration to the next section. For now, I’ll just note that surface water greatly accelerates the sequestration of CO 2 , so a volcanically active world without water is likely to build up large amounts of CO­ 2 in its atmosphere and thus have a high surface temperature, as is the case on Venus.





Though it warms the surface, CO 2 also cools the upper atmosphere; Venus actually has a colder upper atmosphere than Earth. Paradoxical though this may seem, the same properties are responsible for both effects: near the surface, CO 2 absorbs heat from the ground and radiates it back down, trapping heat in the lower atmosphere; in the upper atmosphere, CO 2 absorbs heat from the surrounding gasses and radiates it into space. Because the upper atmosphere is so thin, this cooling has almost no direct impact on surface temperature, but it can slow down thermal escape of atmospheric gasses. In combination with CO 2 ’s high molecular mass this means that, at a given surface temperature, the minimum mass limit for a body to retain a CO 2 -dominated atmosphere should be lower than for an nitrogen-dominated atmosphere.





Water

Some water will exist in the atmosphere of any planet with surface oceans of water like Earth (~0.25% average, locally 0.001-5%), but for some water-rich worlds it may be the primary component. Earthlike worlds may pass through a stage of steam atmospheres outgassed from the molten interior during formation, but if interior heat remains high and this stage lasts more than a few million years it could cause significant loss of the water to space . If a planet with surface water warms significantly—as may have once happened to Venus and may eventually happen to Earth—then the oceans may evaporate completely into the atmosphere, though again this can only happen briefly before the oceans are lost to space.









2 /He atmosphere anyway, so in general it should be difficult to find a world with land on its surface and a water-rich atmosphere. However, a waterworld—one where a significant portion of the planet’s total mass is water— Any planet with high enough gravity to limit thermal escape of water due to photolysis is likely to have retained its primary H/He atmosphere anyway, so in general it should be difficult to find a world with land on its surface and a water-rich atmosphere. However, a—one where a significant portion of the planet’s total mass is water— can lose water at high rates for billions of years and still have more to spare . For waterworlds with Earthlike surface temperatures the atmosphere is likely to largely resemble that of a world with continents but a hot waterworld could have a long-lived steam atmosphere. Especially hot waterworlds may possess no liquid oceans at all, but instead transition to a supercritical fluid and then a compressed plasma above a rock and high-pressure ice core .





At Earthlike temperatures water will form clouds, and these clouds can significantly increase the albedo of a world to as much as 0.8. Earth’s overall albedo is 0.3, even though most of the land and ocean has a lower albedo, due to water clouds. But that albedo could conceivably vary from 0.25 to 0.5 with fairly minor changes in climate .





Hydrocarbon

Methane (CH 4 ) is a major gas in Titan’s atmosphere (5.7%), and trace amounts of ethane (C 2 H 6 ) exist there as well. Early life on Earth may have converted some of the primordial hydrogen atmosphere to methane, though methane would have been unstable in the warm, water-rich atmosphere.





Image of Titan. NASA





2 a CH 4 /CO 2 ratio greater than 0.1 can cause the formation of a haze that will Low amounts of methane can act as a strong greenhouse gas, but in an atmosphere with significant CO­a CH/COratio greater than 0.1 can cause the formation of a haze that will lower surface temperature 2 (unlikely for planets in the habitable zone) higher levels of methane tholins, a variety of unstable compounds that form the orange-red haze of Titan . Lacking CO(unlikely for planets in the habitable zone) higher levels of methane can also react with nitrogen to form, a variety of unstable compounds that form the orange-red haze of Titan . Presuming that either organic or inorganic production of methane would be related to temperature, formation of these hazes should limit methane levels on most oxide worlds. And like hydrogen, significant levels of methane cannot coexist with O 2 .





Carbon planets of similar size to Earth should generally form with CO 2 atmospheres, but large planets that retain large amounts of hydrogen—or small planets that somehow produce hydrogen—should have some methane as well, or even have hydrocarbon-dominated atmospheres at very high carbon/oxygen ratios.





