Orbital Resonance - Coincidental 'near' Ratios of Mean Motion

Coincidental 'near' Ratios of Mean Motion

A number of near-integer-ratio relationships between the orbital frequencies of the planets or major moons are sometimes pointed out (see list below). However, these have no dynamical significance because there is no appropriate precession of perihelion or other libration to make the resonance perfect (see the detailed discussion in the section above). Such near resonances are dynamically insignificant even if the mismatch is quite small because (unlike a true resonance), after each cycle the relative position of the bodies shifts. When averaged over astronomically short timescales, their relative position is random, just like bodies that are nowhere near resonance. For example, consider the orbits of Earth and Venus, which arrive at almost the same configuration after 8 Earth orbits and 13 Venus orbits. The actual ratio is 0.61518624, which is only 0.032% away from exactly 8:13. The mismatch after 8 years is only 1.5° of Venus' orbital movement. Still, this is enough that Venus and Earth find themselves in the opposite relative orientation to the original every 120 such cycles, which is 960 years. Therefore, on timescales of thousands of years or more (still tiny by astronomical standards), their relative position is effectively random.

The presence of a near resonance may reflect that a perfect resonance existed in the past, or that the system is evolving towards one in the future.

Some orbital frequency coincidences include:

(Ratio) and Bodies Mismatch after one cycle Randomization time Probability
Planets
(9:23) Venus−Mercury 4.0° 200 y 0.19
(8:13) Earth−Venus 1.5° 1000 y 0.065
(243:395) Earth−Venus 0.8° 50,000 y 0.68
(1:3) Mars−Venus 20.6° 20 y 0.11
(1:2) Mars−Earth 42.9° 8 y 0.24
(1:12) Jupiter−Earth 49.1° 40 y 0.28
(2:5) Saturn–Jupiter 12.8° 800 y 0.13
(1:7) Uranus−Jupiter 31.1° 500 y 0.18
(7:20) Uranus−Saturn 5.7° 20,000 y 0.20
(5:28) Neptune−Saturn 1.9° 80,000 y 0.052
(1:2) Neptune−Uranus 14.0° 2000 y 0.078
Mars system
(1:4) Deimos−Phobos 14.9° 0.04 y 0.083
Major asteroids
(1:1) Pallas − Ceres 1.2° 700 y 0.0066
(7:18) Jupiter − Pallas 4.1° 4000 y 0.15
87 Sylvia system
(17:45) Romulus−Remus 0.7° 40 y 0.067
Jupiter system
(1:6) Io−Metis 0.6° 2 y 0.0031
(3:5) Amalthea−Adrastea 3.9° 0.2 y 0.064
(3:7) Callisto−Ganymede 0.7° 30 y 0.012
Saturn system
(2:3) Enceladus−Mimas 33.2° 0.04 y 0.33
(2:3) Dione−Tethys 36.2° 0.07 y 0.36
(3:5) Rhea−Dione 17.1° 0.4 y 0.26
(2:7) Titan−Rhea 21.0° 0.7 y 0.22
(1:5) Iapetus−Titan 9.2° 4 y 0.051
Major centaurs
(3:4) Uranus−Chariklo 4.5° 10,000 y 0.073
Uranus system
(3:5) Rosalind−Cordelia 0.22° 4 y 0.0037
(1:3) Umbriel−Miranda 24.5° 0.08 y 0.14
(3:5) Umbriel−Ariel 24.2° 0.3 y 0.35
(1:2) Titania−Umbriel 36.3° 0.1 y 0.20
(2:3) Oberon−Titania 33.4° 0.4 y 0.34
Neptune system
(1:20) Triton−Naiad 13.5° 0.2 y 0.075
(1:2) Proteus−Larissa 8.4° 0.07 y 0.047
Pluto system
(1:3) P5−Charon 58.5° 0.2 y 0.33
(1:4) Nix−Charon 39.1° 0.3 y 0.22
(1:5) P4−Charon 9.2° 2 y 0.05
(1:6) Hydra−Charon 6.6° 3 y 0.037
Haumea system
(3:8) Hiʻiaka−Namaka 42.5° 2 y 0.55

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