Laplace resonance

The orbital resonance linking Jupiter’s moons Io, Europa, and Ganymede, whose orbital periods are approximately in a 1:2:4 ratio. Their orbital longitudes obey a three-body relation that helps sustain Io’s tidal heating.

Mean-motion resonance: An orbital configuration in which orbiting bodies’ periods form a ratio of small integers. The Laplace resonance is a three-body example of this broader orbital pattern.
Io: Jupiter’s innermost large moon, known for intense volcanism driven by tidal heating. Its eccentric orbit and extreme volcanism are linked to the resonance.
Pierre-Simon Laplace: A French mathematician and astronomer who made major contributions to celestial mechanics. The resonance bears his name because he analyzed the moons’ orbital relationship.
Io–Europa resonance: The 2:1 mean-motion resonance between Io and Europa, in which Europa’s orbital period is about twice Io’s. This pairwise resonance is part of, but does not alone define, the Laplace relation.
Laplace angle: The combination of orbital longitudes λIo − 3λEuropa + 2λGanymede, which librates in the Laplace resonance. Its libration captures the defining three-body alignment condition.
Europa: Jupiter’s icy moon, whose surface covers a likely global subsurface ocean. It occupies the middle orbit and participates in the three-moon timing relation.
Jupiter: The Solar System’s largest planet, orbited by a diverse system of moons. Its gravity governs the orbits whose periods are locked in the resonance.
Europa–Ganymede resonance: The 2:1 mean-motion resonance between Europa and Ganymede. This neighboring pairwise lock combines with the Io–Europa lock in the three-body pattern.
Orbital longitude: An angular coordinate locating an orbiting body along its orbit relative to a reference direction. The Laplace angle combines the moons’ orbital longitudes.
Ganymede: Jupiter’s largest moon, with an intrinsic magnetic field and a differentiated interior. Its outer orbit completes the resonance’s 1:2:4 period pattern.

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