Silicates

2 , O, silicon monoxide (SiO), and various metals and metal oxides. A thin atmosphere may begin to form at 1500 K but even at 3000 K surface pressure should remain below 0.1 atm. Sodium and Potassium (K) clouds may form, and in some cases Planets in extremely close orbits of their stars should be so hot that their rocky surfaces sublimate, forming an atmosphere of Sodium (Na), O, O, silicon monoxide (SiO), and various metals and metal oxides. A thin atmosphere may begin to form at 1500 K but even at 3000 K surface pressure should remain below 0.1 atm. Sodium and Potassium (K) clouds may form, and in some cases there may even be a bizarre “salt cycle”, with NaCl forming clouds and then raining down into a lava ocean . Even with high surface gravities, any planet hot enough to form such an atmosphere will also be losing it to space, and so gradually losing mass .









The clouds of such a world may appear black or grey with fairly low albedos, but at high temperatures these worlds will glow a dull red.





Trace Gasses





2 ) and water produced by volcanoes react to produce sulfuric acid (H 2 SO 4 ), which forms the thick yellowish clouds Various other gasses present at low concentrations can have an impact on the chemistry and outward appearance of a planetary atmosphere. I’ve already mentioned the tholin haze of Titan, methane haze of early Earth, and possible sulfur haze of some gas giants. On Venus , sulfur dioxide (SO) and water produced by volcanoes react to produce sulfuric acid (HSO), which forms the thick yellowish clouds . It can condense and rain downwards, but it never reaches the surface; the intense heat in the lower atmosphere evaporates it before it does.





Finally, it isn’t a haze but most planets with rocky surfaces are likely to have some amount of atmospheric Argon (Ar); it’s produced by the radioactive decay of Potassium, and is heavy enough to not be easily lost by any but the hottest or smallest planets.

Oceans

I put oceans last because no liquid is stable in vacuum (aside from some metals that are very unlikely to appear naturally), so for a planet to have surface oceans it must necessarily have an atmosphere. So far as I’m aware, aside from the briefly molten states of planets during formation there aren’t likely to be any planets that are entirely liquid with no solid core. The requirement for an atmosphere to get surface liquids places a fairly large minimum mass limit on ocean worlds, and any large planet is likely to have both gathered a significant amount of solid material during formation and have interior pressures too high for any liquid.





Water

Naturally. There’s some debate about exactly how Earth received all its water—in particular whether it was part of the original material that formed the planet or it was delivered later by comets—but however it arrived, some amount of water seems to have made it into every planet and major moon in the solar system, so it doesn’t appear hard to come by. Earth’s water regularly cycles in and out of the interior, such that there is now several more ocean’s worth of water stored in the mantle (lest you picture giant aquifers, it all exists either mixed into magma or as individual molecules within the crystal structures of certain minerals). Thus, we could probably afford to entirely lose the oceans a couple times over before the planet became completely dry.





Feedbacks between surface oceans and the mantle should tend to prevent an Earthlike planet from being completely inundated while less than 0.2% of the planet’s mass is water, but there seem to be plenty of exoplanets with much more than that. Once a global ocean surpasses 155 km in depth for an Earth-mass planet, the pressure at the ocean’s base will be so intense as to force water at the bottom into unusual, dense, high-melting-point varieties of ice . Initially this ice layer is only a few kilometers thick and heat from the interior can form a secondary liquid ocean below it, but as the ocean grows deeper the ice layer thickens and the lower ocean thins. Past around 230 km, the ice layer is over 50 km thick and liquid water exists only intermittently in a thin layer at the base.





Varieties of waterworld ocean structures, with increasing total depth to the right (depth not to scale). Noack et al. 2016





Open water has a very low albedo of 0.06, but of course water oceans are likely to be accompanied by ice and clouds with much higher albedos. It is actually blue on its own independent of the color of the atmosphere, but various minor impurities could conceivably alter its color—green being common on some areas of Earth due to the presence of plankton, but just as alien vegetation could be many different colors, alien microbes could color their seas many hues. In the past, Earth's oceans may have passed through stages of green, red white with regions of black , and pink , due to a mix of organic and inorganic processes.





