An Apple Pie From Scratch, Part IVc: Planets and Moons: Habitability

Building a habitable world is perhaps the trickiest bit of astronomical worldbuilding. Part of this comes from the dizzying array of factors involved: Both planetary systems and individual planets are complex, chaotic systems, and everything has to work out just right to allow for life, then continue to do so for billions of years to allow for complex life. But a big part of the problem comes from how little we know about what makes a planet habitable. We’ve only been able to spot planets outside the solar system—exoplanets—for a couple decades, and planets of similar size to Earth for less than half that time. Much of what we thought was secure knowledge before then has been overturned, and for all that we’ve discovered since then we won’t really be able to say what makes a planet habitable until we start finding other inhabited planets—assuming there are any in the neighborhood besides Earth.

There are two opposing assumptions to keep in mind here, both of which color how we view our place in the cosmos. The first is the mediocrity principle, the assumption that because our solar system is just one of many star systems in the nearby universe, it’s more likely to be an average system than a particularly unusual one. We shouldn’t expect any one feature of our system to be unique, because the same formation processes that created it here could just as easily have happened elsewhere.

The other assumption is the anthropic principle, which states that the mere fact that intelligent life appeared here means that our solar system is necessarily an unusual system. If the conditions required for life are quite rare, then life would only appear in such rare systems and so we have every reason to suspect our solar system might be unique.

Take the example of Earth’s large moon: According to the mediocrity principle, we shouldn’t expect such large moons to be particularly rare, or necessarily linked to the emergence of life; But according to the anthropic principle, we shouldn’t be surprised if large moons turn out to be rare, and we should also expect intelligent life only to appear around planets with similarly large moons. Most frustrating of all is the possibility that a large moon is a rare feature, but that it has nothing to do with life and the fact that Earth has both is just a coincidence.

This is just one approach to these principles; we could also take the mediocrity principle to mean that our solar system is average for an inhabited system, and take the anthropic principle to mean that we’re most likely to have appeared in a region of the universe where other systems may be habitable as well (the anthropic principle is also involved in a wider discussion about the fundamental laws of physics, but we won’t get into that here). Taken together, the two principles mean that any feature of our solar system that turns out to be unusual is fairly likely to be related to the emergence of life, though it’s not guaranteed.

In this discussion we also have to be aware of various types of selection bias. We now have a couple different methods to detect exoplanets, but they are all heavily biased towards the detection of larger and more massive planets in certain types of orbits—generally those with lower semimajor axes. So we have to be careful when making conclusions based on observed exoplanet properties, because they may not necessarily reflect the properties of all planets.

There’s another type of bias that I expect is fairly common in this field but I haven’t seen named, so I’ll go ahead and call in anchor line bias (similar but not identical to anchoring, a cognitive bias rather than a statistical one). We know that Earth has life, and that any model predicting a range of conditions that allow for life must include the conditions on Earth. So if several models are constructed based on differing reasonable estimates of input values that produce different ranges of predicted habitable conditions, those models where the range excludes Earth can be obviously rejected but those that don’t cannot.

Suppose that Earth is near the extreme lower end of habitability with regards to some property. Several models are produced with some random error, such that they predict somewhat different ranges of habitability for that property. Those that have lower bounds above Earth’s value are rejected; those that have lower bounds below Earth are considered plausible. Thus the average of the lower bounds for all plausible models is below the actual lower bound, causing Earth to appear to be closer to the average of habitable planets with regards to that property than it actually is.

But we can’t assume this is always happening: Suppose now that Earth is near the average for some property. Several models are produced with random error, but also with some common systemic error that causes their average to be higher than the real one. Again models that exclude Earth are rejected, and a set of plausible models that include Earth are retained, the net result being that Earth appears to be more borderline than it actually is. Even if a majority of models exclude Earth, only the plausible ones are published, so it can be hard to identify the error.

We can’t tell which of these two cases is occurring for any given property, so even knowing that anchor line bias is at work, we can’t determine if the Earth is more average or extreme than our models predict.

At any rate, the advantage of all this uncertainty is that we have a lot of freedom in constructing fictional habitable worlds. But too much freedom is no fun, so—bearing all these possible biases in mind—let’s see what the likely restrictions are based on what’s been discovered so far.

Back to Part IVb

Habitable Zone

Concept of the Trappist-1 planets. NASA/R. Hurt/T. Pyle

For the purposes of this post I’m still defining “habitable” in terms of the ability to support complex life—life that has to potential to develop humanlike intelligence—and assuming that complex life requires liquid water and sufficient sunlight for photosynthesis. Again, we’ll discuss possible alternatives another time.

Note that this definition includes a temporal component as well; for a planet to develop complex life, it has to maintain habitable conditions for long enough for life to appear and evolve complexity. It’s hard to say exactly how long that might take given only one example (we’ll talk a bit more about estimating minimum timescale from that example in a later post) so for now we’ll use the current age of the Earth, 4.5 billion years, as a reasonable necessary period of habitability. Within our own solar system, Venus and Mars both likely had habitable conditions for at least hundreds of millions of years following the Late Heavy Bombardment, but only Earth has managed to stay habitable, so only Earth counts as “habitable” by our definition.

So really what we’re asking is, how do we get a planet with liquid surface water that remains in that state for billions of years?

Water itself is fairly common; it’s composed of the first and third most common elements in the universe. Even in the water-poor innermost regions of the protoplanetary disk, water could have been delivered from planetoids flung in from beyond the iceline. Getting that water to be liquid requires a narrow range of temperatures, and the easiest way to constrain a planet’s surface temperature is to constrain the incident sunlight. Thus, the concept of the circumstellar habitable zone: close enough to the star to melt water, but not so close as to evaporate it.

We already discussed equilibrium temperature in the last post, and the fact that its estimate for Earth is a severe underestimate at 255 K (-17 °C), compared to the actual average of 288 K (15 °C). Earth produces too little internal heat to significantly alter the surface temperature, so the anomaly must be due to an additional factor in the balance between absorbed sunlight and emitted heat that the equilibrium temperature calculation doesn’t account for.

The missing element is the greenhouse effect. For all the constructed controversy around it in recent years, the physics is pretty straightforward: Certain gasses like CO₂, water, and methane are transparent to visible light but opaque to certain wavelengths of infrared. So visible light passes unimpeded through the atmosphere, is absorbed by the surface, is reemitted as infrared, and then is absorbed by greenhouse gasses and partially reemitted back down to the surface. This effectively reduces the rate at which the planet loses heat, and so the planet’s surface temperature has to rise (increasing the rate at which heat is emitted) in order to reestablish an equilibrium.

Mechanism of the greenhouse effect, and humanity's influence on it. Australian Government

In terms of effect on temperature, water is actually the strongest greenhouse gas on Earth, accounting for over half of the total warming. But water remains in the atmosphere a few days, and its concentration in the atmosphere is determined by temperature. Were there no other greenhouse gasses in Earth’s atmosphere, the water would quickly settle out of the atmosphere before it could cause significant warming, and with less water to cause greenhouse warming temperatures would fall, causing more water to settle out of the atmosphere, and so on until the planet freezes over.

But if there are other greenhouse gasses present, water will tend to amplify their effect. CO₂—which resides in the atmosphere for decades, longer if accounting for processes that tend to cycle it back into the atmosphere, and does not immediately react to temperature change—accounts for most of the rest of greenhouse warming (~20-30% of the total) so it is the CO₂ level that primarily determines surface temperature, and this should usually be the case for Earthlike inhabited worlds. Methane or hydrogen may have played bigger roles in Earth’s past, but neither can exist in high concentrations alongside oxygen (methane still accounts for ~5% of the total warming, and ozone makes a similar contribution). If we want to warm a habitable planet, CO₂ is the best option.

But does this mean a planet has to form with just the right amount of CO₂ for habitable temperatures? And how does the concentration of CO₂ remain in this narrow range for billions of years, even as the star grows brighter?

To answer this, we have to see how the climate is controlled by a set of feedback cycles, which are ongoing processes where the end state of one instance affects the initial state of the next. There are two types: In a positive feedback, the process tends to reinforce changes in the initial state. Think of them like a pencil placed on its end; introduce a little tilt to the pencil, and it will become unbalanced and start to fall, tipping over more and becoming more unbalanced, until it topples over completely. Positive feedbacks are unstable, and a system dominated by them won’t last in its current state for long.

In a negative feedback, the process tends to counteract changes in the initial state. Think of them like a ball resting in the bowl; push the ball to the side, and it will roll back towards the center and lose energy to friction until it comes back to rest where it began. Negative feedbacks are stable, and a system dominated by them will last in its state indefinitely so long as the feedbacks continue to work. So if we want to keep a planet at a comfortable temperature and habitable for billions of years despite all outside influences, we need negative feedbacks to do the job.

Fortunately, we have quite a powerful one in the form of the carbon-silicate cycle, a.k.a. the “deep carbon” or “inorganic carbon” cycle. You may have heard “carbon cycle” used to describe the conversion of CO₂ to sugars and O₂ by plants and conversion of those compounds back to CO₂ by animals, but really that’s just a sideshow. The carbon-silicate cycle is a much larger, slower process that loops massive amounts of carbon through the atmosphere, oceans, crust, and mantle by geological processes. It can be aided by the presence of life, but doesn’t require it, and so it’s been going steadily since early in Earth’s history and through life’s appearance and many changes.

Stages of the carbon-silicate cycle on Earth. In principle it could also work by inorganic deposition without the need for animal shells. Source

It starts with volcanoes, which both release CO₂ stored in the planet’s interior and create vast tracts of new, exposed rock that contains, among other things, calcium. This exposed rock weathers quickly, and in the presence of water the calcium-bearing minerals will react with atmospheric CO₂ to produce calcium (Ca⁺) and bicarbonate (HCO₃^-) ions. Both ions dissolve in water and wash downstream to the ocean, where they combine to form calcite (CaCO₃) and other carbonate minerals that settle on the seafloor and also tend to trap some water with them—this is where marine life can help the process along by forming carbonate shells and then sinking to the bottom when they die. These minerals eventually make their way to subduction zones, where one tectonic plate is pushed under another and descends into the mantle (more on where and why this happens in the next post). Once in the mantle, the water helps to dissolve the minerals, splitting the calcium and CO₂ and creating a low-density magma that rises through the overlaying plate and bursts through to form volcanoes, closing the loop.

