have shown a bewildering variety of possible systems, with planets of wildly varying size and compositions appearing just about anywhere within them. System architectures (that is, the particular arrangements of orbits and distributions of mass) thought impossible a few decades ago are old news today. So we’ve got quite a lot of freedom here.

If there is any one rule governing the structure of planetary systems, it is diversity. Both observations of exoplanetary system

Nonetheless, there are some patterns to how planetary systems form and how the resulting architectures develop, and so there are some rules we should follow in building a system and designing the planets within it. This is a large and complex topic, so I’ve split this part into 3 sections: In section a, we’ll go over the current theories of how planetary systems form and talk about how to build a realistic system architecture based on those theories; in section b , we’ll talk more about what these planets will be like, what their physical characteristics are likely to be and what different types of surfaces they might have; finally in section c , we’ll focus in on the specific question of habitability, and what exact conditions a planet needs in order to have a good shot at developing complex life.

and particularly large, dense regions may obscure the stars behind them. A spaceship travelling at a significant portion of light speed would notice the increased drag from the denser medium, so nebulae might provide barriers to the expansion of nearby interstellar species.

Stars typically form not individually but in clusters of thousands within, immense clouds of gas. Actually, calling them “clouds” is a bit misleading; though they are thousands of times denser than the typical interstellar medium, that still leaves them orders of magnitude less dense than near-Earth space. For the most part they wouldn’t even be visible from up close, though bright stars may illuminate the surrounding gas

At first the high relative velocity of molecules within the nebula holds it back from gravitational collapse (as any particles that fall towards a denser region gain enough speed to shoot back out again), but eventually it fragments and collapses into star-mass clumps. Exactly how is still debated—it may be due to magnetic interactions or turbulent flow patterns within the gas—but it seems the early formation of some massive stars that later supernova produces shockwaves in the gas that can catalyze the formation of other stars

. The interior temperature can exceed 2,000 K, hot enough to ionize the hydrogen and helium and emit some light, but in the early stages it is so obscured by surrounding gas that it can only be observed by radio, X-ray, or gamma ray emissions. Mass continues to fall into the star from the surrounding gas cloud, but some of the outlying material has too much angular momentum to fall directly into the core, and instead orbits it ever faster as it falls inward. Collisions between these gas particles tend to average out their angular momentum so that they converge on a common axis of rotation, transitioning from a spherical cloud to a disk shape where collisions are minimized—the protoplanetary disk , which is initially hundreds to thousands of AU in diameter.

Once the clumps have begun collapsing, the formation of stars and planets is pretty fast compared to the mindboggling stretches of time that we’ve been dealing with so far. Within about 10,000 years the cloud has collapsed to form a, a core of gas dense enough to resist further gravitational collapse

. Though the star may lose as much as 10% of its mass this way, the jets also carry away much of its angular momentum, reducing the centrifugal acceleration of matter in the protostar and thus helping it to collapse further

After around 100,000 years the core is dense enough to begin fusing deuterium, expanding the protostar somewhat. Jets of plasma from the protostar’s poles may impact the surrounding gas, creating bright. The exact mechanism for these jets is poorly understood, but as with pulsars and active black holes they are believed to arise from interactions between infalling gas and the protostar’s magnetic field

By about 1 million years enough of the gas envelope has cleared for the protostar to be observed in the infrared and sometimes the visible spectrum. At this point it is referred to as a T Tauri star (technically the term only refers to the predecessors of F to M-type stars; pre-main-sequence A and B-type stars are referred to as Herbig Ae and Herbig Be stars respectively, and O-type stars have already entered the main sequence by the time they can be observed). The star has accreted most of its final mass and the remaining disk material amounts to 1 to 10 Jupiter masses for a sunlike star. More massive stars generally have more massive disks, but there’s plenty of individual variation and some stars can lack disks entirely. The disk may still extend several hundred AU, or it may have been cut down to 50 AU or less by encounters with other stars.

By 10 million years of age hydrogen fusion will finally start in the star’s core, putting it on the main sequence. The solar wind will blow away any remaining gas in the disk or surrounding cloud not bound to a solid object. Thus, 10 million years is our window for the formation of planets. Smallmay continue to combine into larger rocky or icy planets, but gas giants must have collected their entire gaseous outer layers by this point. And indeed, it seems that most early stars lose their protoplanetary disks within just a few million years

How exactly planets form is an area of ongoing research. There are two plausible models for the formation of planets in the protoplanetary disk: The core accretion model, whereby solid dust grains join together to form planetesimals, and only after large cores are formed do gasses accrete onto them to form gas giants; And the disk instability model, whereby the gas in the disk fragments and collapses, just as in the formation of stars.

