Why Do Some Orbits Lock Together? Small Nudges That Keep Arriving in Step
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When two bodies orbit with periods in a simple whole-number ratio, their gravitational tugs arrive at the same point in the orbit repeatedly and accumulate rather than cancelling. That accumulation both stabilises some arrangements and destroys others.
Why a simple ratio matters
Two bodies orbiting the same central object pull on each other continuously, and those pulls are tiny compared with the central gravity. If the orbital periods are unrelated, the pulls occur at different points of each orbit every time round and average out to nothing over a long period. If the periods are in a simple ratio, such as two to one or three to two, the bodies return to the same relative positions repeatedly, so the pull always arrives at the same point in the orbit and always in the same direction. Tiny effects then accumulate over thousands of orbits into changes that are anything but tiny.
Where they are found
The solar system contains a great many, and they are conspicuous:
- •Three of Jupiter's large moons lock in a four to two to one chain
- •Neptune and Pluto are in a three to two arrangement that protects them
- •Gaps in the asteroid belt fall at ratios with Jupiter's period
- •Gaps in Saturn's rings fall at ratios with the periods of nearby moons
- •Mercury rotates three times for every two orbits of the sun
- •Many discovered planetary systems contain chains of locked planets
Why some stabilise and some destroy
The same mechanism produces opposite outcomes depending on the geometry, which is the part that surprises people. In a protective arrangement the accumulated pulls act to correct any drift, so the two bodies are held in step and are prevented from approaching closely, which is why Pluto crosses Neptune's orbit and never comes near it, since the arrangement guarantees that Neptune is always elsewhere when Pluto reaches the crossing. In a destructive arrangement the accumulated pulls stretch the orbit progressively until the body crosses the path of something larger and is ejected or absorbed, which is what cleared the gaps in the asteroid belt and in Saturn's rings. Which occurs depends on where in the orbit the repeated pull falls.
What happens to a day
The same effect applies to rotation as well as to orbits and produces some of the most familiar arrangements in the solar system. A body raised into tides by a nearby larger one loses rotational energy through the friction of those tides until its rotation matches its orbit exactly, a one to one lock, after which it keeps one face permanently towards its companion, which is why the moon shows the same side to Earth and why almost every large moon in the solar system does the same. Mercury settled instead into a three to two lock with its orbit, rotating three times for every two circuits, which its stretched orbit makes more stable than the simpler alternative.
How they form
Bodies are not born in these arrangements and arrive in them through gradual orbital change. A moon whose orbit is being expanded by tidal interaction with its planet drifts outwards slowly, and as it does its period changes continuously until it reaches a ratio with another moon, at which point the accumulated effects can capture it and the two then drift outwards together maintaining the ratio. Planets forming in a disc of gas migrate inwards and are captured the same way, which is thought to explain why so many discovered systems contain locked chains. Capture requires the drift to be slow, since a body passing through a ratio quickly is not caught, which makes the arrangements evidence about how the system evolved.
The takeaway
Periods in a simple whole-number ratio mean the bodies return to the same relative positions repeatedly, so tiny mutual pulls arrive at the same point each time and accumulate instead of averaging away. The same mechanism protects Pluto from ever approaching Neptune and cleared the gaps in the asteroid belt and Saturn's rings. Bodies are captured by slow orbital drift, which makes these arrangements evidence about history.