Hydrocarbon

The only other surface oceans in the current solar system are the methane oceans of Titan. Titan has a full “methane cycle” analogous to Earth’s water cycle, with clouds, rain, rivers, and seas. The seas themselves are mainly restricted to the poles and are likely composed of a mix of 3/4 ethane ( C 2 H 6 ), 10% methane (CH 4 ), 7% propane (C 3 H 8 ), and smaller amounts of butane ( C 4 H 10 ), hydrogen cyande (HCN), nitrogen ( N 2 ), and Argon (Ar).



Carbon planets could also have oceans, though for an earthlike temperature the methane and ethane may more readily bond into larger molecules without settling out of the liquid and so come to resemble tar. What sort of climate cycles such a world might have has not received much formal research.





Sulfur

2 —though perhaps with more SO 2 and sulfuric acid—and so experience a strong greenhouse effect. Over a fairly broad range of temperatures (388-718 K at 1 atm, but hotter in a thick Venus-like atmosphere) As mentioned, a planet experiencing intense, sustained volcanism due to high internal heat would likely have a sulfur-dominated surface, like Io. But were such a planet significantly larger than Io, the planet could retain an atmosphere. It would likely resemble Venus’s atmosphere and be dominated by CO—though perhaps with more SOand sulfuric acid—and so experience a strong greenhouse effect. Over a fairly broad range of temperatures (388-718 K at 1 atm, but hotter in a thick Venus-like atmosphere) this could allow for liquid sulfur or sulfuric acid, and potentially an atmospheric sulfur cycle . The possibility has received little formal research, but so far as I’m aware this is about as hot as a planet can get and retain a reasonable resemblance to Earth; i.e. a thick atmosphere, recognizable surface geology, and long-term stability of the planet’s properties.





Lava

All planets of significant mass should go through a period with a molten surface, and massive impacts can cause local or global melts. But in both cases these states are brief, lasting millions of years at most. However, a planet in a very close orbit to its star heated to ~2200 K could form a permanent ocean of calcium and aluminum oxide (CaO and Al 2 O 3 ) under a thin silicate atmosphere (as permanent as the planet is, anyway, given continuous loss of mass to the escaping atmosphere).





Any planet close enough to its star to maintain a lava ocean is very likely to be tidal-locked, so it will have a dayside exposed to extreme light and a completely dark nightside (because the angular diameter of the star as viewed from the planet is likely to be quite large, the dayside should occupy somewhat more than half the surface). So long as the dayside remains below 3500 K, the silicate atmosphere will be quite thin and lava oceans fairly viscous, so heat transport will be inefficient and the nightside crust will remain solid, forming what we might call a “lava eyball planet”. For a dayside peak temperature of 2500 K, the nightside could remain as cold as 50 K . This means that a lava ocean and a nightside icecap could coexist on the same planet. Before you ask, air pressure is too low for surface liquid water to exist in the transition zone—the silicate atmosphere freezes out before reaching the nightside, and any more volatile gasses would rapidly escape on reaching the dayside, so in effect the nightside has no atmosphere. Local water aquifers under the ice are a possibility, and so life may be as well. What you might find instead near the dayside/nightside terminator is bands of metals that condensed out of the atmosphere as they cooled while moving towards the nightside.









Above 3500 K the atmosphere is thick and hot enough to melt the whole surface of even a tidal-locked planet

. Albedo of the surface may be around 0.1, though alkali and silicate clouds may darken the planet further. But at such high temperatures the planet itself will produce a good bit of red light.





Others

In addition to those liquids mentioned, nitrogen, ammonia (NH 3 ), hydrogen sulfide (H 2 S), hydrogen cyanide (HCN), CO 2 , and perhaps even hydrogen could all plausibly form surface oceans, but have received almost no formal study.





Regions of stablity for oceans of different compounds. Ballesteros et al. 2019

Alien Skies

Perhaps the most popular and effective way to establish a fictional world as alien and interesting is to have the characters look up, so it would be remiss of me not to address what they might see in our constructed systems. I’ve already discussed the color of the atmosphere; what effect this has on the color of objects seen through the atmosphere depends on exactly why the atmosphere is that color. If the sky is colored due to scattering, that color will be subtracted from light passing through it; the sun appears yellow from Earth’s surface rather than its true white because of the scattering away of blue light. If the sky is colored by particulate matter, this color will be added; any object seen from Mars’s surface will be tinged red (scattered light can also tinge other objects to some extent, if they're far dimmer than the primary light source in the sky).





