Two bodies go round the same way. The inner one is faster, so now and then it overtakes. Each such lining up is a conjunction.
When the periods stand in a whole-number ratio, conjunctions always happen at the same place on the orbit. If the inner one laps twice for every one of the outer, they line up in exactly the same direction every time.
If the ratio is not a whole number, the meeting place creeps round a little each time until it is scattered over the whole orbit.
That difference becomes the whole difference over long times.
At conjunction the two are closest, so their mutual pull is strongest, and the orbit receives a small push there.
Scattered meeting places give scattered pushes. They add and subtract and, in the long run, cancel.
Meeting always at the same place gives the same push every time. Each is small, and they line up and pile on.
That is resonance: a very slight force reshaping an orbit, on the strength of a ratio of periods alone.
Between Mars and Jupiter lies the asteroid belt. Count the asteroids there by semi-major axis.
Clean holes appear in the count. They sit exactly where the period stands to that of Jupiter as to , to , to , to .
Asteroids there were pushed the same way by Jupiter again and again until their orbits stretched, and in time they came near Mars or Jupiter and were thrown out. The holes are what the sweeping left.
Kirkwood noticed them in . They are not holes in space: they appear only when the count is made by semi-major axis, and looking at those places shows nothing unusual.
Resonance does not only sweep. It also confines.
Pluto stands in a to resonance with Neptune. Its orbit reaches inside that of Neptune and yet they never collide, because the resonance keeps them from ever meeting where the paths approach.
Io, Europa and Ganymede have periods locked as to to . It is called the Laplace resonance, and it is the only threefold lock of its kind. The lock keeps their orbits slightly distorted, and the resulting friction drives the volcanoes of Io.
Sweeping out, or locking in. The same resonance works in opposite directions depending on how the bodies are arranged.
Resonance is not confined to one orbit against another. It arises between the spin of a body and its orbit as well.
The Moon turns exactly once for every lap it makes, and so keeps the same face toward the Earth. It is a to resonance, ground down to that state by tides.
Mercury is different: three turns for every two laps, a to resonance. Its orbit is elongated, so the grinding is strongest only near perihelion, and it stopped short of one to one.
The next article takes up those tides: the force that ground the Moon to a halt and is still slowing the spin of the Earth.