. Thus this may have been how the first planets in the universe formed, but now is likely only responsible for a small minority of observed planets (though there may be a selection bias).

In the core accretion model, formation of a gas giant requires first the formation of a large rocky core of about 10 Earth masses, which then has enough gravity to collect hydrogen and helium gas from the surrounding disk. This explains why the appearance of gas giant exoplanets is strongly correlated to the metallicity of the parent star, moreso than for terrestrial planets with a lower total mass of metals.

. Even if combination outruns fragmentation, it has to do so fast enough to form a core big enough to accrete hydrogen gas before the 10-million-year deadline; even once passing the kilometer-size threshold growth rate is an issue. The best solution so far is a model called “”, whereby a few lucky seeds will, by chance, experience all the right collisions to grow significantly larger than the surrounding debris, at which point they can continue to grow by accumulation of centimeter-sized pebbles

Core accretion is not without its issues, though. Electrostatic forces can explain the joining of dust particles up to meter-sized boulders, and gravitational forces the joining of kilometer-sized planetesimals, but there’s a gap in between where collisions can just as easily result in fragmentation or bouncing as combination

. Further out other materials like methane, ammonia, and carbon monoxide have their own respective icelines, which affect the composition of bodies formed beyond them. Altogether these low-temperature fluids are classed as volatiles , as opposed to the refractory materials that remain solid even near the inner edge of the protoplanetary disk (though these are to some extent relative terms; materials can be more volatile or refractory in different regions of the disk).

. With the obscuring gas and dust cleared the iceline has since moved out to 5 AU, but these icy asteroids are now protected by a surface layer of dust

Planetesimal formation may be easier outside the—A.K.A.or—the boundary at which the young star’s light warms the disk material to 150 K, warm enough to sublimate water ice in the disk. This would have been at 2.7 AU from the sun during planetesimal formation in our solar system, as attested by the predominance of icy asteroids beyond this boundary and relative absence within it

. Further out, large planets may form too late to accrete many gasses, and so we get ice giants like Uranus and Neptune that have significant hydrogen/helium atmospheres but are still mostly formed of other volatiles like methane, ammonia, and water.

. But the best place for formation of gas giants is just outside the iceline, where the disk is still fairly dense and short orbital periods cause frequent collisions

The presence of ice beyond the iceline both provides more material for planetesimal formation and makes for “stickier” debris that more easily passes the intermediate size barrier. The lower temperature also helps gasses accrete to the core once it forms, such that the initial mass necessary for a gas giant can drop to as little as 3.5 Earth masses at 100 AU from a sunlike star

, but the fact that they occur at all throws a wrench into our neat model of inner rocky planets and outer gas giants. Systems with dense disks and high metallicity should be able to occasionally form gas giants inside the iceline, but notfar inside

. It was the first in a class of planets we call “”, of which we’ve now found over 100 examples. Our detection methods are biased towards these high-mass, close orbiting planets, and we expect that in reality they only appear in 0.5% of all systems

So this seems to neatly explain the stark division of planets within our solar system, with small, rocky planets inside the iceline and gas giants and ice giants outside it. And so we thought it would be for every star system, until in 1995 we discovered the first exoplanet around a main sequence star: 51 Pegasi b , a gas giant with at least half Jupiter’s mass, orbiting just 0.05 AU from a star slightly larger than the sun



To explain hot jupiters, we have to add in an entirely new mechanism, planet migration. As a growing planet core moves through a protoplanetary disk, it gravitationally attracts material in the disk, and the disk material attracts it back. Faster-moving material inside the planet’s orbit will pull it forwards along its orbit, and slower-moving material outside will pull it back. For a typical disk we expect the latter effect to win out, sapping orbital energy from a planet and causing it to drift inwards towards the star. Thus, hot jupiters could be planets that formed outside or not far inside the iceline and then migrated inwards.

. There’s clearly some elements we’re still missing, but for now that means there’s a lot of freedom in constructing fictional planetary systems.

and for another, any large planets that do manage to form should all pile up at the inner edge of the disk, rather than ever managing to stay spaced out as we see them today

But planet migration introduces as many problems as it solves, at least with our current models. For one, small planetary embryos should spiral into the star long before they have the opportunity to grow any larger

. Past that, protoplanetary disks around larger stars don’t last long enough for gas giant formation, and even around A-type stars the lower time for migration leads to a paucity of hot jupiters

For all this hullabaloo over gas giants, they’re not actually all that common. Modelling suggests that they only occur around 6% of sunlike stars, varying with mass: They’re almost absent from M-type red dwarfs, but may appear around as much as 20% of A-type stars

with the reverse trend regarding stellar mass, becoming almost ubiquitous around M-types (the inversion point between these planetary abundance trends is near Neptune’s mass)

Unlike gas giants,can take their time forming. After the gas of the protoplanetary disk is cleared, the system will still be filled with hundreds to thousands of planetesimals in the 0.01 to 0.1 Earth mass range. While the disk was present they were mostly kept on circular orbits and so out of each other’s way, but with it gone they can pull each other into eccentric orbits and collide, thus eventually consolidating into a small number of terrestrial planets over the next 100 million years , a period researchers call the

. At this point interactions with the little remaining debris settle the planets into circular, low-inclination orbits, though a few last impacts—such as the one believed to have produced Earth’s moon—can still occur.

