The scientific method. Credit: Wikimedia  CC BY-SA 4.0

I’m sure this is not interesting to most people, but I wanted to get it onto the Internet for those who become interested in Pluto’s planethood during the flyby and want more details.

Determining the definition of a planet is really a scientific question. The first step in science is not writing down a hypothesis but rather observing nature, which means describing the things we see, naming them, and breaking them into a classification system. This clarifies our thinking and enhances discussion about unsolved problems. If we have muddled thinking then we will do muddled science.

In defining “planets”, we are faced with a continuum of bodies from dust specks up to giant stars. We have decided that planets and stars are essentially different categories because stars emit light, but drawing the boundary isn’t so simple.  Even planets make some of the light that they emit (mostly in the infrared) because of their warmth. That warmth comes from many sources including gravitational collapse and radioactive decay.  We have decided that a star is an object that has nuclear fusion as the source of its warmth. Planets are bodies that do not have nuclear fusion.  Still, this is not an adequate boundary because there are objects that formerly supported nuclear fusion but don’t any more, and there are objects that will eventually support nuclear fusion but haven’t started yet. Are they planets? A more precise boundary is this: a planet is a body that never has supported nuclear fusion and never will.  Those that do not meet this requirement are either protostars (on their way to nuclear fusion), brown dwarfs (which supported fusion of deuterium for a brief period), stars, or stellar remnants (like black holes or neutron stars).

Comparison of planet and star sizes. The boundary between planets and stars (the left edge of figure 3) is defined by nuclear fusion. Credit: Wikimedia  CC BY-SA 4.0

We started with a general feeling that stars and planets are different, then we found a boundary in nature that translates this feeling into something specific.  To define the lower end of the planet size-scale we must do the same thing:  we have a general feeling that meteoroids (mere rocks) are different than planets, but how do we translate this feeling  into something specific?  The continuum of sizes includes dust specks, meteoroids, asteroids, and planets. Is there a natural break in the continuum that captures our intuition in a scientifically useful  way?

Gibral Basri and Mike Brown, in their paper,”Planetesimals to Brown Dwarfs: What is a Planet?”, discuss several natural boundaries we might choose.  They ask, is it a planet when it is large enough so that:

1. gravity holds it together as a rubble pile?
2. gravity overcomes material strength and pulls it into a round shape?
3. internal convection begins in its mantle?
4. gravitational compression is enough to drive chemical reactions in the interior?
5. gravity causes significant volumetric compression?
6. gravity captures and holds enough volatiles that it become an ice giant or gas giant?
7. free electron degeneracy pressure becomes important, so the planetary radius begin to decrease with added mass rather than increase?
8. fusion begins? (but that makes it a star)

This list is in order of increasing size, so item 1 happens with smaller bodies, but item 8 happens only with larger bodies. Where in this list do we draw the line? Clearly it must be something smaller than item 6, because Earth and Mars don’t meet item 6 and yet they are planets. Clearly, also, it must be something larger than item 1, because a mere rubble pile — a sandbar in space — doesn’t meet our intuition of a planet, which is a single body rather than a loose agglomeration of bodies.

We might also consider these boundaries: is it a planet if it is large enough for

• differentiation to occur, so heavier materials sink to form a core, mantle, and crust?
• gravity to hold an atmosphere?

We can rule those out.  As for the first, differentiation can occur for even very small bodies (small asteroids) if they got hot enough through impacts or tidal forces or radioactive decay, and it depends on too many factors so it isn’t measurable for planets in other solar systems. As for the second, planets like Mercury don’t hold an atmosphere and yet our intuition says Mercury is a planet.

So that leaves us with the numbered list between items 2 and 5.  Items 3, 4, and 5 don’t seem related to our intuition about the nature of planets. They occur in the interior of bodies and are therefore “invisible” to whatever formed our intuition about it. This leaves only item 2:  a planet must be gravitationally rounded.

The IAU Definition of a planet from the 2006 General Assembly

The International Astronomical Union (IAU) included this as part of definition of a planet.  According to many scientists (myself included), this gravitational roundness and the lack of nuclear fusion should be the only requirements in the definition of a planet. Ironically, the gravitational rounding requirement is mere window dressing in the IAU definition, because there are no bodies orbiting the sun that cleared their orbital neighborhoods and are too small to be round.

Eventually we will do the right thing and eliminate the dynamical requirements (a) and (c) from the IAU definition and add the requirement that a planet never has fusion so it applies to other solar systems.  The dynamical requirements produce absurd results when we try to compare planets around other stars.  This frustrates the comparison of planets, and thus it does the exact opposite of what a scientific classification system is supposed to do.  Gravitational rounding and lack of nuclear fusion really are the right requirements for defining a planet.

Even saying a planet must be gravitationally rounded is not sufficiently precise. Gravity changes the shapes of some bodies very slowly, and it might take a billion years to overcome material strength and pull a body into a rounded shape. Stern and Levison, in their paper, “Regarding the criteria for planethood and proposed planetary classification schemes,” recommend a specific timescale in nature to make it even more precise. They suggest that we use the Hubble Time, which is the inverse of the expansion rate of the universe, or about 14.4 billion years. That’s approximately the age of the universe, so basically it says that if a body is big enough to ever round itself out by gravity then it is a planet. This is a slightly more inclusive boundary than saying the body must already be round. Vesta for example used to be round, but it was knocked slightly out of roundness by a giant collision, yet it is still large enough that over a Hubble time it will relax to roundness again according to some estimates.  Therefore, Vesta would still be a planet according to Stern and Levison’s refined definition. This detail, like all scientific questions, is open for debate and should be continually reassessed as we learn more. Classification systems are frequently refined in other branches of science, and it should be the same in planetary science, too.

Vesta is out of hydrostatic equilibrium (gravitational roundness), although we can see that is used to be rounded before a major impact blew out a large chunk. Smaller asteroids, by comparison, are far from round.