Now here’s the important bit: The rate at which CO₂ is released into the atmosphere is fairly constant, but the rate at which calcium-bearing minerals weather is tied to temperature. If there is excess CO₂ in the atmosphere it will drive temperatures up, weathering will increase, and more CO₂ will be pulled out of the atmosphere and stored on the seafloor. If there’s a shortage of CO₂, the planet will cool and weathering will slow down while volcanic activity replenishes the atmosphere’s CO₂ supply. Whether the change in conditions is rapid or gradual, the concentration of atmospheric CO₂ will always trend towards the level necessary to maintain the temperature that best matches CO₂ production with CO₂ consumption, which happens to be a temperature that allows for liquid water on the surface and abundant life.

Interactions involved in the climate feedback. Green arrows indicate one effect increasing another, the yellow error indicates one effect decreasing another. Gretashum, Wikimedia

This elegant cycle is the prime factor that has kept Earth’s climate stable throughout most of its history. It is a long loop and so can take thousands of years to correct sudden upsets, as we are now discovering to our detriment. In the past unusual volcanic events have pumped extra CO₂ into the atmosphere—triggering brief warm periods and mass extinctions—or exposed vast masses of fresh calcium-rich rock—triggering cold snaps—but throughout Earth’s history the system has always returned to normal eventually. And so it should be do the same for other planets moderated by the carbon-silicate cycle even over a broad range of initial temperatures, CO₂ concentrations, and land areas. Thus, if we put an Earthlike planet with water and CO₂ in any orbit that could allow for habitable conditions with the right amount of greenhouse warming, there’s a good chance that it will become habitable without the need for further interference.

But robust as the carbon-silicate cycle is, it has to contend with positive feedback cycles affecting the planet’s climate as well. We already discussed one between greenhouse warming due to water and atmospheric concentration of water due to temperature. But even more potent is ice-albedo feedback, which is caused by the large difference in the albedos of ice (0.6-0.8) and open ocean (0.06). If a planet suddenly cools, it can cause the formation of sea ice that reflects away more of the incident sunlight, cooling the planet further, and the reverse can happen if a planet with some sea ice suddenly warms. Usually the carbon-silicate cycle overpowers the effects of ice-albedo feedback in the long term, but the latter cycle can operate on much shorter timescales—decades rather than millennia—and so can amplify brief upsets to the climate equilibrium. A sufficiently large upset could cause the oceans to evaporate away entirely, creating a “hothouse” world like Venus, or freeze over, creating a “snowball” world like Europa, before the carbon-silicate cycle can act. A planet could eventually recover from either condition (it’s easier for a snowball than a hothouse) but life may not.

Ice-albedo feedback loop; the same process can work in reverse, encouraging more freezing. Source

The ultimate limits on habitability are caused by two other positive feedbacks that kick in at certain levels of incident sunlight. To return to our feedback analogies, we might think of this like a ball placed in a bowl at the top of a hill. So long as the ball isn’t pushed hard enough to get it over the rim of the bowl, it’ll return to the center; but once it’s out of the bowl, it’s not going back in.

At the inner edge of the habitable zone, the sunlight is intense enough to keep a high concentration of water in the atmosphere even without the help of CO₂, and indeed CO₂ is expected to be largely absent on these worlds because of permanently high temperatures causing rapid consumption by weathering. But unlike with CO₂, no surface process can consume water as fast as its supplied by evaporation of the oceans. Some water is consumed by photolysis (breakup into hydrogen and oxygen due to solar radiation), but this causes permanent loss. If a planet’s orbit is within the moist greenhouse limit, water loss by photolysis is fast enough to deplete the oceans entirely within 10s to 100s of millions of years, drying out the planet and turning it into a hothouse. But a planet orbiting a low-mass star may bypass the moist greenhouse limit and run directly into the runaway greenhouse limit, at which point the entire oceans promptly evaporate to the upper atmosphere, and then are gradually lost from there.

Image of Venus. NASA/JPL

As distance from the star increases, the concentration of CO₂ necessary to maintain ideal temperatures does as well. Near the outer edge of the habitable zone, the concentration is so high that CO₂ clouds form. Though they may still contribute to the greenhouse effect, these clouds are reflective enough that, on balance, they cool the planet. Past the maximum greenhouse limit, an increase in CO₂ levels causes more energy loss due to reflection of sunlight by clouds than energy gain due greenhouse warming. This reverses the carbon-silicate cycle into a positive feedback (greater CO₂ causes lower temperatures causes less CO₂ consumption) and the planet cools to a snowball.

Concept of Earth in the Cryogenian. NASA.

These two limits define the edges of the “classical” habitable zone. Based on climate models, researchers have placed the zone in our solar system at 0.99 to 1.70 AU from the sun. But these models are very simplified representations of planetary climates, and even just incorporating the effects of water cloud formation has recently pushed the inner boundary to 0.95 AU. Even so, this puts Earth near the cusp of crossing the moist greenhouse limit, and indeed we do expect this to happen within the next 1.5 billion years.

Recognizing the limitations of current theoretical models, some researchers have designated these limits as the conservative habitable zone and also defined an optimistic habitable zone based on the assumptions that Venus and Mars had surface liquid water 1 billion and 3.8 billion years ago, respectively; accounting for the sun’s warming since then, this pushes the boundaries out to 0.75 and 1.77 AU. Both assumptions have their issues: in Venus’s case, we only have evidence that it couldn’t have had water less than 1 billion years ago and not that it did before that point; in Mars’s case, we don’t know that it was at the outermost limit for water at the time, but neither do we know that any planet could manage to retain surface water longer than Mars did. But they’re decent ballpark estimates.

The optimistic and conservative boundaries of the "classical habitable zone", with some known exoplanets. Kopparapu 2018

These limits are based on levels of sunlight, so you can obtain rough estimates for them in other systems based on equivalent insolation:

B_n = boundary distance in new system

L = luminosity of star (ratio to sun)

B_s = boundary distance in solar system

However, because different stars produce different spectra of light—and in particular because water reflects more blue light than red light—habitable zone boundaries will be at higher luminosities for bigger, hotter stars. Fortunately the same team that gave us our classical habitable zone estimates also provided a formula to compensate for this (that also accounts for planet mass, as—all else being equal—larger planets better resist the moist greenhouse limit):

B_n = boundary distance in new system (AU)

L = luminosity of star (ratio to sun)

S_eff = effective luminosity at boundary, equivalent to 1/B_s² from above but precise values in table 1 here.

T_* = star effective temperature – 5780 K

a, b, c, d = coefficients from table 1 here.

These habitable zone limits (and the others we’ll discuss in a moment) can all be estimated using my worldbuilding spreadsheet.

Extending the Habitable Zone

The classical habitable zone is defined for a very Earthlike planet; short days, large oceans, and a similar atmosphere. But ever since the zone was defined, researchers have been considering how more alien worlds may be able to retain habitable conditions outsize the typical limits.

One easy but counterintuitive move is to get rid of as much water as possible. Water is vital to both Earthlike life and the carbon-silicate cycle, but it’s a bit dangerous to have around because it both amplifies the greenhouse warming of CO₂ and causes ice-albedo feedback. Land typically has an albedo of 0.15 to 0.4, intermediate between ice and water, and so compared to an ocean-dominated planet, a land-dominated planet will be cooler near the inner edge of the habitable zone and warmer near the outer edge, extending the limits of the habitable zone. Thus the habitable desert planet, a long-time favorite of many authors, is not only feasible but probably easier to come by than a more Earthlike world. They wouldn’t all be hot, marginal worlds, either; lakes and seas with forested shorelines could still exist on an otherwise dry world, and the range of surface temperatures would be much the same as for a wetter world.

Concept of Kepler-62f. NASA/Ames/JPL-Caltech

Still, such a world would likely have less total biomass than a similar-sized Earthlike world, and may have a tougher time developing complex life. Worse, the lack of ocean basins means it cannot experience subduction or plate tectonics, a vital component of the carbon-silicate cycle. Fortunately there are alternative tectonic modes that could sustain the cycle as well (more on them another time) but they may not do as good a job stabilizing the climate over the long term.

But assuming that the carbon-silicate cycle could operate even with extremely low surface water, the limits can be pushed to surprising extremes. A planet with almost no surface water, low CO₂, and an albedo of 0.8 could orbit as close as 0.38 AU—inside the orbit of Mercury—without passing the moist greenhouse limit. Such high albedo is likely unreasonable, though; for a more reasonable value of 0.2, the limit is at 0.59 AU. In these cases most of the planet is dry and barren, but what little water there is collects in ice caps at the poles or on the nightside of a tidal-locked world and melts around the edges, forming a small habitable strip with liquid water. This marginal existence in the twilight zone between a glacier and a sweltering desert may not seem the ideal place to develop life, but all the elements are there.

Inner edge of the habitable zone for dry planets with N₂ atmospheres, albedo of 0.2, and humidity of Ф (red lines), compared to the "classical habitable zone" (black lines). Zsom et al. 2013

A more moderate approach is to slow the world’s rotation, or make it fully tidal-locked. These worlds could develop large permanent cloud formations that substantially increase their albedo, pushing the limit to 0.66 AU. Around K-type and early M-type stars such planets could even pass the moist greenhouse limit with habitable temperature and slow-enough water loss for oceans to survive billions of years, remaining habitable right up to the runaway limit. Once the orbital period drops below 5 days the climate essentially returns to that of a rapidly-rotating planet and the protective cloud formations no longer form, but that shouldn’t occur even at the inner limit of this zone for stars over 0.1 solar masses.

