Thursday, April 15, 2010

Orbital Resonance

An orbital resonance is a gravitational phenomenon in which two bodies that are both orbiting around one parent body are in a specific pattern. For example, if for every orbit Planet Bill makes around a star, Planet Joe makes exactly three, the two bodies are in an orbital resonance (the notation for this is 1:3). It may seem unlikely that such a correspondence would occur in the physical universe and that this is a purely abstract notion, but this is not the case. In fact, gravity often pushes objects into these resonances when the objects are of comparable size, but ejects them if one is too much bigger than the other, as with Jupiter and an asteroid.

In fact, there are resonances in our Solar System! The simplest case is the one between Neptune and Pluto. For every two orbits Pluto makes, Neptune makes exactly three. This is why it is impossible for the two bodies every to collide, despite the fact that their orbits cross. This is the only stable resonance involving two planetary (although Pluto is a dwarf planet) bodies, but other objects outside of Neptune's orbit are in resonances with Neptune, known as Trans-Neptunian objects. Most of these are smaller than Pluto, but one larger one is known: the dwarf planet Eris. However, Eris is not known to be in an exact orbital resonance with Neptune.

Other Trans-Neptunian objects sometimes are in resonances with Neptune, the most common being (object:Neptune) 2:3, corresponding to Pluto and other bodies, 3:5, 4:7, 1:2, and other rarer ones such as 2:5, 3:4, 4:5, 1:4, 1:5, 1:3, 3:7, and 6:11. Some of the latter sometimes correspond to only one known object, and may be coincidental. Some are also unstable, and smaller objects can often be ejected from a resonance by a gravitational pull quite easily. The special case of a 1:1 orbital resonance is addressed in the post, Lagrangian Points.



A chart showing known objects, resonances, and distances of various objects beyond Neptune's orbit.

Resonances of a different kind impact asteroids in the main asteroid belt. Jupiter's gravitational pull has a great effect on the asteroid belt, and unlike Neptune's resonances, are much closer to each other. Therefore, rather than objects commonly existing at these resonances, repeated encounters with Jupiter ejects the asteroids onto another orbit. Due to this, there are gaps, called Kirkwood Gaps, that exist at the main orbital resonances with Jupiter, named after Daniel Kirkwood, who observed and explained the nature of the gaps in 1857. The population of asteroids in relation to the gaps is shown in the image below.



This image shows four main resonances and the effect they have on asteroid population. There are other weaker ones that cause a lower number of asteroids to keep stable orbits, but they are no nearly as drastic. Two examples are 7:3, shown at 2.71 AU, and 9:4, at 3.03 AU.

There are a few other major resonances in our Solar System, including a 1:2 between Saturn's moons Dione and Enceladus and the 3:4 one between Saturn's moons Hyperion and Titan. However, the most famous resonance in our Solar System is the only known Laplace resonance, or one involving more than two bodies.

It is the 1:2:4 resonance between three of the four Galilean moons of Jupiter. Io is the 1, Europa the 2, and Ganymede the 4. This remarkable property supposedly emerged with a gravitational encounter of Ganymede and another body, resulting with the instability of Ganymede's orbit. Due to the gravitational pull of Io and Europa coupled with that of Jupiter, Ganymede settled into its position in the resonance.

Outside of the Solar System, many other orbital resonances probably exist, between exosolar planets, and one known example is a pair of planets orbiting the star cataloged as GJ 876. They are comparable in size to Jupiter, and both orbit extremely close to their parent star, within what would be the orbit of Mercury, but have a 1:2 resonance. This type of resonance among major, Jupiter-sized planets is more significant than any other one known, and is unique, as far as we know.

There are also other types of resonances, such as secular resonance, which is the alignment of the precessions of two bodies. Precession is the cycle in which the axial tilt of a body orbits around back to its starting position. For the Earth, the axial tilt is 23.44º, and it takes approximately 41,000 years to run a full cycle. During this time, the axial tilt varies from 22º to 24º. Where the north pole points in space is known as the celestial north pole. Over time, this pole moves over the heavens, and the north star therefore changes. Currently, the closest major star is Polaris, but over the next tens of thousands years it will progressively move away and then back when the cycle is complete. As a result, Vega will also be the north pole star for a time in each cycle.

This and other types of resonance are common throughout the Solar System within seemingly complex and random gravitational interactions.

Another type of synchronization that may be called a resonance, is the tidal force of a satellite on a parent body. Over time, the pair of bodies tug on each other gravitationally, pushing the slightly heavier side of each inward so that the period of rotational of the smaller body is eventually exactly the same as its revolution period, and is tidally locked. Many moons in the Solar System exhibit this feature and the most well known is our own moon. We only see one face of it because it is tidally locked to the Earth. In addition to this however, there also is a gravitational tug from the moon that is slowly tidally locking the Earth and the Earth day is slowly getting longer, increasing by mere fractions of a second each year. In addition, the two moons of Mars, at least eight of Jupiter's moons, fifteen of Saturn's moons, five of Uranus, two of Neptune, and the Pluto-Charon system (both bodies are locked to each other). Also, there is one known extrasolar instance of mutual tidal locking in which a star and its giant planet are tidally locked to each other.