Past that, we can summarize most of what we want to know with two values, the apparent diameter and the apparent magnitude; how big and bright is it in the sky?





The apparent diameter of a spherical body is straightforward trigonometry:





δ = apparent diameter

r = radius of spherical object (any unit so long as D is the same)

D = distance from observer to center of spherical object





Apparent magnitude can be a bit trickier. For a star, an absolute magnitude that is independent of the distance from the observer can be calculated based on luminosity:









M = absolute magnitude

L = luminosity (relative to sun)





Note that magnitudes are logarithmic, to match human perception of light; we perceive large changes of luminosity in bright conditions to be equivalent to small changes in dim conditions. This allows us to see details at night without being overwhelmed by excess information in the day, and we should probably expect it to be a trait shared with any organism that has sight as a dominant sense. Note also that brighter objects have lower magnitudes for…historical reasons? I’m honestly not sure. So a decrease of magnitude by 1 corresponds to an increase in luminosity by a factor of ~2.5.





bolometric absolute magnitude, meaning that it accounts for all light across the spectrum. To compare how stars other than the sun would appear to human eyes, we have to apply a bolometric correction factor. Unfortunately there’s no easy, simple formula to estimate this factor, but And finally, note that this is aabsolute magnitude, meaning that it accounts for all light across the spectrum. To compare how stars other than the sun would appear to human eyes, we have to apply a. Unfortunately there’s no easy, simple formula to estimate this factor, but extensive tables exist for observed factors for given effective temperatures .





This correction is specific to the spectral range of human vision, of course, but there’s some justification for thinking that an alien organism with a similar natural lifestyle might have a similar visual range, regardless of the star it lives near—more on that when we discuss biology.





Once an absolute magnitude is known—bolometric or visual—the apparent magnitude can be calculated for an observer at a given distance:

m = apparent magnitude

M = absolute magnitude

D = distance to observer (parsecs; 1 psc = 3.261 ly = 2.063*105 AU = 3.086*1013 km)





For planets (or other similar bodies) the process is similar, starting with a planetary absolute magnitude that indicates the reflection of light by a planet orbiting a given star independent of the planet’s distance from that star or the observer’s distance from the planet—but is not on the same scale as stellar absolute magnitude.









H = planetary absolute magnitude

M

= star absolute magnitude (4.74 for the sun)

r = planet radius (Earth radii)

p = geometric albedo.





The geometric albedo used here, which represents the light reflected by a planet directly back at the light source, is different from the bond albedo used for the effective temperature calculation before. The two are typically similar but the geometric albedo can be higher or lower than the bond albedo, and for solar system bodies it is usually the former, with airless bodies tending to have the greatest difference. Earth has a bond albedo of 0.3 but a geometric albedo of 0.43.





That in mind, the apparent magnitude of the planet—which is on the same scale as that of stars—can then be approximated based on the relative positions of the star, planet, and observer:









m = apparent magnitude

H = planetary absolute magnitude

D S = distance from star to planet (AU)

D O = distance from observer to planet (AU)

α = phase angle (degrees); angle between the lines connecting the center of the planet to the star and to the observer.

This is a rough approximation, but thanks to the logarithmic scale small errors shouldn’t change the results too much. It also assumes that the bodies are fairly far apart, such that the observer can see most of one hemisphere, and the planet produces no light of its own.





By way of comparison, here are the maximum apparent diameters and magnitudes of several objects as seen from Earth (for Venus, the two maxima are achieved at different times):





Body Sun Moon ISS Venus Sirius Apparent Diameter (°) 0.54 0.57 0.017 0.018 1.6*10-6 Apparent Magnitude -26.74 -12.90 -5.90 -4.92 -1.47





6.5 apparent magnitude is the approximate limit for detection by human eyes on a clear, moonless night, though if all other stars or sources of light were removed there is no specific limit—the human eye is somewhat sensitive even to individual photons. The Hubble Space Telescope is sensitive to 31.5 magnitude. There is no such limit for apparent diameter; even a point source of light is visible if it is bright enough. But 0.02° is about the limit to perceive an object as anything other than a point.