On the outer side of the HZ, poorly-performing CO₂ can be augmented with methane, which can push the outer edge to about 1.81 AU, but only for mid K-type stars and hotter. However, too much methane in the presence of CO₂ could form a haze, and methane cannot coexist in high concentrations with oxygen.

A more dramatic improvement can be made with hydrogen, which can act as a greenhouse gas at sufficient pressure and condenses at much lower temperature. Just 5% H₂ in an otherwise N₂/CO₂/H₂O atmosphere can push the outer edge to 1.94 AU, 50% can push it to 2.4 AU, and an H₂-dominated atmosphere with 100 times Earth’s sea level pressure could push it all the way to 15 AU. Maintaining such an atmosphere is a challenge given that hydrogen easily escapes into space and is not produced in large amounts on Earth currently, but a sufficiently large planet past 2 AU may be able to retain an early hydrogen atmosphere for billions of years. If life appears on such a world, however, there’s a good chance it will metabolize the hydrogen into methane or produce oxygen that will react to form water, destroying its own environment.

Outer habitable zone limits for planets with given H₂contents. "Effective flux" is a measurement of the sunlight the planet receives relative to Earth. Ramirez and Kalteneggar 2017

But if the rate of hydrogen consumption is linked to temperature and the planet is continuously outgassing more hydrogen, then a stabilizing negative feedback may result: Excess consumption of H₂ will cause temperature to drop and consumption with it, allowing the H₂ to be replenished by volcanic activity; and excess production will increase consumption. But unlike the carbon-silicate cycle, this feedback would be totally dependent on life, and if a sudden rise in H₂ and temperature caused a mass extinction—as has happened with CO₂ in Earth’s past—the dwindling population of survivors may be increasingly incapable of consuming enough hydrogen to prevent their own demise.

But even if these solutions aren’t viable in the long turn, a planet that forms just past the conventional habitable zone might be kept warm by a hydrogen or methane atmosphere until the sun is warm enough that it can lose that atmosphere without issue.

Expanded habitable zone with extremely dry and H₂-greenhouse planets accounted for, with the positions of some likely-rocky exoplanets shown. Seager 2013

Irregular Orbits

These habitability models have a habit of assuming planets in stable, circular orbits with nothing affecting insolation save for the slow brightening of the star. But even on Earth we can see how obliquity affects climate: high latitudes experience major seasonal variations due to how the day length and insolation per surface area changes as either hemisphere is pointed towards or away from the sun, due to our axial tilt of 23.5°.

cmglee, Wikimedia/NASA

A planet with 0° tilt would experience no seasons at all, and as obliquity rises seasons become more pronounced. Once the tilt surpasses 45° the tropical region—where the star is directly overhead for part of the year—overlaps the polar regions—where the star is permanently below the horizon for part of the year. This causes an odd reversal of roles over the course of the year: near the equinoxes, the equator receives direct sunlight and heat flows from there to the poles; but near the solstices, one of the poles receives continuous strong sunlight and so heat flows from there to the equator and thence to the other pole. Averaged over the year, it is actually the poles that receive the most heat on a planet with obliquity greater than 57°, though they still have the most variation. Each pole experiences one extreme summer-winter cycle each year, peaking during solstices, while the equator experiences two equinox summers and two solstice winters in the same time.

How much obliquity affects habitability depends largely on the efficiency of heat transport across the planet. Planets with thicker atmospheres will tend to transport heat better, and rotation rate also has an effect; on a slow-spinning planet heat will move directly from hot to cold latitudes, but on a fast-spinning planet the Coriolis effect will cause the formation of climate bands that partially insulate different latitudes from each other. On a low-obliquity planet, inefficient heat transport causes the equator to be much warmer than the poles, such that only the poles may be habitable near the inner edge of the habitable zone and only the tropics near the outer edge. For high-obliquity planets it is the equator that remains more habitable near the inner edge, though there is no condition where the poles are significantly more habitable than the equator near the outer edge. Where heat transport is efficient, all regions of the planet remain habitable through most of the habitable zone.

The arrangement of continents also has an effect. Continents cool more efficiently than oceans, and so a continent over a pole is more likely to be covered in glaciers and remain cool throughout the year regardless of obliquity. A high-obliquity planet with little surface water may remain habitable year-round only at the equator.

But eccentricity can also form seasonal variations, with summer at periapsis and winter at apoapsis. Unlike obliquity-forced seasons, eccentricity-forced seasons are uniform across the planet’s surface rather than offset by hemisphere, though a low-obliquity, high-eccentricity planet will still have more variation between equator and poles than a high-obliquity, low-eccentricity planet. And because planets move faster near periapsis, summers will be shorter than winters, and moreso the greater the eccentricity.

As a general rule, for a given semimajor axis the average temperature of a planet will increase with greater eccentricity. Even though summers are shorter, the inverse-square relationship of sunlight intensity to distance from the sun means that the increase in insolation due to moving inwards of the semimajor axis is much greater than the sunlight decrease from moving the same distance outwards. This means that the habitable zone is slightly further out for high-eccentricity planets, and indeed a frozen planet in a circular orbit just outside the typical habitable zone may be thawed out by an induced increase in eccentricity.

NASA/JPL-Caltech

Of course, a planet can have both high obliquity and high eccentricity. If the periapsis coincides with one of the solstices—say, the northern summer solstice—then the eccentricity will reinforce the obliquity-forced seasons in the northern hemisphere and weaken them in the south—thus a short, hot summer and cold, long winter in the north and mild seasons with reversed lengths in the south. If this is a high-eccentricity planet near the outer edge of the habitable zone, the northern hemisphere may freeze over completely during the winter and be unable to thaw in the summer, leaving only the mild southern hemisphere habitable. If the periapsis does not coincide with a solstice, then the situation can become more complicated.

Take the case where the northern summer solstice is 1/4 of an orbit behind the periapsis, so that the equinoxes coincide with the periapsis and apoapsis. For a planet with intermediate obliquity like Earth, the entire planet will experience a single summer-winter cycle per year, but rather than being neatly split by hemisphere the seasons will gradually move south across the surface: the north pole will experience peak summer somewhere between the northern summer solstice and periapsis, then rapidly transition through fall to winter by the northern winter solstice, and then experience a long, gradual spring; the equator will have regular eccentricity-forced seasons, with summer peaking near periapsis; and the south pole will have summer between periapsis and the northern winter solstice, a long, gradual fall, and then winter near the northern summer solstice and a rapid spring. For a high-obliquity planet, the poles will exhibit much the same patterns but the equator will have a warm summer at periapsis, a cooler summer at apoapsis, and winters in between. Move the northern summer solstice closer to periapsis and this will cause summers and winters to be shorter and more intense at the north pole and longer in the south, while the equator of a high-obliquity planet will get a bewildering patchwork of seasons of varying length (see here for some good examples of seasonal temperature variation for various orbital characteristics).

But more than just messing with the calendar, a combination of high eccentricity and intermediate obliquity can help push out the outer edge of the habitable zone by preventing a cold planet from freezing over completely. A planet with an eccentricity of 0.5 and obliquity of 30° may be habitable with a semimajor axis past 2 AU around a sunlike star.

However, we should not expect these values to remain stable throughout a planet’s history. The Earth experiences periodic variations in obliquity, called “Milankovitch cycles” due to the gravitational influence of other planets. These cycles amount to little more than a 2° change in tilt, but this is enough to push the Earth between glacial and interglacial periods in our current ice age. Other planets may experience more extreme variations, both in obliquity and eccentricity, and these can cause similar shifts in ice cover at the poles. But changing ice cover can be dangerous due to ice-albedo feedback. Recent modelling of this feedback and other climate-moderating effects for planets with large obliquity and eccentricity indicates that a point of critical instability is reached if the obliquity surpasses 35° while the planet is in a period of low eccentricity; either the polar ice caps will melt completely or they will expand to cover the whole planet, putting it in a snowball state. A later increase in eccentricity may help thaw the planet again, and an initial eccentricity over 0.2 will prevent the snowball from forming in the first place.

Note that both obliquity and eccentricity will be reduced by tidal forces for planets in the habitable zone of low-mass stars, so unless they’ve been recently induced by other planets don’t expect them to be remain high by the time complex life appears in such systems.

To get a handle on how obliquity and eccentricity compare and affect sunlight exposure, we can calculate the irradiance (sunlight exposure without accounting for atmospheric effects) for a given latitude, declination of the sun, and distance from the star relative to the semimajor axis:

Q_day = average irradiance across the day (W/m²)

S₀ = solar constant; 1367 W/m²

L = stellar luminosity (ratio to sun)

d = current distance from sun (AU); a(1 + e) at apoapsis and a(1 – e) at periapsis where a is the semimajor axis and e is the eccentricity

φ = latitude; negative in the southern hemisphere

δ = declination of the sun; the angle from directly overhead that the sun appears at noon on the equator; 0° at the equinox, ε (the planet’s obliquity) at the northern summer solstice, -ε at the northern winter solstice.

h₀ = hour angle of sunrise (°); cos^-1[-tan(φ) tan(δ)] except where [tan(φ) tan(δ)] > 1, in which case the sun doesn’t set and h₀ = 180°; or [tan(φ) tan(δ)] < -1, in which case the sun doesn’t rise and Q_day = 0.

(where the year length is much longer than the day length and so d does not vary significantly in one day)

This is a pretty hideous formula, so to save you a lot of time I’ve included a calculator for irradiance at different latitudes throughout the year in the worldbuilding spreadsheet. We can see that on Earth at 45° north latitude Q_day varies from 502 W/m² at northern summer solstice to 117 W/m² at northern winter solstice. Were Earth to have 0° obliquity, it would require a semimajor axis of 1.2 AU and an eccentricity of 0.42 for similar maximum and minimum Q_day at the same latitude. This isn’t to imply that this eccentric Earth would have an equivalent climate, and indeed this is a criminally oversimplified model of seasonal change (because it doesn’t account for surface albedo, thermal inertia, heat flow between latitudes, and various feedbacks)—but it’s a decent starting point.