One other special type of tidal locking is the Mercury-Sun system. For every two revolutions of Mercury around the Sun, Mercury revolves thrice on its axis. This relation is known to be stable, but it is a unique case.

Resonances are mysterious connections in the heavens which are difficult to find and even more difficult to understand.

Sources: http://www.cfa.harvard.edu/mpec/K08/K08S05.html, http://upload.wikimedia.org/wikipedia/commons/1/1c/TheResonantTNO_90AU.svg, http://adsabs.harvard.edu/abs/1983Natur.301..201D, NASA, http://adsabs.harvard.edu/abs/1991Icar...94..399M

9 comments:

Laurel Kornfeld said...

Dwarf planets are planets too. Please do not blindly accept the controversial demotion of Pluto, which was done by only four percent of the International Astronomical Union, most of whom are not planetary scientists. Their decision was immediately opposed in a formal petition by hundreds of professional astronomers led by Dr. Alan Stern, Principal Investigator of NASA’s New Horizons mission to Pluto. Stern and like-minded scientists favor a broader planet definition that includes any non-self-luminous spheroidal body in orbit around a star. The spherical part is important because objects become spherical when they attain a state known as hydrostatic equilibrium, meaning they are large enough for their own gravity to pull them into a round shape. This is a characteristic of planets and not of shapeless asteroids and Kuiper Belt Objects. Pluto meets this criterion and is therefore a planet. Using this broader definition gives our solar system 13 planets and counting: Mercury, Venus, Earth, Mars, Ceres, Jupiter, Saturn, Uranus, Neptune, Pluto, Haumea, Makemake, and Eris. At the very least, you should note that there is an ongoing debate rather than portraying one side as fact when it is only one interpretation of fact.

Louis said...

Please note that I still formerly regard Pluto as a planetary body, which includes the main planets and the so-called "dwarf planets". However, it is wrong to say that I've "blindly accepted" this decision, because I happen to have given the matter great thought, and I personally believe that Pluto is a dwarf planet for the following reasons. First, although it and other bodies are in hydrostatic equilibrium, so are some satellites, such as Ganymede and Titan, and this is not suitable criteria including all such objects as planets. In addition, you failed to address the main reason why Pluto and the others were demoted, i.e. because they had not cleared their neighborhoods. For all the dwarf planets, especially Ceres, share an orbit with objects similar in size and mass to their own. I believe that having a specific ratio between the mass of the planet and the objects sharing its orbit should define a planet, and the objects sharing Pluto's orbit make up a total mass that amounts to much more than that of Pluto. Furthermore, Pluto and other Trans-Neptunian objects have elliptical orbits, and Pluto's crosses Neptune's. Pluto clearly does not fit in with the other eight planets, but does deserve a status higher than minor planet, and I therefore respect the IAU's decision regarding Pluto. Besides, I only mentioned this in passing, and a fuller explanation is available elsewhere on this blog.

Laurel Kornfeld said...

Dwarf planets should be considered a subclass of planets; the fact that the IAU resolution specifically precluded this is highly problematic. Dr. Alan Stern coined the term "dwarf planet" to indicate objects large enough to be in hydrostatic equilibrium but not large enough to gravitationally dominate their orbits. The term refers goes back to a 2000 study that he and Dr. Hal Levison did in which planets were classed into two groups, "uber planets" and "unter planets." Dwarf planets are the unter planets. However, Stern and Levison never meant for them to not be considered planets at all.

There is no reason an object should be required to "clear its orbit" to be considered a planet. This was never an issue until a group of dynamicists decided to make it so in 2006. Such a requirement would preclude many exoplanets which have highly elliptical orbits and, in at least two cases, two giant planets that cross one another's orbits, circling their star in a 3:2 resonance like Neptune and Pluto.

Ceres is much larger in mass and size than almost every other object in the asteroid belt (with the exception of Vesta and Pallas), as Pluto and Eris are much larger in mass and size in comparison to almost every other known object in the Kuiper Belt. Being in hydrostatic equilibrium and being geologically differentiated make these objects more akin to planets than to asteroids.

Satellites in hydrostatic equilibrium, such as Ganymede and Titan, have in the past been referred to as "secondary planets." They have a lot of the same characteristics of primary planets; one can land objects on them, and some may even harbor subsurface oceans that could contain microbial life. I do not see why these objects should not be their own subclass of planets. Ganymede is actually larger than Mercury; the only difference is it and other secondary planets directly orbit other planets instead of the Sun.

Not fitting in with the other eight planets does not make an object not a planet. We need to consider the idea that there are more than two classes of planets--terrestrials and jovians. Just as dwarf stars are still stars and dwarf galaxies are still galaxies, dwarf planets should be considered a subclass of planet. This one amendment would go a long way toward resolving the debate.

Louis said...

Again, I wish to stress that I am in no way saying that the dwarf planets are not a subclass of planets. In fact, I encourage the idea for Pluto and the others to be part of the broader term planetary bodies, but I still do think there needs to be an underlying distinction.