If any gas giants are present, they will perturb the orbits of objects near resonant orbits (that is, objects with orbital periods that are a simple fraction of the gas giants’ orbital periods) which may encourage the formation of asteroid belts rather than planets, but otherwise planets seem to pack into the inner system about as closely as they can without destabilizing each other

. Planetesimals at the inner edge of this belt would occasionally encounter Neptune (or Uranus) and be flung inwards, pushing the planet outwards. These planetesimals would continue down the chain of giant planets until they reached Jupiter, which was massive enough to turn these planetesimals around and fling them deep into the Oort cloud or out of the system entirely, pushing itself inwards.

But the fun isn’t done yet: According to the Nice Model of solar system evolution (named for the city in France, though I’m sure it’s friendly at parties) the solar system after the oligarchy stage would have been much more compact than it is now, with Neptune (or perhaps Uranus in the outermost position) orbiting only 17 AU out, and as much as 50 Earth masses of material remaining in planetesimals in theoutside it

About 700 million years after the solar system formed, Jupiter and Saturn reached their 1:2 orbital resonance point, which would have increased both planets’ eccentricities and wrecked hell with the rest of the system: Saturn was shoved outwards and the ice giants pushed out in turn (Neptune passing Uranus if it was previously inside it), plowing into the Kuiper belt and scattering it. Interactions with these bodies would have helped stabilize the planet’s orbits again, and some would be caught as highly-inclined moons or Trojan asteroids, but many would be flung into the inner solar system and cause the, a period of massive impacts for all the inner bodies

which proposes that Jupiter migrated in to Mars’s current position and then was pulled back out again by Saturn’s formation. But in any case the structure of a system at the end of the oligarchic stage, when all the planets have formed, is not necessarily the same structure it will have billions of years later.

The Nice Model isn’t universally accepted, however, nor is its link to the Late Heavy Bombardment. The most popular alternative is thehypothesis

, but “law” may be too lofty a title for a rule that only works if you’re willing to count the asteroid belt as a planet and just forget about Neptune. A softer and more reliable rule, based on observations of exoplanetary systems, is that as you move outward each successive planet tends to have an orbital period between 1.5 and 3 times that of the previous planet. As per Kepler’s 3 rd Law, this corresponds to 1.3 to 2.1 times the semi-major axis:

There’s a lot of variation in how systems can look once all the planets have formed and settled out into a stable configuration, but there are also a few common trends. Perhaps the most obvious in our own solar system is the fact that, as you get further from the sun, the orbits of the planets become more spaced out. 19century astronomers attempted to quantify this trend with the Titius-Bode Law





a 1 , a 2 = semi-major axes

P 1 , P 2 = orbital periods

Where the bodies’ masses are negligible compared to the common parent body.





(See my previous post on orbits if any of the terms here are unfamiliar)



But forget averages, what if we want to really pack these planets in there? The smallest period ratio observed so far is 1.17 for two planets in Kepler-36, which appear to be in a stable configuration . The theoretical limits of stability are set not by period ratios, but by the radius of the Hill sphere, the region around an orbiting body where its gravity dominates the attraction of satellites, as opposed to the gravity of the parent body. This Hill radius approximates to:









R H = Hill radius

a = semi-major axis

m = mass of the orbiting body

M = mass of the parent body





For two bodies orbiting the same parent, we can define a mutual Hill radius, which is effectively equivalent to what the Hill radius would be for a single body with the total mass of the two bodies orbiting halfway between them:









R Hmut = mutual Hill radius

a 1 , a 2 = semi-major axes

m 1 , m 2 = masses of the orbiting bodies

M = mass of the parent body





Once the minimum separation between two bodies drops below 8.6 mutual Hill radii, the long-term stability of the system falls dramatically . Above this limit even tightly packed systems can be stable for billions of years. In theory the minimum separation can be about halved if two bodies orbit retrograde to each other, but for a planet to orbit retrograde it would almost certainly have to be a captured body from outside the system, and it’s hard to imagine a planet entering into a captured orbit so close to another without colliding or otherwise interfering with it .