So far as I can tell, the largest apparent diameter of any planet viewed from any moon in the solar system is Jupiter as viewed from Metis, at 67° (as mentioned, my apparent magnitude formulas aren’t valid this close, but I’d estimate it to be in the neighborhood of -21 at maximum). Viewed from a flat area on Metis facing Jupiter, the planet would stretch over 1/3 of the distance from horizon to horizon, which means the moon spends 1/6 of its orbit in Jupiter’s shadow. However, for most major moons the planets are surprisingly small in the sky; from Ganymede, Jupiter appears 7.65° in diameter (smaller than the palm of your outstretched hand) and about -16 in magnitude; from Titan, Saturn appears 5.46° in diameter (16.85° including the rings) and -14 in magnitude. They’d certainly make for impressive sights, but not loom across the sky quite as much as sometimes depicted.





But that’s just our system. As a general rule, planets in the habitable zone of stars smaller than the sun will observe their stars to be larger but dimmer in visual light compared to the sun as seen from Earth. In the tightly-packed TRAPPIST-1 system, many of the planets are of similar size to Earth but much closer together. From TRAPPIST-1f—the most likely to be habitable (based purely on its orbit)—the star appears 1.67° in diameter and -20.2 in magnitude (by visual light). The nearby planet TRAPPIST-1e appears 0.48° in diameter, almost as large as our own moon. If TRAPPIST-1e were replaced with a Neptune-sized planet, it could actually eclipse the star as seen from TRAPPIST-1f. A larger planet might destabilize that particular system, but at any rate it appears feasible for such interplanetary eclipses to occur in tight systems.





Concept of the system Gliese 581. ESO





The direction to an object in the sky depends on an interplay of distance, inclination, obliquity, latitude, time of day, and time of year that I won’t dig into here. But just as a point of reference, here’s the formula for the maximum angle between the horizon and a satellite—be it a moon, ring system, or whatever else—that has a circular, equatorial orbit:









θ = maximum angle between horizon and satellite

L = latitude of observer

a = satellite semimajor axis (any unit so long as r is the same)

r = radius of planet





As a final note, we may want to talk about how light sources in the sky affect ambient light conditions on a planet’s surface; i.e., how “well-lit” the ground will appear. For this, we can return to measures on insolation. At the equator at midday during the equinox, the sun is delivering about 1360 W/m2 to the top of the atmosphere and on a clear day 1050 W/m2 will make it to the surface without being scattered away, but if we include light that is scattered but still makes it to the surface then we can raise that value to 1120 W/m2.





That’s for a surface directly facing the sun. As a surface is angled to the sun, the light is spread over a greater area, reducing the insolation at any one spot (the sunlight also has to pass through more of the atmosphere, increasing the amount scattered). Walk just 30° north or south of the equator—or sit still and wait for 2 hours—and insolation will be halved, even though to our eyes it still appears perfectly bright. Again, this comes back to the logarithmic nature of our perception of light (and adjustment of sensitivity by dilating and contracting the pupil). An overcast day can have less than 1/10 the insolation of a sunny day and still appear decently lit.





We could describe all light delivered in terms of power per area like this, but by convention it’s often described in terms of illuminance, which is measured in lux, a unit attuned to the specific spectrum of human vision. 1 W/m2 of just visible light is equivalent to 683 lx, but no light source is that efficient; for sunlight on Earth the ratio is only 93 lx/(W/m2). That means our ideal clear midday equinox at the equator experiences about 100,000 lx at the surface, but it can drop to 1/4 in the shade. By sunset even lit areas drop to a few hundred lx, and at twilight to 3 lx. A clear night with a full moon can have around 0.05-0.3 lx, and a moonless, overcast sky with no nearby light sources can drop to 0.0001 lx.