First, the ability for a planet to clear its orbit shows that it has orbital dominance, and otherwise, there are other candidates. For example, Vesta is still considered a dwarf planet candidate, despite it not being a close spheroid.

Hydrostatic equilibrium can be approximate, and there are objects that are borderline. To accept these as planets would be to have uncertainty about the number and nature of planets, and a decision would have to be made to demote some of these candidates. If, however, one keeps the planets and dwarf planets distinct, the commonplace knowing of the eight planets will be preserved, and the loss of Pluto is much less confusing than the addition of 5 additional planets.

Also, clearly satellites are not planets, But what is Pluto but a satellite? Both Pluto and its companion Charon orbit around a common center of gravity and neither attains the notion of satellite. Your argument is inconsistent to regard one as a planet and simply disregard the other.

Finally, there is, in all probability, a large chance that more planetary objects will be discovered, and some of these will most likely attain Pluto's size. To include new planets will further complicate the well-known system of eight planets. Amending the system will lead to more complexity, not simplicity. On this blog, the eight planets will be considered planets, and the others dwarf planets. It is simply a matter of naming, and the dwarf planets will not be changed in nature by their classification. People may disagree, but this is how the matter stands, and how it shall remain.

Laurel Kornfeld said...

"People may disagree, but this is how the matter stands, and how it shall remain."

It may stand that way with you, but I hope you acknowledge that there are many who disagree. Even Dr. Neil de Grasse Tyson, in his recent NOVA broadcast, recognized that there is no consensus on a definition of planet and on where Pluto fits in the scheme of things.

I'm glad you're not saying dwarf planets are not a subclass of planets. However, that is exactly what the IAU said! Therein lies a good part of the problem.

In my blog, I suggested that borderline objects, those of which we are uncertain as to whether they are in hydrostatic equilibrium, be placed in yet another category, sub-dwarf planets (inspired by the classification of sub-brown dwarf stars). This category would apply to objects 200-400 miles in diameter. With Vesta, we are lucky that next year, Dawn will arrive and provide us with data on this body's geological characteristics and composition. Pluto, in contrast, is 1430 miles in diameter, and its status of being in hydrostatic equilibrium is not in doubt. Objects like Pluto and Eris should not be in the same category as borderline ones like Vesta.

Hydrostatic equilibrium can be approximate, but "clearing an orbit" is even more so. The IAU's language is extremely vague. If applied literally, it could exclude every planet in our solar system. As is, it precludes either object in a binary from being considered planets. And it is biased against objects further from their parent stars, as these objects have larger orbits to clear than those closer to their stars.

Why is it a problem if the number of planets is uncertain? No one objects to an ever changing number for Jupiter's moons or for stars or for exoplanets. Any attempt to keep the eight biggest planets distinct from the dwarf planets equates to drawing an artificial boundary. Why put Earth and Jupiter in the same classification? Earth actually has far more in common with Pluto than it does with Jupiter.

Why not instead add new subclasses of planets as we make new discoveries? That gives us terrestrial planets, gas giants, ice giants, dwarf planets, super Earths, hot Jupiters, sub-dwarf planets, etc. Memorization of a particular number or order of planets does not have much educational value. Do we ask kids to memorize the names of all the rivers in the world? Why not instead teach them the concepts of each type of planet so they understand what characteristics define that particular subset?

Why are satellites in hydrostatic equilibrium not secondary planets? Compositionally, many are quite similar to terrestrial planets. We can still distinguish them from primary planets in every day conversation. However, they clearly have elements in common with some of the primary planets and could potentially be sites for future unmanned and manned exploration.

I never said to disregard Charon. Since Pluto and Charon orbit a common barycenter, they could be considered a double planet system. Some have suggested that in cases like this, the larger object should be designated as the primary planet and the smaller as the secondary. The IAU has suggested nothing and failed to address the issue at all.

Why the preference for simplicity over complexity? We live in a complex universe; new discoveries are reinforcing this all the time. Simplifying things for convenience could be viewed as a disservice to the public.

In his book "The Case for Pluto," Alan Boyle describes our solar system as having four terrestrial planets, four jovian planets, and many more. This is an equally valid way to understand our solar system.

Louis said...

Thank you for your comments. I appreciate your arguments, and your knowledge of Pluto. It is an interesting topic, and perhaps a more final decision will be made in the future.

Noah Elkins said...

Although I agree with the Professor, I kinda feel sad for Pluto...

Stan J said...

Hi,

I've been looking at the orbital resonance subject for a piece of fiction I'm playing around with but I'm having trouble wrapping my head around the idea of an object being ejected from its orbit. I'm specifically thinking about a large object like Enceladus and its inhabitants being put in danger by Dione and what I'd have to change about the system to make that happen. I got as far as maybe putting their orbits closer together and making Dione much larger but that's about where my brain fizzled out (if not before).

This is probably a strange request but if you had any ponderings on the matter it'd be much appreciated. It certainly wouldn't make me any thicker.

Stan

Stan J said...

Sorry, I meant to leave a diagram link. My brain fell asleep about four hours ago.

https://en.wikipedia.org/wiki/Enceladus#Orbit_and_rotation