One way to increase the stability of closely-packed systems—even beyond that 8.6 mutual Hill radii limit—is with mean-motion resonances. We discussed how orbital period resonances with the giant planets could have destabilized the early solar system, but such resonances can have a stabilizing effect as well. They’re something of a double-edged sword because though they stabilize orbital periods, they can upset eccentricities, which may cause one of the bodies to cross the orbits of other bodies, leading to collisions. But if two or more bodies can enter resonance and stay there without encountering this fate—which becomes easier if the bodies are of similar masses or if the period ratio is between two close numbers (e.g. 2:3 resonance is more stable than 3:7) then this can keep their orbits neatly in place. If the two bodies are of very different masses—e.g a gas giant and a terrestrial planet—then a collision becomes a significant danger, so it may be reasonable to leave resonant orbits with gas giants empty. Within our solar system, asteroids clump together at 3:2 and 4:3 resonances with Jupiter, but gaps have opened at the 4:1, 3:1, 5:2, and 7:3 resonances.









Laplace resonance. In our solar system Pluto is in a 2:3 resonance with Neptune (which also allows it to cross Neptune’s orbit, as they are never near each other during these crossings) and the moons Io, Europa, and Ganymede have a 1:2:4 resonance, an arrangement called a In exoplanetary systems resonances are common among giant planets, but curiously rare for terrestrial worlds . However, there are a suspicious number of terrestrial pairs with period ratios slightly larger than 1.5 or 2.0, indicating that they probably formed in 2:3 or 1:2 resonances but the inner planet migrated slightly inwards due to interactions with the last remnants of the protoplanetary disk .





When small planets do fall into resonances they can allow for extremely tight systems, such as the TRAPPIST-1 system which manages to pack 7 planets within 0.062 AU of the star with close to a 2:3:4:6:9:15:24 resonance chain . Formation of such tight inner systems may be aided by gas giants in the outer system, which can push planets from more distantly separated resonant orbits into closer ones .





But if we want to pack in even more planets, then we might begin to consider co-orbital configurations, where two planets share the same orbital period (or very close to it). There are, broadly speaking, 3 categories of co-orbital configurations. The simplest is a binary planet, where two similarly-sized planets closely orbit a common barycenter that itself orbits a star. Arguably this is true of any planet-moon system, and indeed the orbital constraints for a binary planet pair are much the same as for moons (I’ll describe these later in this post) but a common convention is that if the barycenter for two objects is inside the more massive body, then it is considered a planet-moon system, but if the barycenter is outside either body then they are binary planets. By this standard, Pluto and Charon are binary dwarf planets.





Trojan planets, where two planets occupy the same orbit but one lags 1/6 of an orbital period behind the other. As I mentioned in Second, there is the possibility of, where two planets occupy the same orbit but one lags 1/6 of an orbital period behind the other. As I mentioned in Part II , such orbits can be stable so long as the planets are not more than 4% the mass of the star . Lining up more than two similarly-sized planets in an orbit this way wouldn’t work (at least not without unrealistic starting conditions ) but it’s feasible for a giant planet to have a much smaller terrestrial planet both ahead (at the L4 Lagrange point) and behind (at the L5 point). Note that a planet formed in this position is unlikely to exceed 0.6 Earth masses, and that it will follow the gas giant as it migrates . Capture of a planet formed elsewhere is a plausible alternative origin, though.





Motion of the asteroid 2010 TK7 relative to sun and Earth. Phoenix7777, Wikimedia





A Trojan planet needs not be exactly on the Lagrange point; if slightly offset from the point a planet can adopt a tadpole orbit, gradually approaching and then receding from the other planet as their differing distances cause them to exchange momentum back and forth. Viewed from a rotating reference frame with the star and other planet held stationary, a planet in such an orbit oscillates throughout a roughly tadpole-shaped region of space, hence the name.





Once the difference in period between two similar-mass planets passes a threshold, they transition from a tadpole orbit to a horseshoe orbit. In this case, the planet with the shorter period—and therefore smaller semimajor axis—gains on the other planet until it is close enough for a sudden exchange of momentum to occur; the faster-orbiting planet is pulled out into a wider orbit and the slower-orbiting planet is pulled in to a tighter orbit. Thus they switch periods (or at any rate switch relative placing if their masses are different) and the now-faster-orbiting planet pulls ahead, circling around the orbit relative to the other planet until it approaches it from behind and repeats the process.









the planets become more massive (20-27 days for 0.25 Jupiter-mass planets around a sunlike star with periods close to Earth’s) So far such orbits have only been observed for some asteroids and 2 of the small moons of Saturn (Epimetheus and Janus), but modelling suggests that they should be possible for similar-mass planets up to 0.04% the mass of their star—roughly Saturn-sized for a sunlike star—though the range of possible period separations narrows asthe planets become more massive (20-27 days for 0.25 Jupiter-mass planets around a sunlike star with periods close to Earth’s) . We can imagine how these types of orbits might have interesting effects on the climate; An Earthlike planet switching from a 380-day orbit to a 350-day orbit would experience a 12% increase in insolation, similar to a mild seasonal shift, but occurring suddenly about every 12 years rather than gradually over the course of one year. And of course year length would vary, potentially leading to a rather confusing calendar.





