Astronomy & Celestial Mechanics
the sky, computed
Concept

Chandler wobble — where it appears

The free wobble of the Earth's rotation axis about its figure axis, a circle a few metres across at the pole with a period of about 433 days. A rigid Earth would take about 305 days; the difference measures the planet's elasticity, and the wobble's survival says something keeps exciting it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A wobble that should have stopped seventy years ago. Left, the path of the Earth's rotation pole across its own crust over 13 years, as the sum of two circular motions: the 433-day Chandler wobble at 150 milliarcseconds and the annual wobble at 90. The spiral is a beat, and its period measured off the drawn path is 6.39 years against the 6.39 the two frequencies require. Right, the same path's radius against time. Two numbers in this figure are the argument. The first is the Chandler period itself: a rigid Earth of dynamical ellipticity 0.0032737 would wobble freely at 305 days, and the observed 433 is 42 per cent longer because the Earth deforms under its own wobble and the oceans move with it — the period is a measurement of the planet's elasticity, made by watching a free motion rather than by forcing anything. The second is the damping: at a quality factor of about 100 the wobble should decay in 38 years, and it has been running for as long as anyone has watched. Something is exciting it continuously, and the excitation is fluctuating pressure at the bottom of the ocean and in the atmosphere. What the figure cannot show is the excitation itself, which is not periodic and is only visible statistically.

A wobble that should have stopped

The Earth's rotation pole wanders across its own crust in a circle a few metres wide. A rigid Earth would do it in 305 days; it takes 433, and the difference is a measurement of the planet's elasticity. At the observed damping it should have died out within a human lifetime, and it has not.

sky · Precession The path of a spin across the sphere of fixed momentum. A body with principal moments 1, 8, 8.6, started about its axis of least inertia with a 3° wobble and an internal energy sink strong enough that the whole motion fits in 80 turns and each circuit of the path can be seen. The disc is the near hemisphere of the sphere of fixed angular momentum, seen from a direction between all three body axes, with the near end of each axis marked. Each thin curve is a contour of kinetic energy on that sphere — a polhode, one of the paths the angular momentum can follow in the body with no dissipation — and the thick curve is the separatrix through the intermediate axis, which divides motions that circle the axis of least inertia from motions that circle the axis of greatest. The coloured path is what the integration did: solid on the near hemisphere, dashed where it passes behind. It starts at the open dot and ends at the filled one.

A spin that left the axis it was given

The first American satellite was spun about its long axis, like a rifle bullet, and soon after launch it was tumbling end over end. Nothing outside it had pushed. A body that cannot change its angular momentum but can lose energy has exactly one place to end up, and a long body spun about its length is as far from that place as a spin can be.

spaceflight · Attitude control

Named alongside it

The objects these essays reach for when they reach for this one.

Angular momentumMoment of inertiaAttitude controlBeat frequencyDynamical ellipticityEarth orientation parametersEulerian periodFree precessionIntermediate axis theoremKinetic energyLength of dayLove number

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