So how many bodies in our solar system meet the size requirements to be a planet? Several hundred that we know of, so far!  This includes the eight classical planets, a few of the asteroids (depending on the precise roundness requirement), over a dozen of the larger planets’ moons, and hundreds of bodies beyond Neptune.  We live in an exciting time when the Kuiper Belt is overthrowing and rewriting our understanding of the solar system and the nature of planets.  Observing nature is cool, because it does that for us.

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When people say Pluto isn’t a planet, they often say it is an icy body and therefore it must be a comet, not a planet.  But are icy worlds simply comets?  Or can real planets be made of ice?  And what is the difference between ice and rock, anyway?  Let’s take a look!

Halley’s Comet as seen in 1910. Image: The Yerkes Observatory

Stars with Long Hair

From antiquity, long before we knew what comets are made of, we knew them as stunning phenomena in the sky. The full, original name “star comet” comes from the Greek meaning “star with long hair.” By definition, the essence of a comet is the “long hair”, the tail. If a solar system body doesn’t display this “hair” each time it goes round the sun, it’s not a comet. (That’s why we had to invent the separate name asteroid for bodies that don’t have the “hair”.) We later figured out what comets are made of. They are clumps of ice mixed with dust, flying so near the sun that they are evaporating. The ice can be a mixture of different compositions:  frozen water, ammonia, and methane, for example.  The tail is the evaporating ice and dust.  Since they do evaporate, they must be relatively short-lived bodies. There must be a source for new ones, a reservoir of icy bodies far from the sun, or else they would be all gone by now.

The original meaning of “comet” is “star with long hair”. On the left, Chris Hemsworth is classified as a comet. On the right, he is not classified as a comet. You can discover more comets and non-comets by clicking on the picture.

Some of those bodies far from the sun have been discovered, and they are not classified as comets. They need something to kick them out of their cold orbits so they can move closer to the sun, start evaporating, and grow tails before they can become comets.  (And if they are too large, like Pluto, then they still wouldn’t grow tails because their gravity will retain the gas and dust as an atmosphere.)  These faraway, icy bodies are classified as Trans Neptunian Objects (TNOs). There are various types of TNOs: Kuiper Belt Objects, Scattered Disc Objects, Extended Disc Objects, and Oort Cloud bodies. Some of these TNOs are called dwarf planets and some are called small solar system bodies, but none of them are called comets because they don’t have the “long hair”.

Possible internal structure of Ganymede, an icy moon of Jupiter. Image credit: NASA/JPL-Caltech

Some bodies that were once TNOs have been kicked into orbits that come closer to the sun, crossing the orbits of one or more giant planets. but they still don’t come close enough to the sun to form a healthy tail. They form only lesser tails at times. They seemed to be half asteroid, half comet, so they were classified as centaurs. (Centaurs in Greek mythology were half human, half horse.) The centaurs of our solar system are icy bodies but they are not comets.

Some of the moons of giant planets are icy worlds and they are supremely interesting:  Europa, Ganymede, Titan, Tritan, and more.  Like the TNOs and the centaurs, they may be icy but they are not comets.

To be sure, some icy bodies are comets, but not all of them are comets.  Icy bodies can be many things, including centaurs, moons, and even planets if they are big enough.  Being icy doesn’t imply that Pluto is a comet.

Planets can be any material or state

Model of the internal structure of Uranus. Note that the icy mantle is believed to be a supercritical fluid, not a solid. Source: Wikimedia

Planets can be made out of any material.  They can be rock, metal, gas, ice, or peanut butter. If space aliens have polluted the Milky Way, there might be a planet formed entirely of plastic bottles and K-cups that floated into a clump off the shoulder of Orion.  Someday we will recycle that planet.  Closer to home, planets like Mercury, Venus, Earth and Mars are made out of rock. Others, like Jupiter and Saturn, are made out of gas. Still other planets are made out of volatiles that have higher melting temperatures, such as methane, ammonia, and water. Planetary scientists call these volatiles ices even when they are in a gas or liquid state, as they are in Neptune and Uranus. So yes, Neptune and Uranus are made out of ices and thus they are classified as ice giants, not gas giants.  And yes, they are planets. Bodies made of ices can be planets.

Planets can also be in any physical state. Some planets can be in the solid state, like Mercury. Others can have surfaces that are in the liquid state, like Earth’s oceanic surface. Still others can be in the gaseous state, like much of Jupiter.  It doesn’t matter which state the matter is in.

The geophysical definition of a planet is simply this:  to be a planet, a body must have enough mass to pull itself into a round shape by its own gravity, and it must not have so much mass that it initiates nuclear fusion (for that would render it a star). Composition and physical state do not matter.  Icy worlds as large as Pluto easily meet this geophysical definition of a planet.

Ice and rock are not fundamentally different

In fact, the distinction between ice and rock is rather arbitrary.  It isn’t a fundamental boundary in physics. When we defined some materials as ices and others as rocks, we drew the line by picking a melting temperature rather close to our body temperature. Why did we do this?  We were influenced by the mental conception of ice that we developed here on Earth, where water gets hard and feels cold to our bodies in the winter, then it gets fluid and feels warmer to our bodies in the summer. We started calling the cold version of this water ice. Compounds that stayed solid all year round, on the other hand, we called rock. Thus, the distinction between ice and rock originated from our human experience.  There is nothing fundamental about that.

Jeffrey Kargel wrote,

By the geologic definitions of mineral and rock, ice can be both, as can the Solar System’s more volatile condensed solids, such as ammonia dehydrate and nitrogen ice. These minerals melt, respond to stress by fracture and flow, react chemically with one another, weather when exposed at satellite surfaces, and generally do many of the things that Earth’s silicate rocks do, although they do so in unique ways. Some of the basic geologic processes of icy satellites, such as volcanism and tectonism, differ little in their fundamental physics compared to the processes that affect Earth’s silicate rocks… [1]

Also, rock can evaporate like ice and form a tail when a rocky body is close enough to the sun.