Artificial lighting falls surprisingly low on this scale. A typical office space with only artificial lighting has around 3-500 lx, and in homes and hallways it can be as low as 50 lx. Streetlights will typically deliver around 5 lx to the sidewalk.





Given all this, we can state as a rule of thumb that about 1/1,000 the light delivered to a surface directly facing sunlight on Earth’s surface (50 lx) could still be considered well-lit, and 1/1,000 of that (0.05 lx) is still marginally visible, at least by human standards. Now, accounting for the specific lux delivered to a surface by a specific star through a specific atmosphere is a devilishly complicated task, so perhaps it’s simpler to just compare the effect of distance from the star on irradiance, the total light delivered to the top of the atmosphere without accounting for human perception:









I = irradiance (relative to Earth)

L = luminosity of light source (relative to sun)

d = distance from light source (AU)





For multiple light sources that illuminate the same side of an object, the irradiances can be independently calculated and added together. If you have a star with a different spectrum from the sun, multiplying this value by 10(bolometric correction)/2.5 should roughly reflect how it would appear to a human or organism with similar color and light intensity perception.





Based on these estimates, objects as far as Neptune, 30 AU from the sun, should appear reasonably well-lit, and objects in the Oort cloud as far as 1000 AU away should remain visible from up close—though in reality it will depend on their albedo.





But if the luminosity of the light source is not known—e.g. if it is a planet or moon reflecting light from elsewhere—than illuminance on a surface directly facing that object can be calculated from its apparent magnitude:









E v = illuminance (lx)

M = apparent magnitude





This means that a body directly overhead with an apparent magnitude of -18.3 is sufficient to keep a surface well-lit on its own and -11 is the threshold for a surface to be marginally visible.





Calling in the Magratheans

Bearing all the possibilities in mind, I’ve put together a system of plausible planets for Teacup A. Like I said last time, the idea is to get something that resembles our solar system, but with a few interesting choices—some of which won’t quite make sense until the next post.





Silhouettes of planets (left to right in order of distance from star) and moons over 0.01 Earth radii (down in order of distance from planet) in the Teacup A system, with sizes but not seperation to scale.





Teacup Ab (m = 0.1 Earth masses, r = 0.46 Earth radii) is a Mercury analog, though slightly larger and less dense (it’s still the densest planet in the system). Its orbital period is only 20.46 Earth days but, being tidal-locked with low obliquity and eccentricity, this causes little change to its surface. Its dayside is a sweltering hellscape reaching over 800 K, but its nightside remains below freezing and, thanks to delivery of ice by comets, has a permanent icecap. Given that the other planets seem to be acting to continuously pump up its eccentricity, it probably experiences a good deal of tidal heating and may experience occasional bursts of volcanism, so much of the dayside is covered in flood basalts with some impact-generated regolith, and overall it isn’t as cratered as Mercury. I was tempted to move this planet further in and make a lava-ice world, but I wasn’t sure how the clouds of escaping atmosphere might affect sunlight levels further out in the solar system (plus it would make those simulations with Orbe in the last post painfully slow). Perhaps I’ll come back to the idea another time.





Teacup Ac (m = 0.5, r = 0.87) is a dry desert planet with a fairly thin but significant N 2 atmosphere. Though close enough to be tidal-locked, due to its eccentricity of 0.15 it has a 3:2 spin-orbit resonance, meaning a synodic day is twice the length of the year; 27.29 Earth days. It also has a small obliquity of 5°, which in combination with its resonance means that there are small regions near each pole that experience direct sunlight only briefly during their respective summers, and some deep valleys that never experience direct sunlight at all. What little surface moisture the planet has will gather in ice caps here, which will spread outwards and melt near the edges. So even though most of the planet is sweltering hot—over 400K near the equator in midday—there are small temperate regions with liquid surface water. Like Mars there are regions of flood basalt and iron oxide dust, but the planet had a wetter period in its distant past when it formed some andesite that has since eroded into lighter-colored silica dust. There are also some salt flats from former lake basins, though many have been covered by lava flows since then.