Finally, it is possible for two planets to have equal periods but radically different eccentricities, an eccentric resonance, such that their orbital paths cross but they never collide. If the planets are similar masses, then over timeframes of hundreds to thousands of years (shorter for more massive planets, ~800 years for Jupiter-sized planets orbiting 1 AU from a sunlike star) the eccentricity is passed from one planet to the other, and then back. Again, we can imagine intriguing climate effects as a planet shifts from a period with extreme seasons to a less variable period. So far such orbits have only been observed for asteroids (Earth has 5 such coorbital bodies) but they should be possible for planets where both have less than 3.5 % the star’s mass. Of course, high eccentricity would cause collisions in a closely-packed system, so regard this less as a method for packing in extra planets than an interesting feature for otherwise sparsely populated systems









So now that we’re placing orbits, where do we stop? How close can a planet orbit a star? As a soft limit, planets cannot form initially inside of the inner edge of the protoplanetary disk, at about 0.1 AU for a sunlike star. Any material that passes this limit during the star’s T Tauri stage will be pulled in by the magnetic field and either fall into the star or be thrown out in polar jets .





But we already know that planets can migrate in past this limit later in the formation process, and not only hot jupiters; recent research has discovered a new class of extremely close-orbiting terrestrial planets with periods measured in hours and surfaces so hot that their rocky surfaces are actually sublimating and being lost to space . The rate of mass loss becomes significant when surface temperatures surpass roughly 2,000 K , which for a planet with a surface like Mercury would be at 0.02 AU from a sunlike star. We might call this the rockline.





The ultimate inner boundary is set by the Roche limit, the point at which the tidal forces from the star become stronger than the planet’s gravity and it is torn apart. For a rigid body, the calculation is straightforward:









d = Roche limit (any unit so long as R is the same)

r = radius of the planet

M = mass of the star (any unit so long as m is the same)

m = mass of the planet





However, planets are often better modeled as fluid bodies; a proper calculation for fluids is more complicated but can be reasonably approximated:









i.e. 1.94 times the rigid body Roche limit.





The actual Roche limit for any body will be between these two values; given that the fluid limit approximation will always be larger, it can be taken as the safe limit. Note that the Roche limit is the same for bodies of different masses but equal densities; thus we can define a Roche limit for specific materials, like rock or ice (though a given material will be more compressed and thus denser for a larger planet; more on that in the next post).





This isn’t a particularly stringent limit; the fluid Roche limit for Earth is at 0.007 AU, less than 1/50 the orbit of Mercury. But some possible exoplanets are observed near their Roche limit, and are expected to be distorted by tidal forces into an American football-like shape .





th planet at 400-800 AU. Were that the case, it would almost certainly be the last planet—and in a more crowded part of the galaxy, it could easily have been ejected by an encounter with another star long ago. There’s no strict outer limit for planetary orbits—except for in wide binary systems—but the further you get from the star, the less material there is available and collisions become less frequent. Neptune is the furthest out known large planetary body at 30 AU, but decent evidence exists for a 9planet at 400-800 AU. Were that the case, it would almost certainly be the last planet—and in a more crowded part of the galaxy, it could easily have been ejected by an encounter with another star long ago.





In terms of eccentricity and inclination, exoplanetary systems show a clear division between lone giant planets with high eccentricity (~0.3) and multi-planet systems like ours with very low average eccentricity (~0.04) and mutual inclination (~1.4°) , with about equal numbers of both types observed (though that sample is heavily biased towards systems with giant planets, which as mentioned are likely a minority of all systems). The lone-planet systems probably used to have more planets, but lost them in an episode of extreme instability that ejected them from the system.

Rotation

We cannot yet observe the obliquity or rotation rate of exoplanets (save for some rare cases of giant planets spinning fast enough to generate notable blueshift) but so far as we’re aware there are no particular constraints on either, other than the influence of tides. They’re largely determined by the last few big impacts during formation, which are more or less random. By default most planets will have prograde rotation and low obliquity—inherited from the average momentum of the protoplanetary disk—but very powerful impacts or close encounters with massive bodies can cause retrograde rotation—as has happened to Venus—or high obliquity—as has happened to Uranus. Judging just by our solar system, initial rotation times of 5-30 hours (before the influence of tides or unusual impacts and encounters) seem to be reasonable, but simulations indicate that much longer periods up to thousands of hours shouldn’t be rare .