If you want to say that rocky worlds can be planets but icy worlds cannot, then to justify it you need to invent some property of ice that makes it fundamentally different from rock. But there is no such property. These materials all exist on a continuum and we drew an arbitrary, human-centered line between them. Planets can exist on both sides of that arbitrary line.

Pluto is not primarily an icy body, anyway

Possible internal structure of Pluto. Source: NASA / Pat Rawlings via Wikimedia

It is perfectly acceptable for a planet to be made out of ice, either fluid ice like Uranus and Neptune or solid ice like the outer layers of Pluto. Nevertheless, this discussion is basically moot. Although Pluto does have an icy exterior, most of its mass is rock. Even if the ice were completely removed from the rock, the amount of remaining rock would be enough mass to qualify Pluto as a planet according to the geophysical definition. Pluto’s ice is just icing on the cake. Adding icing to a cake doesn’t take away the cake. Adding ice to a planet doesn’t take away the planet. It just makes it a bigger, more interesting planet.

Summary

There’s no reason to say icy worlds are comets simply because they are icy. There’s no reason to say icy worlds cannot be planets.  Icy worlds are beckoning, and we will probably find that many of them are everything we could want a planet to be.  They can be complex with dynamic atmospheres, subsurface oceans, cryovolcanism, even liquid lakes on the surface.  I can’t wait for the first close-up views of an icy, Kuiper Belt planet:  Pluto, along with its five known moons this July. It will be awesome!

Reference: Jeffrey S. Kargel (1998), “Physical chemistry of ices in the outer solar system.” In B. Schmitt, C. de Bergh, and M. Festou (Eds.), Solar System Ices, Vol. 1. (pp. 3-4). Dordrecht: Springer.

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To get ready for the New Horizons flyby of Pluto (this July!), I’m writing a series on the science of Pluto and the Kuiper Belt.  Here is the next installment.

The trajectory of the New Horizons spacecraft as it encounters Pluto (along the inclined orbit) and passes into the Kuiper Belt. Image credit: NASA

There are some very strong hints that the planets haven’t stayed in their original orbits and the giant planets tossed around the smaller ones.  These hints will help us understand several cool things about the structure of the Kuiper Belt including how Pluto got into an orbit that is so tilted and resonant with Neptune.  (Orbital resonance was described in a prior post, at this link.)

A Little Orbital Mechanics

Orbital mechanics is the strange physics of how bodies orbit one another. Let’s say you are in a spaceship in low Earth orbit trailing the Space Station, and let’s say you are trying to catch up to it.  You might think you need to go faster, right? Actually you need to slow down. Attempting to slow down makes you you swing closer to the Earth so your potential energy is reduced causing you to actually go faster, and also your orbital path is shorter. You then orbit the Earth in less time than the Space Station, so you come out ahead.  Attempting to speed up makes you go slower and attempting to slow down makes you go faster. Strange, right?

Here’s another weird thing about orbital mechanics:  the combination of real and apparent forces can make you orbit an empty location in space. Centrifugal force is an apparent force you feel when you are spinning.  If you spin a bucket of water over your head, the water feels the centrifugal force holding it in the bucket when it is upside down so it doesn’t fall out onto your head.  When your spaceship is in a circular orbit around the Earth, the centrifugal force the spaceship feels just exactly balances the gravity from the Earth, so it never moves closer to nor farther from the Earth. That balance gives it a circular orbit.  Another apparent force is the Coriolis force.  In the Wizard of Oz, when Dorothy’s house was spinning in the twister, if she tried to walk across the room she would have been thrown toward the wall.  We call that tendency to swerve off a straight line when you’re in a spinning reference frame the Coriolis force.  If you are orbiting the Earth then you will feel the gravity of both the Earth and the Moon, and these two real forces plus the apparent forces will balance each other in five special locations.  These are called the Lagrange points. If you are very close to a Lagrange point but not exactly right at it, then the real and apparent forces will tend to push you back toward the Lagrange point, and they can even make you go into orbit around the Lagrange point. Two of the five Lagrange points are stable so you really will orbit them. The other three are almost stable so you can go around and around for a long time before you finally break free.  This is very cool, because you are orbiting a point in space where nothing exists.  There is no actual gravity from that point to make you orbit it.

Now all of this was to introduce the next concept.  In a recent post I talked about orbital resonances and how the planets give little kicks to each other. Pluto is in a 2:3 resonance with Neptune, so every time Pluto orbits the sun twice, Neptune orbits the sun exactly three times. Therefore, the kicks from Neptune don’t hit Pluto randomly but in an orderly pattern. It turns out this pattern of kicks is stable like the Lagrange points. If Pluto’s orbit wasn’t exactly in the 2:3 resonance — let’s say it completed slightly more than two orbits for Neptune’s three, then the kicks from Neptune would tend to pull Pluto along faster, and since going faster makes it swing farther from the sun it would actually slow down and take longer to go around, which would move it back toward the exact 2:3 resonance. And if Pluto were completing slightly less than two orbits for Neptune’s three, then the kicks would tend to pull Pluto backward as if to slow it down, but that would make it swing closer to the sun so it actually speeds up and moves forward closer to the exact 2:3 resonance. Unlike the Lagrange points, these resonances are not specific locations in physical space. Instead, they are locations in “parameter space.” When the parameters of the orbit (i.e., the semi-major axis, the eccentricity, and so on) are close enough to what they need to be for resonance, then the forces of orbital mechanics will push the planet through this parameter space closer to that special set of parameters. Cool, right?

That’s enough orbital mechanics. Now, what does this have to do with the origins of the Kuiper Belt?