There is one last way to get seasons. A rapidly-rotating star will form an equatorial bulge, much as a planet does, with flattened poles. Because the material in this bulge is farther from the core and less dense, it is cooler and less bright than the poles. If a planet is in an orbit highly inclined from the star’s equatorial plane, then the planet will receive more light when over the poles than when over the equator. This can lead to as much as 15% variance in surface temperatures, on par with eccentricity or obliquity-forced seasons. As with eccentricity-forced seasons the luminosity changes would be applied across the whole planet, but summer wouldn’t necessarily be shorter than winter, and in this case each year has 2 summer and 2 winters. I shudder to think of what the seasonal calendar might look like for a mix of all 3 types of seasons.

Before we move on, a couple extra notes on rotation rate: we already established that slower rotation tends to decrease the difference between equatorial and polar temperature. It also tends to cool down the planet overall due to the aforementioned formation of clouds at the substellar point. This is useful at the very inner edge of the habitable zone but problematic further out, especially in combination with the longer nights. In Earth’s current orbit, a day 16 times longer than our current one appears to be the ideal to maximize habitable surface area. However, warmer poles could also increase the weathering rate, causing further decreases to global temperature in the long run, though exactly how that plays out depends on the distribution of continents.

Size

Being in a suitable orbit in the habitable zone is, unfortunately, no guarantee that a planet will be habitable. Mars orbits comfortably within even the conservative habitable zone estimate, and stubbornly remains dead. It’s even a dry desert world, which should make it easier to stay habitable.

What went wrong? First off, there’s the issue of size; Mars is only 0.107 times the mass of Earth, making it difficult for it to hold onto a thick atmosphere. But it shouldn’t be impossible; give Mars an Earthlike atmosphere today, and it’ll hold onto it for an impressively long time. It may not last billions of years, but given volcanic activity like Earth’s the losses could be compensated for with outgassing. After all, Earth and Venus lost their primary atmospheres and formed their current ones through outgassing.

But crucially, Mars lacks significant volcanic activity. The modern surface shows the scars of plentiful volcanism when the planet was young and what may even be the early stirrings of plate tectonics, but the volcanic activity declined over time and these scars only remain because the surface has been largely dormant for billions of years. No tectonics, no thick atmosphere, and no carbon-silicate cycle. So if we’re going to build a habitable world and rely on tectonics to both produce the atmosphere and stabilize the climate, we better be sure we know what it needs to work.

A common misconception about the Earth’s interior is that the crust is a thin solid layer floating on an ocean of magma, but in reality the mantle is mostly solid as well. There are regions of melt, which are more common the lower you go, but it doesn’t become completely liquid until the outer core. However, mantle rock is under such intense heat and pressure that it undergoes continuous plastic deformation, such that—viewed at large scales over long periods of time—it can act as a fluid. Caught between the warm core and cool exterior, the fluid convects, and what we observe as tectonic plates on the surface are really just the uppermost portions of immense convection cells extending all the way down to the core-mantle boundary.

Though I’ve been speaking about the carbon-silicate cycle in the context of plate tectonics with subduction, in theory it’s not the only way to produce such a cycle; so long as there is volcanism to outgas CO₂ and produce exposed calcium and some method for these materials to be buried, melt, and close the loop, the cycle can work. Broadly speaking plate tectonics appears to be the most favorable to the development of complex life—for a few reasons but most notably for its stability in CO₂ production—but many of the alternatives could be sufficient as well. We’ll discuss these alternatives in a later post, but for now the important point is that all these processes are also results of mantle convection.

As an added bonus, convection drives the outer core dynamo, which produces Earth’s magnetic field. As mentioned in the last post, a magnetic field isn’t absolutely necessary for a planet to hold an atmosphere, but it certainly helps and may be more important for young planets with more hydrogen in their atmospheres or forplanets near the inner habitable zone boundary in danger of losing their water to a moist greenhouse.

So if we want tectonic activity on our habitable worlds, we need internal convection, and for that we need heat. Sunlight doesn’t help—it can be hardly be expected to melt the core and leave the crust intact—so we have to rely on interior sources. Earths interior produces around 47 TW of heat continuously though this includes heat from the crust, which doesn’t contribute to mantle convection. So far as we know it has two main sources: primordial heat, left over both from the impacts that first formed the Earth and from friction when heavier elements separated from lighter ones and fell to the core; and radiogenic heat, resulting from the decay of unstable isotopes like uranium, thorium, and potassium. How much each source contributes is a long-running debate, but observations of geoneutrinos—particles produced by radioactive decay that rarely interact with matter and so flow freely through the Earth—indicate that roughly 30 TW is radiogenic, with the rest presumably being primordial. But that’s just today; radioactive isotopes are depleted over time and primordial heat is radiated into space, meaning that heat production is declining over time. Except in the case of a massive, surface-sterilizing impact, a planet won’t get more of either source, so however much it starts with has to last for billions of years.

Which brings us back around to the matter of size. The rate at which a planet radiates heat to space is determined by its surface area, while—for a given composition and density—the heat capacity and total amount of radioactive isotopes is determined by volume. As a planet gets smaller, the volume declines faster than the surface area. A planet with 1/2 the radius of Earth will have 1/4 the surface area and 1/8 the volume. This relationship, called the square-cube law, turns up in a lot of contexts, so remember it. This means that a smaller planet will lose primordial heat faster and have cooler interiors for proportionally similar levels of radioactivity. This is what ultimately killed Mars: its interior cooled, its crust thickened, mantle convection slowed, and today it experiences only sporadic volcanism. It cannot replace its atmospheric losses, and even if it did have a thick atmosphere it couldn’t sustain warm temperatures without an effective carbon cycle.

Exactly what the minimum mass is for a planet to sustain tectonic activity for billions of years has not been studied in depth. A rough estimate based on the decay rate of uranium—the most important of Earth’s radiogenic elements—and the observation that Mars’s tectonics appear to have halted 2 billion years ago (implying that the heat flow then was the minimum necessary for tectonic activity), results in a critical mass of 0.23 Earth masses. It’s a simple model with old figures, but it does about match with more recent studies showing that volcanism on worlds with plate tectonics should continue for up to 10 billion years on 0.25 Earth mass planets and that 0.1 Earth mass planets cool too quickly for plate tectonics to ever set in.

But a planet need not necessarily produce all its own heat. If a planet experiences strong tidal forces from its star, and it has some obliquity, eccentricity, or non-synchronous rotation—all of which cause the tidal bulge on the planet to turn away from the star—then the tidal forces will drag the bulge back towards the star, causing internal friction and a good deal of heat. For an Earthlike planet with high eccentricity orbiting in the habitable zone of a star below 0.3 solar masses, the tidal heating alone could be enough to drive plate tectonics even in the absence of other heat sources. Freed from the need to produce and retain heat, the minimum size of such a world is set by the requirement for the escape velocity to be high enough to prevent excessive loss of atmospheric gasses—which, as discussed last time, should put it somewhere around 0.05 Earth masses.

Though there is a dearth of research on the minimum habitable planet mass, there’s been quite a bit of interest in super-Earth planets of 1-10 Earth masses since they started turning up in exoplanet surveys, and the studies have yielded wildly different results. The initiation of plate tectonics requires that the crust fracture and be pulled down into the mantle, but whether or not that happens depends on a balance between the stresses imposed on the crust by convection in the mantle and the resistance of the crust to breaking. All else being equal, greater pressure and heat on a larger world should lead to greater stresses, but they may also lead to a stronger crust as well. And the greater temperature and pressure may increase the viscosity of the mantle which will reduce the stress, and water content may play a vital role as well, and the more complex the models become the more assumptions we have to make and the more clear it becomes that we don’t really understand how plate tectonics works on Earth, let alone how it might work on an alien world.

Still, even lacking plate tectonics a super-Earth should have enough internal heat to cause some kind tectonics that could sustain a carbon cycle, so maybe that’s enough to call them habitable.

NASA/Ames/JPL-Caltech

If we’re willing to make that assumption, then setting the upper limit returns to a matter of atmospheres. Where a small planet has trouble holding onto any atmosphere, a large planet holds onto too much. Planets even slightly larger than Earth are at risk of retaining their primordial hydrogen/helium atmospheres and experiencing too much greenhouse heating for habitability within the typical habitable zone (as mentioned these planets could be habitable outside that zone, but the appearance of life is likely to eventually remove the hydrogen and thus cool the world to a snowball). Observation of exoplanets indicates that past 4 to 5 Earth masses planets transition from super-Earths to sub-Neptunes with thick atmospheres and surface pressures too high for life.

If we use 0.25 to 4 Earth masses as our habitable range and assume an Earthlike composition, that gives us an approximate planet radius range of 0.66 to 1.45 Earth radii, and thus a surface gravity range of 0.57 to 1.91 Earth gs (if I vary core mass fraction to 0.1 or 0.6, I can expand the radius range to 0.61-1.55 and the gravity range to 0.51-2.31). If we’re extremely optimistic and extend the range to 0.05-10 Earth masses (and similarly vary core mass fraction) the radius range extends to 0.36-1.93 and the gravity range to 0.30-3.78.

Relative sizes of planets with Earthlike compositions and a plausible range of habitable masses.

All else being equal higher surface gravity should reduce the average slope of topographical features, making for flat terrain and overall smaller geological features. However, as established, we don’t really know if all else is equal regarding the tectonic processes that form these features in the first place. So though the hard limits on the slopes of mountains and the height of cliffs may be larger on small worlds, it isn’t clear how often planets of different sizes would approach their limits. For lava tubes at least, there is a trend of increasing size with lower gravity for Earth, Mars, and the Moon. We can be more confident that surface gravity will have a direct effect on the biomechanics of any complex life that emerges—requiring more robust limbs for walking and larger wings for flight—but how exactly that plays out is a subject for another time.