A hard lower limit on rotation period could be based on the point at which surface velocity matches orbital velocity, meaning that centrifugal acceleration will tend to tear the planet apart—for Earth this would be 1.43 hours. In reality this is too optimistic, as a planet with high rotation would start stretching out such that its equatorial radius increased (or rather, it would likely form 2 lobes of material that stretched far further from the center than the initial radius).



Concept of Haumea, a dwarf planet elongated by its rapid rotation (once per 3.9 hours). Stephanie Hoover, Wikimedia

Accounting for the influence of tides, the period until a planet becomes tidal-locked to its star can be estimated from the star’s mass and initial conditions of the planet :









t = time to tidal-lock (billion years)

Q = dissipation factor (~100 for typical solid planet of Earthlike size)

a = semimajor axis (AU)

P = initial rotation period (hours)

M = star mass (sun masses)





Naturally you can set the initial rotation period lower to avoid tidal locking in closer orbits, but only until you start approaching that centrifugal acceleration limit. Even with an initial period as low as 2 hours, any planet in the habitable zone of a 0.34 solar mass star will become tidal-locked after 4.5 billion years. A large moon can also slow tidal-locking, though in the habitable zone of smaller stars such a moon is less likely to form and will be more quickly ejected from orbit of the planet due to the gravitational influence of the star.





For a given rotation rate, the day length can be defined two ways: The sidereal day, which is the period it takes for the planet to rotate a full circle as measured by observing distant stars; and the synodic day, the period it takes for the sun to return to the same point in the sky (e.g. noon to noon). Earth’s 24-hour “day” is a synodic day; the sidereal day is 4 minutes shorter. A prograde-rotating planet will have one more sidereal day a year than synodic days to offset the star’s apparent rotation around the planet, and a retrograde-rotating planet will have one less (assuming a prograde orbiting planet):









d syn = synodic day length (any unit, so long as all three use the same)

d sid = sidereal day length

P = year length





This is an average over the year; planets with eccentricity will experience slightly longer synodic days near periapsis and shorter ones near apoapsis. However, eccentricity would have to be pretty extreme—or the days very long compared to the orbital period—for this to be significant.





A tidal-locked planet has an effectively infinite synodic day length, though if there’s some eccentricity or obliquity regions near the edge can pass back and forth over the terminator and thus experience effective “days” as long as the year.

Moons

A moon can form in 3 primary ways: It can form in orbit of a planet much as planets form around stars; A planet or smaller object that formed elsewhere can be captured into the orbit of a larger planet, turning it into a moon; Or an impact between two planets can form a debris disk that then coalesces into a moon.





This first possibility is most relevant to moons of large gas giants. According to current modelling, a giant planet of similar scale to Jupiter will form its own circumplanetary disk of gas and dust after formation, like a scaled-down version of the protoplanetary disk. The disk even has its own temperature gradient and iceline, due to heat from collisions in the denser inner regions.





Planetesimals (moonesimals?) will form in the disk and tend to migrateinwards until the innermost moon reaches the inner edge of the disk, where it will stop, and other moons will capture into a chain of 2:1 resonances . But if more than 3 or 4 large moons lines up in this resonance chain, the orbit of the innermost moon may be destabilized enough to send it crashing into the planet. The next innermost moon will then migrate to the inner edge and the resonant chain of moons will follow, and this cycle can repeat several times. Thus, the dry inner moons are lost and a small number of water-rich moons in resonant orbits remain—plus often one non-resonant large outer moon formed at the very end of the process, like our Callisto.



Moon formation and migration in a typical model for a Jupiter-sized planet. "Rp" is radii of the planet, "Tk" is ~0.03 years; the orbital period at 20 Rp. Ogihara and Ida 2012

The mass of these resulting moons will usually be around 1/10,000 that of the planet, meaning that even a giant 10 times the mass of Jupiter will not regularly form moons over around 0.3 Earth masses. Larger moons are possible but likely very rare. These moons will have very high water mass contents—up to half or more of the total mass—but tidal heating could warm them enough to cause much of the water to be lost, as has happened to Io.





For an analog of Saturn, which formed slower than Jupiter and didn’t clear a large gap in the protoplanetary disk, the inner edge of the circumplanetary disk reaches the planet’s surface and allows the inner moons to migrate into collision with the planet, leaving just one or two large icy moons in wide orbits .