Clues in the Solar System

A young star with a protoplanetary disk. Credit: ALMA (NRAO/ESO/NAOJ); C. Brogan, B. Saxton (NRAO/AUI/NSF)

The planets formed out of a flat disk of gas and dust like a giant Frisbee spinning around the newly forming sun.  Therefore, they orbited in approximately the same, flat plane; we call it the ecliptic plane.  We can find the ecliptic plane when we look at the planets in the night sky. They will all be in the same great circle that seems to go around the Earth, all following approximately the same narrow path crossing the same constellations year after year. That path is the side view of the ecliptic plane. We see it as a side view because the Earth is in the plane along with the other planets.

When planetary bodies get too close to each other they can scatter out of the plane. We call the resulting tilt of their orbit relative to that plane the inclination of the orbit. Consider two cars going the same direction down a long, straight highway. If the cars collide just slightly off-center, they can careen completely off opposite sides of the road, even though they were going pretty straight down the road to begin with.  The slightly off-center alignment gets exaggerated by the crash. Likewise, the planets were not all exactly in the ecliptic plane, but pretty close. When they swing near each other, the gravitational “crash” exaggerates their slightly off-center alignment, throwing them in opposite directions out of the plane, giving them both larger inclinations. Also, if a heavy truck collides with a tiny car, the car will get scattered farther off the road than the truck will.  Likewise, if a smaller body like Pluto interacts with a heavier one like Neptune, Pluto will get the larger inclination as a result.  By looking at the inclinations of the many bodies of our solar system, we can get a clue as to how much scattering has taken place.

The semi-major axis is like an average distance from the sun, so the first four triangles on the left are Mercury, Venus, Earth and Mars, followed by the circles that are in the main ateroid belt, and so on out to the TNOs. TNOs are Trans-Neptunian Objects, including the Kuiper Belt, the Scattered Disc, and the Detached Objects. The smaller bodies can be far out of the ecliptic plane, showing they were scattered by the larger ones. Even the classical planets are not perfectly in the plane.

Another clue about scattering in our solar system is the eccentricity of planetary orbits. Eccentricity is defined so that a circular orbit has an eccentricity of zero, while an extremely elliptic orbit approaches the limiting value of one.  Note in the next plot how the TNOs tend to fall on the same arc. That’s because they all have perihelions (closest approaches to the sun) in a narrow range of values near Neptune, which scattered them, but depending on how much they were scattered they can travel varying distances from the sun, and that distance gives them both a higher eccentricity and a higher average distance from the sun (semi-major axis) so the two are mathematically related. Note also the large eccentricity of Mercury, showing how it has been scattered by other bodies.

High eccentricity also indicates that bodies have been scattered.

Migration of the Giants

To explain these and many other clues, scientists have come up with models of what apparently happened in the solar system’s past.  Two recent models, the Nice Model and the Nice 2 Model, have been highly successful at explaining many of these things.  (“Nice” is pronounced like “niece” since it refers to the city in France.)

According to these models, several billion years ago the four giant planets were in more circular orbits with smaller inclinations.  Uranus and Neptune were closer to the orbit of Saturn at that time, and the Kuiper Belt was vastly more dense than it is today and much closer to the sun, just outside the orbits of the giants.  Then, Jupiter and Saturn slowly drifted into a 1:2 resonance with each other. That was brought about through the gravitational tugging of the many small bodies around them. Once they reached this resonance, Jupiter and Saturn kicked each other into more eccentric orbits. That made them start kicking Uranus and Neptune, flinging them farther out, plunging them into the heart of the early Kuiper Belt. Then Uranus and Neptune began flinging most of the bodies of the Kuiper Belt far away, out into the Oort Cloud or completely out of the solar system. The survivors — those that were not tossed as violently — are what we see as the modern Kuiper Belt.  Though they weren’t thrown as far, they were still tossed into higher inclinations and higher eccentricities, explaining the shape of modern Kuiper Belt.

Click for larger view. Simulations by Wikipedia User:AstroMark (whom I guess is Mark Booth). Left: the solar system before the 1:2 resonance. The four circles are the orbits of Jupiter, Saturn, Neptune and Uranus. (Yes, Neptune was closer to the sun than Uranus back then according to about half of the simulations.) Middle: Uranus and Neptune have switched places and have plunged into the Kuiper Belt. Right: the majority of the Kuiper Belt has been scattered away. Image source: Wikimedia CC BY-SA 3.0

Although I used the word “plunged”, the migration of Neptune and Uranus took tens of millions of years. As they moved, their orbital periods were getting longer. Inevitably, Neptune’s period got close to resonance with one Kuiper Belt body after another.  Some of those bodies were very close to the special location in parameter space for the 2:3 resonance, so the forces of orbital mechanics pushed them even closer to it and they went into orbit around that point. As Neptune kept migrating outwardly, this location in parameter space also moved, but orbital mechanics kept pushing the resonant bodies so they all migrated together. Like a wave moving toward the beach sweeping up the surfers in its path, Neptune swept many bodies into this resonance. This explains why there are so many plutinos:  they didn’t form in that 2:3 resonance; they were swept there one-by-one as Neptune’s influence rolled through the Kuiper Belt like a giant wave.

This 2:3 resonance is not the only one that swept up planetary bodies during the gas giants’ migration. Other resonances are populated as well.  Many of these resonant bodies are likely to be confirmed as dwarf planets when we get a better measurement of their sizes.

