Astronomy & Celestial Mechanics
the sky, computed
Series

Precession — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The path of the celestial pole over 25,772 years. The circle the Earth's rotation axis traces among the stars, at a radius equal to the obliquity, with the bright stars that fall near it and the years at which each is closest. Polaris is the pole star for a few centuries either side of now, and nothing else on the circle is nearly as close.

    The pole star has a shelf life, and the sky has a slow hand

    The Earth's axis traces a circle among the stars once every 25,772 years. Polaris is at the pole now, was not four thousand years ago, and will not be in two thousand more.

    part 1 · sky
  2. The wobble inside the wobble. Left: the two components of nutation over 40 years, from the four largest terms of the standard series. The long wave is the regression of the Moon's node in 18.613 years, which is where nearly all of it comes from; the ripple on it is the semi-annual solar term at 1.3″ and the semi-monthly lunar one at 0.2″. Right: the loop the pole actually traces over one node cycle, in arcseconds on the sky, with the mean pole at the centre. The loop is 14.89″ by 19.90″ — taller than it is wide, because the longitude term is foreshortened by sin ε while the obliquity term is not, which is the one thing a schematic of this is always drawn getting wrong. Over the same 18.6 years precession itself carries the pole 936″ along its circle, 47 times the loop's own height, so nutation is a wobble on a path and not a path. It is nonetheless 99,480 times the 0.2 mas astrometry of a modern catalogue, which is why a position has to say whether it is referred to the mean pole or the true one.

    The wobble inside the wobble

    Precession and nutation are the same torque. The difference is that the Moon's orbital plane turns once in 18.6 years, so part of the pull oscillates instead of accumulating — and a catalogue position is not a direction until it says which pole it is measured from.

    part 2 · sky
  3. 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.

    part 3 · sky

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