Mean Motion Resonances in The Solar System
There are only a few known mean motion resonances in the Solar System involving planets, dwarf planets or larger satellites (a much greater number involve asteroids, planetary rings, moonlets and smaller Kuiper belt objects, including many dwarf planet candidates).
- 2:3 Pluto–Neptune
- 2:4 Tethys–Mimas (Saturn’s moons)
- 1:2 Dione–Enceladus (Saturn’s moons)
- 3:4 Hyperion–Titan (Saturn's moons)
- 1:2:4 Ganymede–Europa–Io (Jupiter’s moons).
Additionally, Haumea is believed to be in a 7:12 resonance with Neptune, and Eris and Makemake may be in 5:17 and 6:11 resonances with Neptune, respectively.
The simple integer ratios between periods are a convenient simplification hiding more complex relations:
- the point of conjunction can oscillate (librate) around an equilibrium point defined by the resonance.
- given non-zero eccentricities, the nodes or periapsides can drift (a resonance related, short period, not secular precession).
As illustration of the latter, consider the well known 2:1 resonance of Io-Europa. If the orbiting periods were in this relation, the mean motions (inverse of periods, often expressed in degrees per day) would satisfy the following
Substituting the data (from Wikipedia) one will get −0.7395° day−1, a value substantially different from zero!
Actually, the resonance is perfect but it involves also the precession of perijove (the point closest to Jupiter), . The correct equation (part of the Laplace equations) is:
In other words, the mean motion of Io is indeed double of that of Europa taking into account the precession of the perijove. An observer sitting on the (drifting) perijove will see the moons coming into conjunction in the same place (elongation). The other pairs listed above satisfy the same type of equation with the exception of Mimas-Tethys resonance. In this case, the resonance satisfies the equation
The point of conjunctions librates around the midpoint between the nodes of the two moons.
Read more about this topic: Orbital Resonance
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