Summary

When the New Horizons spacecraft flies past Pluto on its historic encounter, here are some cool things to remember:

1. Pluto likely formed much closer to the sun, along with the other Kuiper Belt Objects. This may help explain why Pluto is mostly rock instead of ice.
2. Pluto (like most Kuiper Belt Objects) has a high inclination and high eccentricity because it was scattered through gravitational encounters with Neptune (and Uranus?) billions of years ago. Its orbit was affected by these encounters more than Neptune’s was affected simply because of their differences in mass.
3. Pluto, and the other bodies in 2:3 resonance with Neptune (the plutinos), were likely swept into this resonance as Neptune migrated away from the sun several billion years ago, and once they got into the resonance they rode the wave until Neptune finished migrating.
4. Many clues about our solar system are in the Kuiper Belt, so the New Horizons mission may be the first of a new wave of planetary spacecraft going out to this third zone of the solar system.

If you enjoyed this post, please share it with others! Do you have questions or comments? Please let me know, below.

Note: this article was amended. Originally it stated that objects farther from the sun have higher velocities yet take longer time to complete an orbit only because the distance is longer. Thanks to reader Robert who pointed out my error. In fact, objects go more slowly the farther they are from the body they are orbiting, their velocities scaling as v=GM/Sqrt(R), where G and M are the gravitational constant and mass of the object they orbit, and R is the semi-major axis, sort of like an average orbital radius. Velocity decreases as R increases. Therefore, as you thrust to try to “speed up”, you are fighting “uphill” against gravity the whole way and you are actually slowing down.  The lost kinetic energy and the new work from your thrusting both go into gravitational potential energy.

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The Pluto flyby is a once-in-a-lifetime event, so to get ready I’m writing a series on the Kuiper Belt. This time we’ll look at how solar system bodies are classified by the way they dance.

Orbital Resonance

When you pump your legs in resonance with the swing’s natural frequency, the energy of your leg motion is consistently transferred into the energy of the swinging. Image: Edd Prince via Wikimedia, CC BY 2.0

The planets’ orbits are affected by something called resonance.

When you were a child you learned how to swing on a swing set by pumping your legs with just the right timing to make it go. You were learning how to achieve resonance between your legs and the swing. Once you had that special timing figured out, the energy of your legs got transferred into the motion of the swing so the more times you pumped, the higher the swing went.

You probably tried messing with the resonance of your legs, too.  You may have discovered that you can pump your legs twice as fast for every swinging motion and it still sorta works. That is a 2-to-1 resonance, denoted as 2:1.  Other resonances could work, though they are not as efficient. You may have also noticed that changing the timing of the leg pump can slow the swing back down and make it stop. That’s because you are making the energy go in the opposite direction, from the swing back into your legs. And if you pump your legs at random times then it makes the swing go all wonky but it doesn’t slow down or speed up overall.

Planets going around the sun can behave similarly. Each time a faster planet passes a slower one, their gravities kick each other like legs pumping a swing. (This is how astronomers discovered Neptune. They could see something was giving little kicks to Uranus’ orbit.) As long as the planets are in orbits where the kicks happen at random times, then it’s like wonky pumping on a swing set. Those planets will wobble a bit but basically stay in their orbits. However, when planets are synchronized, then the kicks will happen at the same place each time around the sun, and one planet can start speeding up while the other slows down.

Check out the video that shows a simple experiment you can do at home to help your mom or dad understand resonances and get them ready to enjoy the Pluto flyby. (You can explain to them how it illustrates Pluto’s orbital resonance with Neptune. That will be discussed, below.)

Resonance in the Asteroid Belt

At a certain distance from the sun, an asteroid completes exactly three orbits for every one orbit of Jupiter (denoted as 3:1). The asteroid in that orbit gets regular kicks from Jupiter like legs pumping on a swing set. This causes the asteroid’s orbit to change year-by-year until it’s in a much different orbit. In addition to this 3:1 resonance, there is a 5:2 resonance, and 7:3, and others at various distances from the sun.  This resonance effect has produced gaps in the asteroid belt. Wherever an asteroid would have been in resonance with Jupiter, Jupiter kicked it away. These are called the Kirkwood Gaps.

The Kirkwood Gaps can be seen in this representation of the main asteroid belt. The outermost orbit in this diagram is Jupiter. Credit: Wikimedia

Number of asteroids at each distance from the sun. Distances that produce resonance with Jupiter are not populated with asteroids, because Jupiter’s synchronized pumping has already pushed them all away. Credit: Alan Chamberlin, JPL/Caltech via Wikimedia

Resonances can do more than empty an orbit, however. They can also fill an orbit.  At the outer edge of the asteroid belt there is a class of asteroids called the Hildas. They have a 3:2 resonance with Jupiter, so they orbit the sun three times when Jupiter orbits just twice. Their orbits are elliptical so by swinging closer to and farther from the sun they pass Jupiter at a safe distance the swing back near Jupiter’s path again while Jupiter is elsewhere around the sun. Thus, they avoid strong kicks from Jupiter that would push them out of the resonance. They do, however, get little kicks from Jupiter, and the kicks actually tend to shepherd the Hildas back into these special orbits.

The following video is in a rotating reference frame. In other words, the “camera” looking down at the solar system is rotating along with Jupiter so it seems that Jupiter (the big dot on the left) is standing still. The Hildas are actually in elliptical orbits around the sun, but in this rotating reference frame they appear to move between three corners of a triangle. Studies have shown that Jupiter probably collected the Hildas by shepherding them into this 3:2 resonance as it migrated closer to the sun billions of years ago.

Resonance in the Kuiper Belt and Beyond

In the outer solar system beyond Neptune, the planetary bodies may been grouped into the following classes based on the type of orbit they have. These are called dynamical classes.

Relatively Stable Orbits

Classical Kuiper Belt Objects (Cubewanos)

The cubewanos are relatively stable because they keep a modest distance from Neptune and they aren’t in any resonance, so the little kicks from Neptune are randomized, like wonky kicking on a swing set.  The kicks make them wobble, but it doesn’t add up to anything consistent. Nevertheless, they may be randomly nudged over time into more unstable orbits from which they will be scattered away.  They are playfully called cubewanos because the first one discovered was numbered 1992 QB1, and the QB1 was given an “o” at the end to make it sound similar to plutino or twotino: “Q-B-One-oh.”