Teacup Ad (m = 1.6, r = 1.44) is a super-Earth waterworld, about a quarter water by mass. The ocean is underlain by high-pressure ice and covered by a thick H 2 O/N 2 atmosphere. Days are around 130 hours long, which means there are permanent cloud formations that somewhat cool the planet, though a strong greenhouse effect keeps the ocean surface close to boiling. The planet is continuously losing mass to space, and has already lost a significant portion of its oceans.





Teacup Ad I (m = 0.03, r = 0.35) is mutually tidally locked to Ad—the month and days of both bodies are all the same length. Tidal forces help spur occasional volcanism, and much of the surface is covered in flood basalts, but the planet is just about too small to hold onto more than a tenuous CO 2 atmosphere. The planet and moon both do decent jobs of lighting each other during their respective nights; Ad has a diameter of 5.7° and a magnitude of -19.8 as seen from Ad I at midnight (with no eclipse), giving it 177 lx of illumination. Eclipses are also common close to the planet’s equinox, lasting up to 2 hours at any one spot on Ad I.





Teacup Ae (m = 0.8, r = 0.96) is our Earth analog. Its surface is a mix of water oceans, vegetated continents, and polar icecaps, and it has a 2 atm N 2 /O 2 atmosphere. It has a somewhat smaller metallic core than Earth—25% the total mass—which gives it a lower density and surface gravity 86% that of Earth. Combined with the thicker atmosphere, this should make flight and eventually space travel easier. Naturally we’ll be spending a lot of time with this planet, so I won’t say much more now.





Teacup Ae I (m = 1.7*10-10, r = 0.00084) is a small captured asteroid, similar in size and composition to Mars’s moon Deimos. It’s mostly rock, but contains some internal voids and pockets of ice. From the surface of Ae it looks similar to a planet or satellite seen from Earth, but its speed and direction should make it stand out.





Teacup Ae II (m = 0.004, r = 0.18) is a rough analog to Earth’s moon, with a surface dark regolith and flood basalts. It has a similar apparent diameter and magnitude to our moon, but because Teacup A appears larger than our sun at this distance, Ae never experiences a total eclipse.





Teacup Af (m = 120, r = 9.64) is a Saturn analog of 0.38 Jupiter masses. Its mass should put it near the peak size a cool gas giant can achieve, but I’ve shrunk it down a little to reflect its temperature and age. Given its equilibrium temperature and some internal heating, it’s near the boundary between Class I and Class II giants, so we’ll say it has white bands of water clouds near its equator transitioning to more Jupiter-like red and orange bands towards the poles..





Teacup Af I (m = 0.00005, r = 0.041), III (m = 0.0004, r = 0.084), and IV (m = 0.00015, r = 0.061) are all small rocky moons.





Teacup Af II (m = 0.000009, r = 0.021) is an unusually dense body, 60% metallic by mass, as the result of some collision long ago.





Teacup Af V (m = 0.2, r = 0.65) is the largest moon in the system, with properties broadly similar to Mars with a rusty red exterior, though it’s colder and has a somewhat thicker CO­ 2 atmosphere.





Teacup Ag (m = 0.0001, r = 0.061) is a small Ceres analog, the largest body in an asteroid belt nestled between the system’s 2 largest giants. Like Ceres, Ag formed when its orbit was inside the iceline, and today it remains 20% ice with a thin covering of dust. The interior isn’t fully differentiated and produces too little heat to cause anything more dramatic than occasional cryovolcanism.





Teacup Ah (m = 400, r = 11.10) is the planet’s most massive and largest planet. It receives similar sunlight to Saturn, and so has a similar, large beige exterior, though distinct weather bands can be seen on close inspection.





Teacup Ah I (m = 10-7, r = 0.0078) and II (m = 10-8, r = 0.0037) are both primarily irregularly-shaped icy bodies, held together by cohesion more than gravity.





Teacup Ah III (m = 0.025, r = 0.33) is our Io analogue, though a big larger. Tidal heating from Ah causes constant, widespread volcanism, giving it a yellow sulfur exterior.





Teacup Ah IV (m = 0.02, r = 0.33) is our Europa analogue with a rocky interior, icy surface, and subsurface water ocean and cryovolcanism thanks to tidal heating.





