Moons in step

Push a child on a swing at just the right moment each time and a small push goes a long way. Push at random and not much happens.

Moons can push each other like that. Three of Jupiter’s big moons do it all the time.

Io is the closest in and the quickest. In the time it takes Ganymede to go round Jupiter once, Europa goes round twice and Io goes round four times. They have kept this up for a very long time.

Because of that rhythm, the moons pass each other at the same places on every lap, and each gets a little tug in the same direction again and again. The tugs keep their orbits slightly oval. That is the reason Io is squeezed and heated until it erupts.

When orbits keep time like this, it is called a resonance.

Whole numbers. Two moons are in resonance when their periods are in a simple ratio, such as 2 to 1. Then they meet at the same point of their orbits every time, and each meeting pulls the same way as the last. Small pulls that would otherwise cancel out add up instead.

Jupiter’s three.

Moon	Time for one orbit	Orbits per orbit of Ganymede
Io	1.769 days	4.04
Europa	3.551 days	2.01
Ganymede	7.155 days	1

The ratios are a shade off 4, 2 and 1, and that small difference is part of the pattern, not a flaw in it: the meeting points drift slowly round Jupiter, and they drift together. One result is that the three moons can never all line up on the same side of Jupiter at once. When Europa and Ganymede pass each other, Io is always on the far side.

What it does. The repeated tugs stop the orbits from settling into circles. An oval orbit means a tide that rises and falls on every lap, and that means heat. This one rhythm keeps Io’s volcanoes going and helps keep Europa’s ocean liquid.

Saturn has the same arrangement on a smaller scale. Enceladus goes round twice for each orbit of the larger moon Dione, and that helps power its jets: the pairing keeps its orbit slightly oval, and the tides that follow do the heating.

A moon that runs fast and slow. Mimas goes round Saturn twice for each orbit of Tethys. The pull of Tethys does not hold Mimas at a steady pace. It makes Mimas run ahead of a steady clock for decades, then fall behind, swinging by tens of degrees either way over a cycle of about 70 years. Anyone drawing Saturn’s moons has to allow for it, and this site does.

Two moons, one orbit. Janus and Epimetheus share almost the same path round Saturn, 50 km apart, and each takes about 16 hours 40 minutes. The inner one is a touch faster, so about every four years it catches the other up. They never collide and never pass. As they close to about 15,000 km, each one’s gravity lifts the other into the opposite lane: the inner moon moves out and slows, the outer drops in and speeds up, and they draw apart again. Nothing else in the Solar System is known to do this.

Gaps and edges. Resonances shape rings too. A ring particle that goes round twice for every orbit of Mimas gets tugged at the same spot each time and is cleared away. The result is the Cassini Division, the wide dark gap in Saturn’s rings that can be seen through a small telescope.

Beyond moons. The same thing happens between planets. Pluto goes round the Sun twice for every three orbits of Neptune, which is why the two never meet even though their paths cross.