What Is An Orbital Resonance?

by Carson
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An orbital resonance is a configuration where the orbital periods of two objects are expressible as a simple fraction of each other. For example, if object A orbits the Sun twice while object B orbits the Sun once, the pair is in a 2:1 resonance. Let’s find out how it works and how it’s important in this article.

How Do Orbital Resonances Work?

You probably know that the orbital periods of objects are irrational numbers in any unit. Therefore, you may wonder whether simple integer ratios exist between those periods. Well, the truth is that they don’t; instead, the objects are kept in sync differently. This only works if one of the two satellites is massive, like a planet. Thus, you don’t see any asteroids in resonance with another asteroid.

If two objects are in resonance, their orbital periods are close to a perfect integer ratio. But the ratio isn’t precise, so the object drifts away from the resonance. But if one of the objects is massive enough to perturb the orbits of distant objects, which a planet does, it changes the orbit of that resonant object. Specifically, the object’s path away from the resonance is reversed. If it is falling behind, it speeds up. And vice versa. This phenomenon is called libration. It is the key to keeping orbits in sync with each other.

The libration of 5370 Taranis, an asteroid in a 2:1 resonance with Jupiter, in a rotating frame with the same orbital period as Jupiter
Data source: JPL Horizons
Plotted with matplotlib

Examples of Orbital Resonances

Although no planets in the Solar System are in resonance with each other, there are many resonant asteroids and minor planets. For example, the dwarf planet Pluto is in a 2:3 resonance with Neptune. Every time Pluto goes around the Sun twice, Neptune orbits the Sun three times. In fact, because of this resonance, while Pluto’s orbit crosses that of Neptune, they never have close approaches or collisions.

Orbital resonances are present in moons as well. For example, Jupiter’s moons Io, Europa, and Ganymede are in a 4:2:1 resonance with each other. Whenever Ganymede orbits Jupiter once, Europa orbits twice, and Io orbits four times. There is also a possibility that the outermost Galilean moon, Callisto, will be captured in this 2:1 resonance chain as well. On the other hand, in the Saturnian system, Enceladus and Dione are in a 2:1 resonance, and Titan and Hyperion are in a 4:3 resonance.

Even more spectacularly, many asteroids are in resonance with the planets. For example, there is a large population of asteroids in the 1:1 resonance with Jupiter. They are called the Jupiter trojans because they mostly gather around the L4 and L5 points of the Sun-Jupiter system. There is also a large clump of asteroids in the 3:2 region, called the Hilda asteroids. Interestingly, there are gaps in the asteroid distribution near other resonances, such as the 3:1, 2:1, 5:2, and 7:3 resonances. These are the Kirkwood gaps, and are caused by periodic perturbations of Jupiter that excite their eccentricities.

Other Types of Resonances

Besides the orbital resonances described above, do you know there are other types of resonances in the Solar System? The ones we discussed are mean-motion resonances, but secular and spin-orbit resonances also exist.

Secular resonances occur when an orbit precesses at the same speed as a planet. The periapsis and the longitude of the orbit move around in a circle due to perturbations of other planets as well as relativistic effects. The rate of perturbation depends on many factors, but they might somehow match that of a planet in either of these factors. If it does, the asteroid receives frequent perturbations from that planet, increasing the orbital eccentricity. An example is the v6 secular resonance, which occurs when an orbit precesses at the same rate at Saturn, happens to be in the asteroid belt. This is a very well-known resonance, which is one of the indicators for the inner edge of the main asteroid belt.

An illustration of a planet undergoing apsidal precession while orbiting a star
Note that the sizes and the precession rates are not to scale
Credit: WillowW – Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=3416065

Another type of resonance is spin-orbit resonance, which occurs when an object’s spin matches its orbital period. The most common type of such resonance is a 1:1 spin-orbit resonance, better known as tidal locking. It occurs when the rotation of a close-in satellite slows down due to tidal forces and is a common phenomenon among the moons of our Solar System. In fact, this is the reason why the Moon only exposes its near side to us, while the far side remains invisible without spacecraft. Other spin-orbit resonances also exist, such as the 3:2 resonance between Mercury’s rotation and orbital period.

Conclusion

In this article, we’ve explained the concept of orbital resonances. Remember:

  1. Mean-motion resonances occur when the orbital periods of two objects are a simple fraction of each other
  2. Secular resonances occur when the orbits of two objects precess at the same rate
  3. Spin-orbit resonances occur when the rotation and orbital periods of an object are a simple fraction of each other

These concepts are very important when studying the dynamical evolution of objects. In fact, asteroids could be retained for a long time due to stable resonances, or escape easily in unstable ones. If you want to see the full effects of resonances on the orbits of asteroids, check out this page from our website. Also, if you want to learn more about them (particularly the examples), please visit the webpages in the references below.

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