Teacup Ah V (m = 0.03, r = 0.41) is our Titan analogue, with a Nitrogen atmosphere and methane oceans on its icy crust.





Teacup Ah VI (m = 0.005, r = 0.25) and VII (m = 0.0008, r = 0.15), the trojan moons, are both small, icy bodies.





Teacup Ai (m = 3, r = 1.82) is half water and other volatiles by mass, and has a substantial subsurface water ocean under an icy surface tinted pink by methane and colored by regions of cryovolcanism and cryolava flows. It has a substantial hydrogen atmosphere, but no surface oceans—at around 50 K, it’s too cold for even nitrogen—and the highest surface gravity of any solid body in the system at 0.91 gs.





Teacup Ai I (m = 0.0001, r = 0.078), II (m = 0.001, r = 0.16), and III (m = 0.0003, r = 0.11) are all icy moons with no particularly unusual features to report just now.





Teacup Aj (m = 25, r = 4.48 ) is our Neptune analog, a blue ice giant out at the edge of the system. Though in reality it’s about twice as far from Teacup A as the point with equivalent sunlight as Neptune.





Teacup Aj I (m = 0.00002, r = 0.046), II (m = 0.0006, r = 0.14), and IV (m = 0.00005, r = 0.058) are, again, typical icy moons.





Teacup Aj III (m = 0.01, r = 0.33) is a bit larger and has a subsurface ocean.





To round things off, Here are the peak apparent diameters and magnitudes of many of these objects to astronomers on Ae (in visual light):





Body A Ad Ae I Ae II Af Ah Aj B Apparent Diameter 0.78 0.06 0.01 0.54 0.10 0.015 0.001 0.001 Apparent Magnitude -25.9 -5.0 -3.4 -12.4 -8.4 -0.35 8.2 -9.4





This has a couple interesting implications for astronomers on Ae: At ideal points, The nearest planets will appear large enough to pick out some surface features, in particular the climate bands on Af, and their change in apparent size throughout the year will be obvious. Af and Teacup B will both shine brighter in Ae’s sky than any star in ours. Presuming human-like eyes, Ah will be dim but visible, Ag (apparent magnitude of 5.7) and Ai (apparent magnitude of 6.2) might be just on the cusp of visibility, and Aj will pass unnoticed before telescopes. Af V (apparent magnitude of -2.2) should also appear as a distinct object, as much as 2° apart from Af, so that could help head off any ideas that objects orbit only around Ae.





Relative apparent sizes of objects (and separation of Af and AfV to scale) from the surface of Earth or Teacup Ae. To see how they'd actually appear, back up or zoom out the page until Teacup A is about the size of the nail of your outstretched pinky finger.

In Summary

Planets mostly fall within 3 regimes of mass-radius relationships: Earth-like terrestrial planets, Neptune-like small gas giants, and Jupiter-like giants.

For terrestrial planets, size is determined by the proportions of volatiles (mostly water), lithophiles (rocky material), and siderophiles (metallic material) and total mass, with larger planets being more compressed.

Heating by sunlight plays a major role in determining the properties of planets at given distances from a star, but many variations are possible.

Gasses with low molecular weights escape more easily from planet's atmosphere.

Lower escape velocity and higher temperature determine the rate at which gasses escape and so also the atmospheres possible after long periods.

Oceans are possible only for planets with substantial atmospheres.

Eyeball planets, carbon planets, sulfur planets, waterworlds, helium-gas giants, and lava-eyeball planets are all theoretically possible though they don't exist in the solar system.

Apparent brightness to human eyes falls much more slowly than actual sunlight in the outer solar system.

Daily lunar eclipses, interplanetary eclipses, and reflected-light days are all possible on other bodies.

Notes

I may come back and expand my list of possible surfaces in the future if I can but it’s tricky to find sources regarding types not seen in the solar system.





Apparently the dynamics of tidal heating were first described by George Darwin, Charles’ grandson.





I find it super amusing that carbon planets sound so valuable to us now, but by the time we have the technology to get to them both diamonds and oil will probably cost peanuts to artificially produce.