Quaoar and Makemake are two of the dwarf planets that are cubewanos. In fact, a recent list of known Kuiper Belt Objects shows 29 of the cubewanos are probably large enough to be dwarf planets and another 102 are possibly large enough to be dwarf planets. (We need better measurements to know for sure.) You might think that makes it a crowded place in the Kuiper Belt, but actually it is not. The distances are vast that far from the sun, and the area of the ecliptic plane per dwarf planet is more than 1000 times greater in the Kuiper Belt than the area per planet in the inner solar system. More than 1000 times!  It is the inner solar system that is crowded. (In my opinion, these Kuiper Belt bodies actually have cleared their orbits and should be classified as planets. More on this, below.)

Resonant Bodies

Haumea is an example of a resonant body. It is in a 7:12 resonance with Neptune. Resonances can be any combination of small integers, like 2:3, or 3:5, or 4:7. We know of 27 resonant bodies that are probably large enough to be dwarf planets, and 66 more that are possibly large enough.

The orbital path of Orcus in a view that rotates to keep Neptune (N) stationary. Note how Orcus keeps a great distance from Neptune. The small orange circle near the center is the orbit of Mars, showing the tiny size of the inner solar system.  Dancing around the giant planets simply cannot fit there. Credit: kheider via Wikimedia

Plutinos

This is a subclass of the resonant bodies. They include Pluto, the dominant member of the Kuiper Belt, hence the name. They are in a 2:3 resonance with Neptune, so every time Neptune goes around the sun three times, they go around twice. There are lots and lots of plutinos.  Orcus and Ixion are two more examples. We know of 19 plutinos that are probably large enough to be dwarf planets, and 32 more that are possibly large enough.

Twotinos

This is another subclass of the resonant bodies. They are in a 1:2 resonance with Neptune, hence the name. They are considered the outer edge of the Kuiper Belt, meaning that they have an average distance from the sun that is larger than the other Kuiper Belt bodies. (But they are in elliptical orbits so they all move into and out of the main bulk of the Kuiper Belt; it’s an abstract edge.) Recent data show three known twotinos are probably large enough to be dwarf planets while 30 more are possibly large enough.

Tostitos

These bodies are a snack, not technically part of the Kuiper Belt, and they are not in any known planetary resonance except with the Earth.  They may be eaten during the Pluto flyby. We have never found a Tostito large enough to be a dwarf planet. #NerdHumor

Detached Objects

These bodies are not considered part of the Kuiper Belt. They avoid Neptune’s gravitational bullying by staying far away from its territory.  They might swing into the heart of the Kuiper Belt at their closest approach to the sun, but never close to the orbit of Neptune, and their farthest distance from the sun is way, way out there. Thus they do seem rather detached, but many planetary scientists are still attached to them.  Seven known detached objects including Sedna are probably large enough to be dwarf planets, and another 10 are possibly large  enough.

Unstable Orbits

Scattered Disc Objects

These bodies are not considered part of the Kuiper Belt. They are in unstable orbits and they are right now in the process of being pushed around by Neptune.  Their orbits may pass through the Kuiper Belt, but they are typically very tilted and elliptic.  Twenty two scattered disc objects are probably large enough to be dwarf planets, including Eris and Salacia. Another 97 are possibly large enough.

Where are the Kirkwood Gaps of the Kuiper Belt?

When you look at the distribution of main belt asteroids versus their distance from the sun (above), you see very obvious gaps wherever there is a resonance. The resonances actively push the asteroids away. But when you look at the known Kuiper Belt objects versus their distance from the sun (below), you don’t see these gaps. Instead, you see clustering of bodies at the resonances. Why the difference?

Click for larger version. Each circle represents a known body beyond Neptune. The location of each circle in the horizontal axis is the semi-major axis of the body, sort of like an average distance from the sun (measured in Astronomical Units, or AU). The vertical location tells the tilt of the body’s orbit relative to the solar system’s ecliptic plane. The size of each circle is an estimate of the size of the body. Resonances are annoted near the top of the figure. You can see that bodies tend to be clustered at some of the resonances. Dark red bodies are plutinos. Blue are cubewanos. More color coding and information is given at this link. Image source: Wikimedia

We think the difference is because of Saturn. Main belt asteroids have to contend with gravitational kicks from both Jupiter and Saturn, and it is hard enough to satisfy one bully at a time, nearly impossible to satisfy two. For the Hildas, they are close enough to Jupiter that it is able to keep shepherding them into the 3:2 resonance despite Saturn’s disturbances. Bodies in other, weaker resonances, however, were not so lucky. When Saturn bumps them, their timing with Jupiter is not quite right so Jupiter kicks them out of the orbit entirely.  In the Kuiper Belt, bodies only need to satisfy Neptune’s bullying.  Uranus is so far away — the distances in that part of the solar system are so much greater — that it doesn’t have enough effect.

Another Reason Why Pluto is a Planet

Here are the statistics on the dwarf planets discovered so far in the outer parts of the solar system.

Dwarf planet dynamical classes

Why don’t we see these different kinds of orbits among the planets in the inner solar system?

The cubewanos are similar to the major planets of the inner solar system, so this is the one class we do see here. This type of body is in relatively stable orbits because they are far enough from the nearest giant planet and also not in resonance with it, so the weak gravitational kicks are random and average out.  There are so many more of these in the outer solar system than the inner because they have more room to orbit without disturbing one another.

The resonant bodies of the Kuiper Belt are relatively stable because they are in highly elliptic orbits that take them far from Neptune every time the giant planet passes by, thus avoiding big kicks. This type of motion simply doesn’t fit as a stable orbit in the small space of the inner solar system. We expect that Mercury will eventually go into a secular resonance with Jupiter (a different kind of resonance than discussed here), and this will push it to a more elliptic orbit. There’s no room for it to stay like that in the inner solar system. It will collide with one of the other planets and be destroyed, or it might thread the needle and escape to the outer solar system, but then it would no longer be defined as a planet according to the IAU’s current definition.