Larger planets are likely to have higher surface temperatures than smaller planets in similar orbits, but this doesn’t significantly impact the boundaries of the habitable zone.

Composition

Many of these size limits are based on the assumption of an Earthlike composition, but this won’t necessarily be true in all cases. Earth is about 1/3 iron-nickel core to 2/3 rocky mantle and crust, but within our own solar system the core mass fraction is as little as 0.03 for the moon and as high as 0.69 for Mercury. Differentiation out of the core is a major source of primordial heat, and a large core can produce a magnetic field and increase surface gravity, so a small core could be a major detriment to the habitability of a small planet.

But perhaps more important is how the core/mantle ratio reflects on the abundance of heavy metals in a planet. You may remember that back in Part I I was hesitant to assume that planets orbiting metal-poor stars would be habitable. This is because radiogenic heat comes mostly from heavy metals like uranium and thorium, and a star system poor in lighter metals like iron can be expected to be poor in heavy metals as well. Fewer heavy metals means less heat, and so as primordial heat is lost the interior may quickly cool too far to sustain tectonic activity.

Even before that point, a planet in the outer regions of the circumstellar habitable zone with tectonics but a cool interior may produce too little CO₂ to keep up with weathering, causing a condition known as limit cycling: CO₂ levels crash and the planet is plunged into a prolonged snowball period with global glacial cover, which stops weathering and allows CO₂ to rise again and eventually return the planet to habitable conditions, but only briefly before another crash back to a snowball. In fact, all habitable worlds—if they are not first pushed past the moist greenhouse limit by their warming star—will meet this fate eventually. Earth’s internal heat is only expected to sustain plate tectonics for another 1.45 billion years and even the largest super-Earths are unlikely to last much longer. Given that many stars last for trillions of years, this leads to the unsettling conclusion that in the far future the universe will be increasingly populated by dead, formerly-habitable planets.

Temperature and CO₂level shifts during limit-cycling of a planet in the outer region of the HZ for a sunlike star. Haqq-Misra et al. 2016

There are some possibilities to extend this habitable lifetime, though. For one thing, a planet could form with a higher proportion of uranium and thorium, and a planet that formed outside the iceline and then migrated inwards could have much more potassium. For an otherwise Earthlike planet this would cause extreme volcanic activity for the first 1 or 2 billion years, but thereafter could extend the habitable period past 15 billion years. A planet with even greater proportions of uranium and thorium may be habitable even later (though also with an extended pre-habitable phase) but we can only take this so far. Heavy abundances should tend to correlate with the presence of iron on the level of systems, but within individual planets uranium and thorium are lithophiles and tend to mix with the rocky mantle rather than the iron core. A larger core mass ratio is worth it for a while, both for more primordial heat from differentiation and a higher abundance of heavy metals, but once it passes 0.6 a larger core cuts too deep into radiogenic heat production.

Of course, a planet could equally form with lower abundances of radioactive isotopes, and indeed we would expect this to be increasingly true as the galaxy ages because the short-lived isotopes are diluted by more stable metals. This further adds to our fears of an increasingly barren universe in the future. But given that smaller stars will become more abundant with time, an increasing number of habitable-zone planets may be close enough to their stars to be sufficiently warmed by tidal heating.

But metal and rock aren’t the only 2 options for planet composition. A carbon planet might have a diamond-dominated mantle that is both more viscous and more conductive than a silicate mantle, meaning such a world will cool quicker and attain lower internal temperatures for a given level of heat generation. Thus, for most of their lives these worlds would have little, if any, tectonic activity and largely static surfaces. Not much work has been done on the likely atmospheric chemistry of such worlds, so we can’t say yet if there might be any negative feedback loops to stabilize the climate, but if there were they would have to operate only with materials available on the surface.

Water is also a relatively poor insulator, though once water becomes a significant portion of a planet’s mass much of it will exist as high-pressure ice, which should do a somewhat better job. This ice won’t contain as much heavy metals as the rocky mantle, though, so an Earth-size planet that’s mostly water may be short of internal heat. But even if it has a sufficiently large rocky interior, a waterworld may lack the exposed rocks necessary for the carbon-silicate cycle (some weathering occurs on the seafloor, but it’s insensitive to surface temperature and so doesn’t experience a strong negative feedback). For a planet with Earthlike tectonic activity, land covering as little as 1% of the surface should be sufficient. But if there is even less land area or the planet is inundated entirely, or if volcanism on this planet produces CO₂ at a much higher rate, then the carbon cycle may enter a supply-limited regime, whereby there is too little weathering to counter CO₂ production and the planet enters a moist greenhouse state, rising in temperature by several hundred Kelvin and losing much of its water to photolysis in the upper atmosphere. If loss of water exposes more land soon after the moist greenhouse begins then the planet may return to habitable temperatures with a lower sea level, but otherwise the planet is likely to lose its oceans entirely before it can recover.

There may still be some opportunity for habitability: The high-pressure ice layer may effectively block both CO₂ release from the interior and CO₂ sequestration from the atmosphere, so if the planet happens to form with the right amount of atmospheric CO2 for habitable temperatures (the chances for which aren’t excellent but aren’t vanishingly small either) then a planet could remain habitable for billions of years—especially if it orbits a small, slowly-evolving star. This is long enough to possible form life, though once it does it might start sequestering carbon on its own and so cause its own demise.

Also, on waterworlds with short days (<8 hours) in the outer regions of the typical habitable zone (~1.23-1.65 AU for a sunlike star) sea ice may be able to absorb CO₂ and sink to the ocean floor at a rate proportional to atmospheric CO₂ concentration, providing a stabilizing negative feedback.

Neither of these options works quite as well as the carbon-silicate cycle on a continental world, and there’s still the issue that the ice on the ocean floor may block access to vital nutrients for life, so overall waterworlds shouldn’t be considered ideal for life. Fortunately, negative feedback between pressure on oceanic crust and production of water from the mantle should ensure that even worlds with as much as 0.2% water content by mass—5-10 times that of Earth—have exposed continents.

Heat: A Simple Model

I’m going to be a bit bold here and attempt to put together an analytical solution for the habitable period of an Earthlike planet based on internal heat generation. I will assume that ultimately the presence or absence of tectonic activity on a planet can be determined by the heat flow at the surface from interior sources. In reality this heat can emerge in several different ways (convection, plumes of melt) and a single value could correspond to different tectonic modes depending on the history of the planet, but even with these wrinkles abstracted out surface heat flow should provide a good first-order estimate. I will also assume that we can divide internal heat sources into the three main categories already mentioned: radiogenic, primordial, and tidal. Again, where this heat is generated in the interior matters, but we can assume that for planets of similar composition, similar total heat production will imply similar results. The aim here is not to predict the tectonic mode for a given planet, but to put reasonable soft limits on the period of habitable tectonics for a planet that otherwise has all the correct conditions for such tectonics.

h_tot = total surface heat flow

h_rad = radiogenic surface heat flow

h_prim = primordial surface heat flow

h_tid = tidal surface heat flow

Radiogenic heat is the easiest to determine, as it is based only on the initial concentrations of radioactive isotopes, the half-lives of those isotopes, the heat released by their decay, and the age of the planet. 99% of Earth’s radiogenic heat comes from 4 isotopes: Potassium-40, Thorium-232. Uranium-235. And Uranium-238, with half-lives of 1.4, 13.9, 0.7, and 4.5 billion years respectively. Taking into account their individual half-lives, rates of heat production, likely initial concentrations in the mantle, and proportion of the planet’s mass that consists of mantle, we can express the total heat produced at any one time:

h_rad = radiogenic surface heat flow (W/m²)

P_man = proportion of planet mass that is mantle; 0.68 for Earth

M_p = mass of planet (kg); 5.97*10²⁴ kg for Earth

R_p = radius of planet (m); 6.37*10⁶ m for Earth

[⁴⁰K] = initial concentration of ⁴⁰K in mantle; 4.64*10^-7 for Earth

[²³²Th] = initial concentration of ²³²Th in mantle; 1.55*10^-7 for Earth

[²³⁵U] = initial concentration of ²³⁵U in mantle; 1.64*10^-8 for Earth

[²³⁸U] = initial concentration of ²³⁸U in mantle; 6.24*10^-8 for Earth

t = age of planet (billions of years); 4.5 for Earth today

e ≈ 2.71828

This predicts a current h_rad for Earth of 0.062 W/m² (32 TW total for the planet) which matches the predictions of geoneutrino surveys. As mentioned, these values could vary quite a bit for other planets, and ⁴⁰K in particular could be 50-100 times more abundant for a world that formed outside the iceline. Were we to assume that abundance of these isotopes was directly tied to the relative size of the core, this would imply that radiogenic heat production peaks when the core contains half the mass of the planet, but the two factors probably aren’t so perfectly correlated across all systems.

Estimating primordial heat production is a bit trickier, partially because rather than just being remnant heat from formation it is still being produced by continuing differentiation in the core and mantle, and partially because the rate at which a planet loses heat depends greatly on the tectonic mode. Attempts to fully model the Earth’s thermal history are hideously complicated and difficult to generalize to other planets, so instead I’ll be using a highly simplified model which essentially models primordial heat as if it were an additional radiogenic heat source, but in this case distributed throughout the entire planet’s mass rather than the mantle:

h_prim = primordial surface heat flow (W/m²)

M_p = mass of planet (kg); 5.97*10²⁴ kg for Earth

R_p = radius of planet (m); 6.37*10⁶ m for Earth

h_prim0 = initial primordial heating (W/kg); 1.2*10^-11 W/kg in my model

t = age of planet (billions of years); 4.5 for Earth today

e ≈ 2.71828

Not that I’ve altered the h_prim0 from my source as there were attempting to use this model for all sources, including radiogenic, and using a lower estimate of current surface heat flow. I’ve normalized my value to achieve 15 TW of primordial heating today, so that combined with radiogenic heating it gets us to 47 TW. Presumably I should be adjusting the decay constant (coefficient of t) as well, but I haven’t thought of a good way to do that and I don’t think it should make too huge of a difference in this case. I’ll proceed with the warning that this model is only meant for planets that experience plate tectonics for a large portion of their lives, and that it probably gets increasingly inaccurate for planets of significantly different size, composition, and age compared to Earth.