Now, claiming that the architectures of moon systems elsewhere will always follow the same pattern as we see in our own system would seem unimaginative and biased, just like saying all planetary systems would resemble ours was before we discovered hot jupiters. So let’s simply say that we expect the patterns seen for Jupiter and Saturn to be common, but not necessarily ubiquitous. A plausible alternative is that moons could form just outside the Roche limit from a circumplanetary disk that is spreading outwards, and then migrate out to their current positions .





capture of other planets allows for a much more diverse range of moons and system architectures. Now, if a planet or smaller body simply passes through the hill sphere of a larger planet, it will not be captured; some event has to remove momentum from the object during that flyby—or over the course of several sequential flybys. There are a few possibilities. If the passing object is largely fluid—a gas giant or waterworld—then tidal forces between it and the planet Fortunately for creative worldbuilders,of other planets allows for a much more diverse range of moons and system architectures. Now, if a planet or smaller body simply passes through the hill sphere of a larger planet, it will not be captured; some event has to remove momentum from the object during that flyby—or over the course of several sequential flybys. There are a few possibilities. If the passing object is largely fluid—a gas giant or waterworld—then tidal forces between it and the planet may be enough . If the planet still has a circumplanetary disk, the passing object may pass through it and so experience drag—it could also pass through the outer layers of a gas giant planet’s atmosphere. If the planet already has moons, they may gravitationally interact with the object and absorb some of its momentum, possibly but not necessarily leading to their own escape. The object could even impact one of the moons. And finally, if a binary pair of objects passes the planet, the influence of the planet’s gravity could break the pair apart, causing one to be ejected with most of the pair’s original momentum and the other to remain behind.





Once a moon is captured, it has a good chance of settling into a stable orbit within a few million years Kepler-1625b I . And indeed, our system appears to include many captured moons, judging by their compositions and irregular orbits. Triton, the moon of Neptune, is the largest such moon, at 0.0036 Earth masses, but there’s no particular reason a moon of similar mass to Earth or larger couldn’t be captured. The recently described exomoon appears to be roughly Neptune-mass (17 Earth masses) and if confirmed was likely captured into its current orbit .





Finally, if two planets collide—as can frequently happen in the final stages of planet formation—most of the material is likely to reform into a larger combined planet, but some can be ejected into space and enter orbit of the reforming planet as a debris ring, which will then coalesce into a moon. An impact between the early Earth and a roughly Mars-sized planet called Theia is widely believed to be responsible for our moon’s formation, and an impact between Mars and a dwarf planet may have formed its bitesize moons, Phobos and Deimos .





There is one last alternative for smaller bodies: A non-spherical asteroid may reflect sunlight unevenly, causing its rotation rate to increase until it’s torn apart by centrifugal forces, forming one or more moons. Such a scenario is implausible for a spherical planet with much more mass relative to its surface area, though it might be vaguely possible for an encounter with another planetary body to greatly increase its rotation rate to the point of tearing itself apart.





The Roche limit for a moon orbiting a planet is calculated in the same way as that of a planet orbiting a star. Moons also have similar constraints as planets for separation of orbits from each other by mutual hill radii, and a similar tendency towards low mutual inclination. But overall irregularly orbiting moons are likely more common than irregularly orbiting planets, because capture of a moon from elsewhere in the solar system is more frequent than capture of a planet from elsewhere in the galaxy.





Though any object within a planet’s hill radius will tend to orbit it for the moment, pertubations from the star or other planets will cause the ejection of objects in the outer region into orbits of the star. The maximum stable semimajor axis for a moon is around 0.49 times the planet’s hill radius for prograde-orbiting moons and 0.93 times the hill radius for retrograde-orbiting moons (see the source for more precise equations accounting for eccentricity).





Thus in our solar system the moons of gas giants can be largely divided into prograde, close-orbiting, low-inclination regular moons and mostly retrograde, far-orbiting, high-inclination irregular moons. Moons formed in place or by impact are more likely to be the former, and captured moons more likely to be the latter.



The orbits of some of Jupiter's irregular moons (the red line is the planet's orbit). Kieff, Wikimedia

All observed major moons and minor regular moons are tidal-locked (save for Hyperion due to the influence of Titan), so their orbital and rotation periods are the same and they have low obliquity. Tides can gradually alter a planet’s rotation rate and the moon’s orbit: A close-orbiting moon with a month shorter than the planet’s day will “spin up” the planet, decreasing the day length and pulling itself into a closer orbit, while a far-orbiting moon with a month longer than the planet’s day will “spin down” the planet, increasing the day length and pushing itself into a farther orbit. The latter case is occurring with the Earth-moon system; the Earth has been spun down from 4-hour days just after the moon’s formation to 24-hour days today, although the rate it has been spinning down has slowed. Resonances between the orbital period of the moon and rotation period of the planet or between the orbital periods of multiple moons may pause this process, but not permanently if other objects perturb the system.