The detached objects are stable simply because they are so far away. Needless to say, that cannot exist in the inner solar system since the space is too small.

The scattered disc objects are in the process of being moved by Neptune. They can exist in their highly elliptical orbits for a long time in the vast space of the Kuiper Belt. The similar objects that exist in the inner and middle solar system (asteroids, comets, and centaurs) cannot exist as long before colliding with a planet, so they must be continually replaced from the Main Asteroid Belt, the Kuiper Belt, and the Oort Cloud. These transient bodies are mostly small, simply because small bodies are so much more common than large ones. On the rare occasion that a larger body begins scattering in the inner solar system (like Mercury may one day, or like Theia may have done in the past) the chances are it won’t survive long before it strikes a planet.  So it’s not surprising we see no planet-sized bodies in the inner solar system belonging to this dynamical class. Again, the space is just too small.

Unfortunately, we based the definition of a planet on our experience in the inner solar system, where planetary dynamics are not diverse. These more diverse dynamical classes are capable of coexisting in the the vast space of the Kuiper Belt, and it was this fact that made the IAU declare the KBOs are not true planets. When we say the inner solar system planets have “cleared their orbits”, what we really mean is that there isn’t enough room inside the inner solar system for these other dynamical classes to exist. They only exist where there is room for them, and that’s by definition. It’s not a property of the Earth or Mars that its orbit is clear. It’s merely the fact that dynamical diversity doesn’t fit within their distances from the sun.  It’s not a deficiency of Pluto that it’s orbit hasn’t been “cleared”.  It’s just that the outer solar system is much bigger than the inner, so it supports a more diverse phenomenology.

So in the final analysis, the IAU definition of a planet is tantamount to this:

To be a planet, a body must: (1) orbit the sun, (2) be gravitationally round, and (3) exist in a location where interesting dynamical classes cannot fit.

There’s no such thing as clearing an orbit where the interesting dynamical classes can fit, because if they can fit, then they exist.  And they will continue to exist until the sun burns out.

I don’t find this a very satisfying definition of a planet, one that determines a priori that the outermost zone of the solar system shall have no planets in it, simply because it can have so many. I would rather let nature show us which of our words describe it best. Planets means wanderers in the original Greek, referring to the lights in the sky that wandered through regular paths against the background of stars. And wander they do in the Kuiper Belt! Their wandering is so interwoven it could even be called a dance. Near the sun it is too crowded for the wanderers to dance, so they circle round and round like donkeys at a grist mill, till finally Jupiter pushes them from their tracks and they die in the escape or survive to the dance beyond. Out there, bodies rarely collide, and they move with a collective complexity that would make choreographers proud.  To my thinking that makes them consummate wanderers, all the more planet-like, not less.  It makes their wandering more beautiful, more interesting, and more surprising, like everything in nature when we finally see it for the first time.

If you found this interesting, please share it!  And I would love to discuss this with you so please comment below.

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About 2300 years ago, a human being measured the world. It was Eratosthenes, the Greek scholar. Imagine how he felt when he first realized what he had done. “Wow, I am the only person who has ever known the size of the world.” It must have been amazing. And humbling. He had noticed that sunlight falls at a different angle in Aswan than it does in Alexandria at the same time of day. That gave him a measurement of the world’s circumference accurate to within about 16%, an astounding achievement. Later, humans began measuring planets in our solar system beyond Earth, then planets around other stars.

Some of the solar system bodies to scale (diameters are to scale but spaces between them are not)

It turns out we live on a medium-sized planet.  It has enough gravity to hold a thick atmosphere, so air pressure keeps water in a liquid state at the surface. Air is needed to make fire so we could invent metallurgy.  To support a technological civilization, a smaller world with only a subsurface ocean probably would not suffice. Other planets in our solar system are indeed much smaller than the Earth, but some are much, much larger. The range of sizes can be compared to the grains of sand in a bucket of lunar soil. You may find only one really big piece in there – a rock – and only a few pieces of gravel, but many, many sand grains and uncountable specks of dust. In terms of sheer numbers, nature tends to favor the small. The same is true in biology. There are only a few really large organisms on the Earth (whales, redwood trees, and gigantic underground fungi), but there are many more medium-sized organisms (people, lobsters, and carrots), huge numbers of insects, and countless microbes. The big ones are the rare cases, and the same is true for planetary bodies. Giants like Jupiter and Saturn are few. Medium-sized bodies like Earth and Pluto are more numerous. Smaller dwarf planets, asteroids and meteoroids are in vast supply.

Three bottles from my sand collection. The size of the grains tells us the power of the waves on each one’s beach. Left to right, coarse to fine, from big waves to small.

Whenever we have a collection of objects like planets or sand, we like to study the distribution of their sizes because it gives insight into the dynamics of nature. I collect sand as a hobby. Whenever I travel I visit the local beaches or rivers to get samples of sand. (This leads to interesting conversations with airline security when they find baggies of the stuff in my luggage. But it’s surprising how many airport security agents love geology.) And sand collectors around the world exchange samples by mail. I’ve got hundreds of tiny bottles in all colors and textures – I find it truly fascinating, and it’s an excuse to spend more time in nature. On some beaches we see the sand is coarse, even gravelly, while on other beaches it is fine like silt. Why is this?  The yearly power of the waves on each beach favor one type of sand grain over another. Big waves push coarse grains from the ocean floor up onto the beach but carry the smaller grains back out to sea. Small waves don’t have the energy to push  coarser grains onto the shore nor to carry the really fine sand back out. The texture of the grains inside sandstone tell us what kind of waves, rivers, or winds collected the sand before it hardened into rock. In a similar way, biologists study the ecology of an island by measuring its animals. Are there a lot of big ones, and where do they get the food to maintain large body sizes? Do the carnivores tend to be bigger than the herbivores? And astrophysicists study the sizes of stars. Whether we are investigating biology, geology, or astrophysics, the distribution of sizes is an important clue.