Tidal heating is, unlike the other sources, not strongly dependent on time. For a planet in an orbit close enough for significant tidal heating, the obliquity and rotation rate won’t take long to reach a tidal-locked state and won’t drift far from it afterwards. But eccentricity can take a long time to dissipate and will produce quite a lot of heat as it does. So surface heat flow from tidal heating for a typical star and Earthlike planet can be approximated based on the properties of the two bodies and their orbit:

h_tid = tidal heat (W/m²)

G = gravitational constant; 6.67408*10^-11 m³ kg^-1 s^-2

M_s = star mass (kg); 1.988*10³⁰ kg / solar mass

R_p = planet radius (m); 6.371*10⁶ m / Earth radius

Q’_p = planetary dissipation parameter; 500 for earthlike planet

e = eccentricity

a = semimajor axis (m); 1.496*10¹¹ m / AU

Eccentricity will decay over time—faster the more heat is produced—but it can be induced by other planets, and determining exactly how much eccentricity is induced and when is not simple. For the purposes of this model I’ll leave it as a free parameter and say that any moderate value is reasonable for a system with other nearby planets.

Now perhaps the trickiest part is actually placing constraints on the total surface heat flux that could allow for habitable surface conditions. I’m going to follow the example of researchers marking out habitable zones of luminosity and define a conservative and optimistic habitable range.

I’ll base the conservative range on the history of plate tectonics on our own planet. The preceding and following tectonic modes may not necessarily be uninhabitable, and indeed the origin of life predates plate tectonics, but given that complex life is only known to have evolved in an environment with plate tectonics it’s good to keep in mind.

The best current evidence indicates that the Earth transitioned from earlier tectonic states to plate tectonics around 2-3 billion years ago; 1.5-2.5 billion years after formation. It may have taken more time for some of the features of plate tectonics that we observe today to set in, but we can be fairly sure that subduction, moving continents, and associated volcanism have been going on in some form since then. Based on my heat model, the Earth’s surface heat flux at the time would have been about 0.19 W/m².

Extrapolation of current trends predicts the end of plate tectonics in roughly 1.5 billion years. Note that for a planet in the outer region of the habitable zone, limit cycling may settle in before this transition, or this transition may trigger it. Again based on my heat model, the heat flux will be about 0.067 W/m²

For our optimistic limits, we can look to two bodies in our solar system that have clearly left the range of healthy, habitable surface tectonics. Io, at 0.015 Earth masses, should have long ago cooled off to a frozen iceball, but tidal heating from Jupiter—caused by eccentricity induced by the other Galilean moons—gives it a surface heat flow of about 2 W/m², far above any Earth has experienced since the moon-forming impact. The result is extreme widespread volcanism that spews massive amounts of CO₂ and other gasses into the moon’s tenuous atmosphere; were a similarly-heated planet in the habitable zone, it would likely experience a runaway greenhouse effect in short order. But even setting aside that issue, the volcanic activity is accompanied by frequent lava flows across the surface. Based on the lack of visible impact craters, it’s likely that the entire exterior of the moon has been resurfaced by lava flows within the last few hundred thousand years. No life remotely resembling Earth’s could form or survive under such conditions.

Really, setting the upper limit at Io’s current heat flow is too optimistic, because even far tamer conditions would probably be too violent for life. But lacking a better example and given the uncertainties of scaling up from Io to a planet tens of times its mass, it’s a decent ballpark number.

By the way, note that this limit is far below the heat received from sunlight at the outer edge of the habitable zone (~120 W/m² average over the whole surface) so I’m doubtful that surface habitability could be maintained through tidal heating alone, though it could support a subsurface ocean as is the case for Europa. A planet with a thick Hydrogen atmosphere (but still not a gas giant) might manage to retain enough heat from internal sources to have habitable surface temperatures, but such an atmosphere would also obscure light from outside. In both cases it’s hard to imagine the scant supply of geothermal energy supporting the evolution of complex life.

At the lower end, I’ll follow the example of academic researchers in using the estimated heat flow on Mars when major tectonic activity ceased 2 billion years ago: 0.04 W/m². Below this value, we shouldn’t expect a planet to produce enough CO₂ to maintain the carbon-silicate cycle, and it may even risk losing its atmosphere. My model predicts the Earth will pass this range in about 4.5 billion years, but that’s ignoring the effect of transitioning to a different tectonic mode or losing its oceans to increased insolation.

I’d expect the realistic limits to be somewhere between those set here, so the prediction of this model is more a reasonable range of habitable lifetime than hard borders.

But, if we are willing to accept this model, then it implies that the minimum mass for a planet with Earthlike composition to sustain habitable tectonics for 4.5 billion years is between 0.1 and 0.35 Earth masses, which decently agrees with other estimates. This doesn’t quite agree with the predicted thermal evolution of Mars, which is 0.1 Earth masses, but that may be partially due to the fact that I assumed similar radioisotope proportions to Earth; Mars has a core mass proportion about 2/3 of Earth, so if we assume (perhaps naively) that its heavy metal abundance is similarly scaled, the result is closer to reality. It’s also probably worth asking if there’s an activation heat for certain tectonic modes that is above the shutdown heat, and if there’s a delay after formation before something like plate tectonics can initiate, but that’s beyond the scope of this model.

I’ve added this model to my worldbuilding spreadsheet as well.

Other Habitability Factors

So let’s assume we have a planet or moon of the right size in the right sort of orbit, and it has the right composition to maintain plate tectonics for a decent amount of time. Are we good? For the most part, yes, but there’s a few other factors we might want to consider.

First off, there are a couple ways other bodies in the system could affect a potentially habitable planet beyond tidal heating or exciting obliquity and eccentricity, and some researchers have proposed that our system’s architecture is particularly well-suited for complex life. For one thing, Earth is unique amongst observed terrestrial planets for having a fairly large moon, though it’ll be a while before we can determine how common that is for exoplanets. Researchers have long supposed that the presence of the moon could help stabilize Earth’s obliquity, reducing the occurrence of snowball episodes. But recent modelling has shown that a moonless Earth is perfectly capable of sustaining reasonable obliquity for long periods (and incidentally that retrograde-rotating planets are more stable) and that in fact the moon is close to the maximum size it can be without destabilizing Earth’s obliquity. And, as we saw earlier, variable obliquity may not be a showstopper for habitability anyway.

Another proposed role for the moon is to cause tides that may have played a role in the origin of life (we’ll discuss that more when we tackle models for abiogenesis) but the sun’s influence alone can cause significant tides. It’s possible that the extreme tides shortly after the moon’s formation—when it orbited much closer to Earth—may have been necessary, or at least helpful in getting life to appear as early as it did or that the moon-forming impact may have had a beneficial effect on the Earth’s internal evolution, but neither proposal has been modeled in detail nor do they require that the moon remain in orbit after performing its vital task.

Another long-held belief is that Jupiter is well-placed to “shepherd” the asteroid belt and reduce the rate of destructive asteroid and comet impact events on Earth. Again, more recent modelling has shown a more nuanced picture: It appears that the presence of Jupiter actually increases the rate of asteroid and comet impacts on Earth, by exciting their eccentricities such that they cross Earth’s orbit. The rate at which this occurs is notably lower than would be the case if there were a Saturn-massed planet in Jupiter’s place, but still higher than if there were no gas giant there at all. The only types of impacts that Jupiter helps reduce are those from long-period comets that enter the inner system from the Oort cloud, which it ejects out of the system, but these are the least frequent types of impacts (though also the most energetic) and even if there were no planet in Jupiter’s place, Saturn would do almost as good a job ejecting comets on its own.

However, though these models compensate for the bias in currently surviving asteroids and comets due to Jupiter’s presence, they cannot account for the competing models of how Jupiter’s presence may have massively changed the architecture of the early solar system. As mentioned, some of these models predict that Jupiter’s influence helped deplete the asteroid and Kuiper belts early on, leaving us with fewer potential impactors to worry about.

And Jupiter could help in a couple other ways. It may have prevented Saturn and the ice giants from migrating into the inner system, and large giants in other systems may similarly prevent the formation of super-Earths that would consume or eject more habitable Earth-mass planets. It may also have scattered icy planetoids into the inner system early in plant formation and then halted their inner migration later, resulting in an Earth that’s wet enough for life and the carbon cycle but not so wet that it lacks exposed landmasses.

Well, good or bad though Jupiter may be in its current position, we’re certainly lucky it stays there. Were Jupiter’s orbital eccentricity increased to 0.2, it would significantly increase the chances of the inner planets either colliding or being ejected from the system. At an eccentricity of 0.4 the long-term survival of Earth becomes almost impossible. Exoplanets with eccentricities this high are fairly common, and are probably more likely for systems that begin with multiple Jupiter-mass giants. Indeed, a large number of observed exoplanets appear to be in single-planet systems due to past periods of instability, collisions, and ejections.

A quick detour: if multiple-giant systems are less favorable to life, and high metallicity favors the formation of gas giants, this might imply that habitable planets will become rarer in the future as metallicity rises—another issue for the future habitability of the galaxy. However, we’d have to compare this to the trend for more low-mass stars to form, which disfavors the formation of giants. I don’t think we have the data yet to make that comparison.