The most stable situation is for the planet and moon to be mutually tidal-locked, with the planet’s day, moon’s day, and month all of the same length, but even then the influence of the star or other planets and moons may introduce instability. If the process continues indefinitely without reaching an equilibrium, a moon will eventually pass inside the Roche limit and be torn apart or recede too far and be lost from the planet’s orbit—though that may take so long as to not be worth worrying about in many cases.





A sidereal and synodic month can be defined for a moon just as with days—and for a tidal-locked moon the months and days will be the same length—and their relationship can be calculated with the same formulas as for sidereal and synodic days.





But if planets can orbit stars and moons can orbit planets, can moons have their own satellites? In some cases, possibly so moonmoon seems to be the most popular right now, because I guess none of us are feeling more creative. In principle Callisto, Iapetus, and our own moon could support small moonmoons— . There’s no agreed term for such a body thoughseems to be the most popular right now, because I guess none of us are feeling more creative. In principle Callisto, Iapetus, and our own moon could support small moonmoons— some have proposed that Iapetus may once have had rings that later fell to the surface, forming its equatorial ridge . But these moonmoons may not be stable over billions of years due to the tidal influences of their planets and the sun. A larger moon like the aforementioned Kepler-1625b I could do a better job of holding onto moonmoons. As a rule of thumb, a moonmoon should be no more than 1/105 times the mass of the moon to remain in a stable orbit.





moonmoonmoon? In principle, yes, but we may be pushing our luck. The planet Kepler 1625b is around 3 Jupiter masses, so if we assume a planet 4 times as massive (close to the maximum size before a planet becomes a brown dwarf) could support a moon 4 times as massive, that gives us a moon of 68 Earth masses. If we stick to the 1/105 rule thereafter, that implies there could be a moonmoon of 0.00068 Earth masses, similar to the dwarf planet Haumea, and a moonmoonmoon of 0.0000000068 Earth masses (4.1*1016 kg) similar to the asteroid But why stop there? Could a moonmooon have its own satellite, a? In principle, yes, but we may be pushing our luck. The planet Kepler 1625b is around 3 Jupiter masses, so if we assume a planet 4 times as massive (close to the maximum size before a planet becomes a brown dwarf) could support a moon 4 times as massive, that gives us a moon of 68 Earth masses. If we stick to the 1/10rule thereafter, that implies there could be a moonmoon of 0.00068 Earth masses, similar to the dwarf planet Haumea, and a moonmoonmoon of 0.0000000068 Earth masses (4.1*10kg) similar to the asteroid Ida —which has a satellite, Dactyl, implying the possibility of a moonmoonmoonmoon, but comparing a lone asteroid to a crowded hierarchy of submoons may be a misleading.





Saturn’s moon Daphnis raising waves in its rings. NASA/JPL-Caltech/Space Science Institute





In addition to large moons, all our gas giants also have rings of debris. Saturn’s rings are of course the most famous and are composed primarily of gravel (1 cm) to boulder (10 m) size chunks of ice. Despite covering an orbital space over 70,000 kilometers wide, the rings may be as little as 10 meters thick. There are several gaps in the rings, often in resonant orbits with large outer moons, and some are occupied by shepherd moons that help keep the ring material in its orbits and are small enough to remain intact by cohesion even though they lie inside their Roche limits.



Long-lasting rings can only exist inside the Roche limit for the material they’re primarily composed of. Brief rings may be formed outside by collisions, but will soon coalesce into 1 or more moons. Even the former aren’t necessarily permanent; we may be lucky to live in the brief (several 100 million year) window before Saturn’s rings collapse into the planet or nearby moons. In general younger systems should have more large ring systems.





Concept of J1407b; the system is only 16 million years old, so the rings are likely leftover debris still coalescing into moons. Ron Miller

The early circumplanetary disk of the gas giants would likely have collapsed to the planet’s surface, so their rings must have formed later. If the Nice Model is correct, these may have formed due to close flybys of planetesimals from the Kuiper belt that were torn apart by tidal forces; some of the fragments were captured into orbit and experienced further collisions that ground them into the fine material of the disk today Plausible alternatives include an impact event between 2 large moons or the stripping of material from a large moon that passed inside its Roche limit, leaving a rocky core that then plunged into the planet . The smaller rings of the other gas giants besides Saturn may be debris from impacts on higher-orbiting moons, or remnants of once-larger rings. A diffuse ring can also be formed by an icy moon with a warm interior that experiences cryvolcanism, shooting plumes of material into nearby orbits, as Enceladus does .





Not only gas giants can form rings. When Phobos passes inside its Roche limit in the next 20-40 million years, it will give Mars a large set of rings , though one unlikely to last more than 100 million years thereafter . Even the asteroid Chariklo has a set of rings .