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
Famous quotes containing the words solar system, motion, solar and/or system:
“Our civilization has decided ... that determining the guilt or innocence of men is a thing too important to be trusted to trained men.... When it wants a library catalogued, or the solar system discovered, or any trifle of that kind, it uses up its specialists. But when it wishes anything done which is really serious, it collects twelve of the ordinary men standing round. The same thing was done, if I remember right, by the Founder of Christianity.”
—Gilbert Keith Chesterton (18741936)
“It is the fixed that horrifies us, the fixed that assails us with the tremendous force of mindlessness. The fixed is a Mason jar, and we cant beat it open. ...The fixed is a world without fire--dead flint, dead tinder, and nowhere a spark. It is motion without direction, force without power, the aimless procession of caterpillars round the rim of a vase, and I hate it because at any moment I myself might step to that charmed and glistening thread.”
—Annie Dillard (b. 1945)
“Lincoln becomes the American solar myth, the chief butt of American credulity and sentimentality.”
—H.L. (Henry Lewis)
“Social and scientific progress are assured, sir, once our great system of postpossession payments is in operation, not the installment plan, no sir, but a system of small postpossession payments that clinch the investment. No possible rational human wish unfulfilled. A man with a salary of fifty dollars a week can start payments on a Rolls-Royce, the Waldorf-Astoria, or a troupe of trained seals if he so desires.”
—John Dos Passos (18961970)