Anyway, you might think that this would mean that systems with hot Jupiters, which would have had to migrate through the inner system, would also lack habitable worlds. But so long as the migration occurs early and then the hot Jupiter stays in a low orbit, this is not necessarily so. Some of the material in the inner system is consumed by the giant as it migrates inward or pushed ahead of it by resonances to later form hot terrestrial planets, but most of it is scattered into high-eccentricity orbits, allowing it to later return to the inner system and resume forming terrestrial planets. Scattering material like this may even help mix up the disk and deliver more water to the inner system, though as mentioned this may or may not be a good thing.

The effects of atmospheric pressure and composition on habitability are hard to quantify, given the variety of gasses that could independently vary. We established in the last section that a cold trap helps prevent water reaching the upper atmosphere and escaping; nitrogen does the job in our atmosphere, but oxygen, argon, or neon could feasibly do the job as well. Oxygen is, of course, vital to aerobic life on Earth, and allows for high-energy reactions that might be hard to achieve otherwise—but we’ll leave a more in-depth discussion of oxygen’s utility to another time.

For an earthlike world in the ideal habitable zone, CO₂ is the one gas we can speak about with confidence, as the level will be set by the balance of the carbon-silicate cycle. For an Earthlike world around a sunlike star to maintain an average temperature above freezing, the atmospheric CO₂ concentration must be at least 0.01 bar at 1.14 AU, 0.1 bar at 1.21 AU, 1 bar at 1.35 AU, and 7.5 bar near the maximum greenhouse limit (more precise estimates in table 5 and figure 1 here). Somewhat more CO₂ is required for a planet to be comfortable above freezing, like earth; if you’re willing to pay for it, Universe Sandbox 2 has a more complex climate model that could help nail down the precise values. Some researchers have proposed that high CO₂ levels and CO produced by photolysis could prevent complex life from developing in the outer regions of the habitable zone, but I’m skeptical that we can draw that conclusion from life on Earth that developed in a low-CO₂ environment.

For Earthlike atmospheric composition, higher atmospheric pressures will broaden the habitable zone, by as much as 0.1 AU around a sunlike star for an increase from 1 to 3 bar. However, higher pressure also increases temperature due to a stronger greenhouse, such that Earth’s average temperature would approach 323 K (50 °C) at around 4 bar, but it’s likely that the carbon-silicate cycle would at least partially compensate (it’s not modelled in this study). For even higher pressures scattering of light overpowers the greenhouse effect, and temperatures drop to freezing at around 34 bar.

Below 0.1 bar, poor heat transport means that a planet can have a boiling equator and freezing poles simultaneously, but a habitable temperate strip is still possible. 0.015 bar is around the minimum for habitability anywhere on the planet’s surface.

Note that this simulation only alters total pressure and holds relative CO₂ concentration constant, hence the thin habitable zone. “h” represents the portion of a planet’s surface that can sustain liquid surface water Vladilo et al. 2013

Finally, we should consider the possibility that Earth is not the ideal for habitability. We’ve already discussed how slower rotation could lead to warmer poles, and how a different star could allow Earth to be habitable for longer. A planet nearer to the center of the HZ would also remain habitable for longer, and decreased surface water and increased eccentricity would make it more resilient to climate upsets, though all these shifts have to be balanced against their immediate impacts on surface conditions. Should super-Earths have no major issues regarding their tectonic activity, their greater size would support more total biodiversity than an otherwise similar small planet. We could also increase habitable area by shifting the arrangement of landmasses; life on Earth is more abundant near coastlines rather than inland deserts and open oceans, and of course is most abundant in the tropics near the equator.

Moons

I’ve been using the term “planet” for our habitable world but there’s no particular reason it couldn’t be a moon, either of a larger terrestrial planet or a gas giant. I’ve left this subject to last because in most respects there’s no inherent difference in the possible physical characteristics of planets and moons, and just about everything I’ve said so far can apply to moon just as well as a planet (though with comments regarding the orbit applying to the planet’s orbit, and—for a moon with 0 obliquity, which is likely—the relative inclination between the moon’s orbit and the planet’s orbit having the same effect as obliquity would for a planet). We did establish in a previous post that moons formed in place around giant planets are unlikely to be larger than Mars-sized, but capture is a perfectly acceptable formation mechanism. However, there are a few factors that we should consider.

First off, in most cases the semimajor axis of the moon’s orbit around the planet should be small compared to that of the planet’s orbit around the star, given that the Hill radius decreases closer to the star. But for the extreme case of a 13 Jupiter mass planet orbiting a 0.08 solar mass star, the hill radius will be 0.37 times the semimajor axis, meaning a retrograde-orbiting moon at the limit of stability could range between 0.66 and 1.34 times its planet’s distance from the star—similar to having an eccentricity of 0.34, but without the large variation in orbital speed (which gives us yet another method for giving a world seasons, though intriguingly for a tidal-locked moon the side facing the planet would consistently get less sunlight than the side facing outward).

Once a moon forms or is captured, it is very likely to become tidal-locked to the planet, tying the day length to the orbital period and thus the semimajor axis. For a wide-orbiting moon, this means very long days, but a close-orbiting moon will have a larger portion of its day occupied by an eclipse by the planet—unless the moon’s orbit is highly inclined relative to the planet’s—and during the moon’s night it will receive significant reflected light from the planet. Neither effect is great enough to significantly affect habitability, but they are worth bearing in mind. Of course, these effects will only occur for the planet-facing side of the moon; the far side of the moon will never see the planet. This suggests the intriguing possibility of a society developing on the far side of a moon, completely unaware of the planet or their world’s status, then sending out explorers and making some startling discoveries.

But if we want short days, we have to be careful about placing the moon too close to the planet. A moon can be tidally heated by a planet just as a planet is by a moon or star, and even for low eccentricities the tidal heating can cause surface heat flows similar to Io for moons orbiting within 5-10 times the planet’s radius. In the habitable zone of a low-mass star the star’s influence can increase the eccentricity of the moon, while the radius of a stable orbit around the planet decreases. Below 0.2 solar masses a stable, habitable exomoon becomes near impossible. But more moderate heating can be beneficial; I’ve already mentioned how it could extend the range of habitable periods and masses, and this is as much the case with moons orbiting planets as planets orbiting stars.

The planet’s magnetic field is another double-edged sword. A close-orbiting moon will be protected from solar radiation by the planet’s magnetic field, slowing atmospheric loss. But the magnetic field also holds large amounts of high-energy particles and plasma in radiation belts, which can erode moon atmospheres in wide orbits and bombard their surfaces with radiation in close surfaces. But the facts that Titan has maintained a significant atmosphere and Callisto experiences fairly mild radiation indicate that there is an intermediate range of favorable conditions.

Taken together, the effects of tidal heating and protection by the planet’s magnetic field could mean the minimum habitable mass for a moon is lower than that for a planet, though only with fairly specific orbital conditions. If we also recall from the last post that a planet with higher atmospheric CO₂ levels should have a lower minimum mass to retain a thick atmosphere, then altogether the lowest-mass habitable world should be a moon in the outer regions of the habitable zone.

Our Little World

For Teacup A, our example system, the standard habitable zone model gives us a conservative habitable zone range of 0.39 to 0.73 and optimistic range of 0.31 to 0.77 AU. The inner boundary can be pushed to roughly 0.26 AU with a slow-rotating planet or 0.15 AU for a low-humidity, high-albedo planet, and the outer boundary to 0.93 AU with a 50% H₂ atmosphere (dry surface or high eccentricity should give a similar effect) or 5.8 AU for a 100 bar H₂ atmosphere.

Considering these boundaries and the constraints on mass established earlier, there are 4 bodies with potential for habitability: Teacup Ac, Ad, Ae, and Af V

Teacup Ac, as you may have put together by now, is designed to fulfill our requirements for a marginally habitable low-humidity desert planet. It’s well within the limits for such a planet, and has a reasonable albedo of 0.3. Low obliquity helps keep the poles cool, especially the north pole that experiences summer during the apoapsis of the planet’s eccentric orbit. Thus the planet has small ice caps with meltwater lakes around the perimeter. With half Earth’s mass and a small core it doesn’t have the warmest interior, and by 6 billion years (the age of the example system) it’s only producing 0.06 W/m² of interior heat, but under the circumstances I’ll say that’s enough to keep it stable. It’s still a fairly harsh environment, so we’ll say that it’s inhabited only by microbes living off what sunlight and chemical energy they can get in the meltwater lakes, perhaps brought here by meteorites from a more hospitable world.

Teacup Ad is a waterworld within the optimistic habitable zone, but its seas are boiling and are underlain by a thick layer of high-pressure ice that block access to vital nutrients. We’ll leave it uninhabited.

Teacup Ae is, of course, our Earth analogue. It sits comfortably within the conservative habitable zone—closer to the inner edge but not as close to Earth—and is within the ideal size range. Though it has a smaller core than Earth, bumping the radiogenic metals abundance up to 1.5 times that of Earth’s gives it 0.086 W/m² of internal heat at 6 billion years, ideal for habitability and plate tectonics. According to a quick check in Universe Sandbox 2, 0.03 atm of CO₂ should give it Earthlike surface temperatures. That’s high by our standards, but I’m sure the local life can get used to it.

The average irradiance Teacup Ae receives from Teacup A is only 74% what the Earth gets from the sun, but that should be plenty for photosynthesis. I’ll give the planet an obliquity of 15°, somewhat less than Earth, but also an eccentricity of 0.1, meaning its distance from Teacup A varies from 0.405 to 0.495 AU. I’ll give it an argument of obliquity of 150°, which puts the periapsis somewhat before the northern winter solstice. This gives the planet stronger seasons in the south (30-40% more day-averaged irradiance in peak summer and less irradiance in winter at mid-latitudes) and a slightly warmer northern fall/southern spring than northern spring/southern fall. Northern summer/southern winter is longer than northern winter/southern summer—by about 14 days (10 Tdays) if we count equinox to equinox—but that’s not a huge difference.