Sieving sand in my first lab at NASA. The sand runs down through a stack of screens to separate them into different sizes. I took this picture when I noticed the amazing sand patterns that formed on the screens.

On the Moon, sand grains are constantly broken down to smaller sizes by the impact of micrometeoroids (dust grains flying down from space at super-high velocity). These impacts don’t just break grains apart; they also melt some of the mineral, which splashes onto smaller sand grains and harden into glass, effectively gluing them together. This process of both breaking down and gluing together eventually reaches a steady state. We call lunar soil mature when it reaches that state. When a really big asteroid hits the Moon it digs deeply into the ground and blows out bedrock to make fresh, immature soil, which is very coarse. After sitting on the lunar surface for millions of years the micrometeoriod impacts make it mature so it displays the characteristic distribution of particle sizes, much finer than immature soil with lots of dust-sized particles. We study the age of lunar soil partly by looking at the distribution of particle sizes.

Left: The measured results from sieving four different granular materials. Right: After some math, the sieve results are converted into these plots that show how much of the soil’s mass consists of each particle size. Note that lunar soil (and the simulated lunar soil) have much smaller particles that beach sand or construction sand. Click to see larger plots.

What happens next to all this lunar dust? On the Earth, the dust is washed out of the soil by rain, and it is carried by streams and rivers into calm, shallow seas where it settles as mud. Over time, the mud hardens into mudstone and the rock cycle turns it into metamorphic or igneous rock. Thus, the geologic processes of Earth remove dust from the soil. Not so, on the Moon. There is no rain to remove the dust, so these tiny particles stay mixed into the soil everywhere on the Moon. Our bodies aren’t adapted to that geology so lunar dust is an engineering challenge.  The particle sizes tell us about the geological processes that created them.

By the way, J.R.R. Tolkien’s story “Roverandom” tells of a dog who visits the Moon. He says the Moon is so clean, it is almost impossible to get dirty there. Ha!

Apollo 17 Astronaut Harrison (Jack) Schmitt on the Moon covered in lunar dust.

We can do this kind of research with entire solar systems, too, where the planets are like grains of sand. We can ask questions such as, what astrophysical processes created this collection of planets? Why are the planets so much smaller in some regions of the solar system than in others? Why are there so many asteroids still floating around? Why are there so many medium-sized planets (dwarf planets) beyond Neptune? What solar system processes are building up or breaking down these bodies in each region?

Nature favors smaller sizes among planets, too. Pluto and Earth are medium-sized planets in our solar system (using the geophysical definition of a planet). Moons are included as “secondary planets.”

We know planets grow by accretion. They start as dust grains orbiting the newly formed star, accumulating through electrostatics and gravity into planetesimals, colliding and growing further into planetoids, and eventually into the planets we see today. Most of this growth happens early in the solar system’s history until their orbits have been largely cleared. When there’s not much material for them left to absorb, the growth spurt necessarily ends. (Still, the Earth accretes about 60 tons of new mass from space every day, mostly in the form of dust.)

In the Main Asteroid Belt we see what looks like an anomaly: all that small stuff never grew into one bigger planet. We see the bodies are actually colliding with one another and busting apart instead of settling down into continual growth. It appears Jupiter is keeping the asteroid belt stirred up with its gravity so it never settles. The asteroid belt is the “beach” of the inner solar system, and Jupiter’s gravity is like waves crashing in from the sea. The particle sizes of this beach tell us something about the energy of the crashing waves. Is this process happening in lots of other solar systems, or do they have calmer seas and no asteroid belts? Or are the seas even rougher out there, so all the smaller planets are swept completely away? One day, when we send robotic probes to other stars to set up colonies in advance of humanity’s arrival, it would be very useful if they find some asteroid belts to mine. The natural place for a beachhead is a beach.

The Kuiper Belt out beyond Neptune is dynamically different than the Main Asteroid Belt. In recent decades we have been measuring the sizes of the Kuiper Belt Objects (KBOs). So far we have found only one example of a family of KBOs that broke apart by colliding. (In the asteroid belt we find many.) We call it the Haumea family because the dwarf planet Haumea appears to be the parent body. A long time ago, perhaps more than a billion years, another large body hit Haumea and blew out a dozen or more fragments. (Haumea’s two small moons are fragments that stayed trapped in Haumea’s gravity.) Scientists performed simulations of collisions in the Kuiper Belt and the Scattered Disc, and according to their results there is only a 47% chance that one such collision would occur. It seems likely, therefore, that the Haumea family is the only one. Unlike the Main Asteroid Belt, the planets aren’t dwarfed because collisions keep breaking them apart, but rather they are done growing because their orbits have been effectively cleared. In the inner solar system, bodies with intertwined orbits can’t coexist for very long (so we say those orbits aren’t cleared). In this third zone of the solar system, they can.

Planetary science is about to enter its heyday: we are collecting a vast wealth of data from the other solar systems in our corner of the Milky Way. It is still hard to measure the smaller planets in those systems, but our techniques and tools are improving so it’s just a matter of time (and of continued funding). This will revolutionize our understanding of solar system dynamics and will place our own solar system into a much larger context. It will help us fill in at least one unknown of the Drake Equation – how many life-supporting planets are out there? It will tell us the prospects for one day expanding our own civilization beyond Sol. It will let us know whether the Earth is unique, not just in our solar system, but in the universe. As T.S. Eliot said,

We shall not cease from exploration, and the end of all our exploring will be to arrive where we started and know the place for the first time.

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