Irradiance of Teacup Ae averaged across the day at different latitudes (shown on the left) in W/m² (also shown by color scale), at regular intervals throughout the year. Produced with my worldbuilding spreadsheet.

Based on the likely luminosity evolution of Teacup A, Teacup Ae should stay within the conservative habitable zone until the system is 14.9 billion years old, and within the optimistic habitable zone until the star is 32.5 years old. If we presume Teacup Ae will become tidal-locked by that time, it could conceivably last through Teacup Ae’s entire main-sequence lifetime and even into the red giant stage.

But internal heat becomes an issue long before sunlight does. Based on my simple heat model the ideal period for plate tectonics should be roughly from 2.5 billion to 7.5 billion years after formation, and habitable tectonic activity should last at most 11.7 billion years after formation. Thus, unlike Earth, Teacup Ae’s carbon cycle will fail while it still orbits in the habitable zone.

As tectonic activity decreases and CO₂ outgassing with it, the polar icecaps will advance and eventually Teacup Ae will start limit cycling; alternating between periods of global ice cover and brief, warmer interglacials. Over time the glacial periods will become longer and the interglacials shorter, until the planet is permanently locked in an iceball state. What little internal heat remains may allow for microbial life to survive in the crust or perhaps pockets of liquid water in the deep ocean, but complex surface life will be wiped out. Eventually the growing luminosity of Teacup A will thaw the surface, but then the planet will skip right past habitable temperatures to a runaway greenhouse.

Teacup Af V is a substantial moon within the habitable zone for hydrogen-rich atmospheres, and is helped along by its arid surface. But it’s small—only 0.2 Earth masses—and orbits too far from its planet to receive significant tidal heating, so we’ll leave it as a quiet, dead world but with some traces of a wetter, more active past.

As with any system, life in Teacup A will only last so long, and the system has already lost some once-hospitable worlds. But we’ve given ourselves a good deal of breathing space; Teacup Ae could remain habitable for twice as long as Earth is expected to be, giving us plenty of time to develop intelligent life.

This post about wraps up the astronomical portion of this worldbuilding journey, at least for now; eventually the inhabitants of Ae will leave home and explore this system we’ve set up for them (I’ll also talk a bit about astronomical factors in regards to climate and alternate biochemistry). And before then I’ll probably have one-off posts outside this series addressing some ideas on the subject I couldn’t get into here. But for now, it’s time to focus in on Teacup Ae, and similar Earthlike worlds. Next time we’ll look at tectonic processes—both plate tectonics and plausible alternatives—and see how we can use the “rules” to produce realistic planet surfaces.

In Summary

To maintain a habitable surface for billions of years, a planet requires stabilizing climate feedbacks like the carbon-silicate cycle to compensate for changing star luminosity.
Rough habitable zones in the solar system are as follows:

Low humidity extreme	Slow-rotating	Optimistic inner	Conservative Inner	Conservative Outer	Optimistic Outer	Methane	50% H₂	100 atm H₂
0.39 AU	0.66 AU	0.75 AU	0.95 AU	1.67 AU	1.77 AU	1.81 AU	2.4 AU	15 AU

Less surface water area, higher eccentricity, and moderately higher atmospheric pressure extend the habitable zone as well but in hard-to-quantify ways.
Seasons could be caused by:

Planet obliquity/moon inclination
Planet eccentricity
High planet inclination around a rapidly-rotating star
Wide moon orbit of a large planet in a tight orbit around a small star.
Motion of stars in a short-period binary system with planets.

Habitable planet size is restricted by the need to be large enough to retain heat and continue outgassing an atmosphere, but small enough to lose the primordial thick hydrogen atmosphere. The ideal range is 0.25-4 Earth masses, but in extreme cases it could plausibly extend to 0.05-10 Earth masses.
Waterworlds lack strong stabilizing climate feedbacks and access to vital nutrients, carbon worlds rapidly lose internal heat, and worlds with especially large or small metal cores probably lack the necessary radiogenic heat to remain warm for long times, so an Earthlike composition appears to be ideal.
A large moon orbiting the planet and a large gas giant outside the iceline may both have positive impacts on habitability, but no evidence so far indicates they are vital.

Notes

This post is a little image-bare compared to my previous ones, but I’ve blown a lot of my stock of nice NASA/ESA/ESO images I found a couple months ago, and a lot of the papers on the subject just have graphs that make no sense until you’ve read half the study. I might come back and add more later, but it seemed like a silly reason to delay for another week.

I just want to give special recognition to Noack and Breuer (2014) for concluding that “[Plate tectonics] on exoplanets is either more, less or equally likely compared to Earth.” It was a useful paper, though.

Sooner or later I’m going to have to come back around to this idea that habitable worlds may become rarer as the universe ages and throw some actual math at it. Just to reiterate the reasoning for now:

Radiogenic elements become diluted in stable metals.
The average age of planets increases, meaning more of them have cold interiors.
Lower-mass stars, which may have issues with habitability, will become more common.
A larger portion of the planets within the immediate habitable zone of aging stars will have previously spent long periods outside the habitable zone.
Higher metallicity will cause more formation of multiple giant planet systems, which will make instability events more likely.
Older systems will have had more time to experience instability from internal or external factors.

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Part Va

Comments

paolo.bellomi@outlook.itApril 30, 2021 at 10:46 AM
Dear Mr. Hersfeldt
I am part of a small team that is in the initial stages of development for a fantasy Role Play Game, nevertheless we would like to keep the astronomical setting as scientifically plausible as we can, in this endeavour your blog has been an invaluable asset, however we reached quite a problematic setback and we would like to ask for your advice directly.
We imagined a Earth-sized habitable moon orbiting around a Gaseous Giant, which orbits around a yellow dwarf slightly smaller than the Sun, having successfully used your Worldbuilding Spreadsheet and managing a good balance in the system we attempted to roughly calculate the irradiance on said moon, but failed miserably as we couldn’t develop a sensible model of its motion.
We would like to know what kind of approximation of the orbit would be the most accurate to input in your model for the “Irradiance Calculation for Fast-Rotating Planets of Varying Obliquity and Eccentricity”, as our attempts only provoked extremely harsh frigid and blistering phases in correlation of the apoapsis and periaxis of the approximated orbit.
We would like to specify that our moon needs to be easily habitable by humans, given that it is necessary for our story.
We wish to thank you regardless of your response for your incredible and extremely complete work, both on the blog and in the spreadsheet, your work has been incredibly useful for us, and without it we would probably ended up with a completely implausible system and a bizarre sky to top the adventure we are developing.
In case you would want to take a look at what we have done until now here is the wordbuilding spreadsheet with our data, thank you very much for your time!
https://mega.nz/file/fDoyzTqZ#96oCb8Dgzi5uUinQTh_5urJBuzV44ZX67595xirqk6g
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AnonymousMarch 7, 2022 at 9:49 PM
If I need a high amount of CO2 to maintain habitable temperatures, would these high concentrations be maintained even with photosynthetic life?
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BrettApril 22, 2023 at 7:24 AM
Good stuff.

So if you've got a habitable exo-moon with a long orbit (say Callisto's 17 days, or even something like the Moon's 28 days), do you think the night-time temperature drop with an otherwise Earth-equivalent moon would be so severe that it would approach freezing across most of the side facing away from the sun? I'm wondering if we should think of these more as mini-seasons rather than night and day.

But on the other hand, atmospheric conditions would dominate. Early Cretaceous Antarctica didn't freeze even in months of winter darkness, as far as we can tell. And each side of the moon would take a lot of sunlight during the long, continuous days.
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Rene KayOctober 8, 2023 at 11:51 AM
I've been reading your blog for a bit now, and what you've created is an incredible resource. I've already used your temperature climate exploration as a guide to figure out the climate zones on my own world.

Presently, I'm trying to design a very dry and hot yet habitable world that was previously a humid, swamp-covered world on the edge of a moist greenhouse for a hundred million years or so during which time an intelligent species evolved. I figure that either water loss to space or subduction of water into the mantle could feasibly change the planet into the dry world it is today. I'm not sure how to simulate this in your worldbuilding spreadsheet.

Is it feasible for an almost-moist greenhouse world to transform into a marginally habitable low-humidity world without becoming entirely uninhabitable during the transition?
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AnonymousNovember 2, 2023 at 9:48 PM
Great resource! I am not scientifically literate but I want to write a soft sci-fi novel that includes three worlds colonized post-Earth. I am planning on having them accessible via a surprise wormhole similar to the one in the movie Interstellar. The worlds are far away from our system. I understand that a wormhole of this nature will be the most miraculous gift from the universe, especially if it leads to three habitable worlds. I'll find a way to hang a lantern on this ridiculously unlikely scenario.

My question(s) for you, which is separate from my justification for the fortuitous portal, is whether it would be possible to have two livable planets within a habitable zone somewhere, plus a moon where humans have constructed underground habitats? If so, could one planet be Earth-like (breathable air, oceans, greenery, etc) with the other planet being still breathable but more desert-like, tundra-like, etc.? Lastly, what's the smallest distance feasible between these miraculous planets in a habitable zone and what should I know about the nearby star?

Thank you for the exhaustive resources. I know the answers to my questions should seem obvious to many readers of your blog but I can barely wrap my head around many of the concepts discussed, hence my questions. My story will be character driven and not strongly focused on the science whatsoever. I merely seek adequate plausibility so I can begin the story.
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AnonymousApril 9, 2024 at 7:14 PM
On the danger of native life matabolizing a hydrogen or methane atmosphere, I had a thought. Technically CO2 is metabolized by our plants, and an alien might mistakenly think that this would send the Earth into a snowball state over a long enough time. But in reality the carbon soaked up by plants returns to the atmosphere in short order from consumption or decomposition. Do you think metabolized hydrogen and/or methane in their corresponding biospheres could experience a similar cycle?

Thanks.
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