Astronomy & Celestial Mechanics
the sky, computed
Concept

Precession — where it appears

The slow turning of a spinning or orbiting body's axis around another direction under a steady torque. The Earth's axis precesses once in about 26,000 years under the pull of the Sun and Moon on its equatorial bulge, moving the celestial poles.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A hotter summer that is also a shorter one. Daily-mean sunlight at 65°N through one year beginning at the March equinox, for an orbit of eccentricity 0.0167 and obliquity 23.44°, drawn twice: with perihelion at the June solstice, when the northern summer is closest to the Sun, and with perihelion at the December solstice, half a precession cycle later. The first summer peaks 6.9% higher, and it is also shorter, because the Earth moves fastest near perihelion: days above 275 W m⁻² number 139 against 144. The energy delivered on those days — the shaded area above the line — is 5.055 against 4.989 GJ m⁻², a difference of 1.3%. The second law makes the intensity and the duration trade against each other almost exactly, so a summer measured by how much energy it delivers barely feels precession at all.

A hotter summer that is also a shorter one

When the Earth passes closest to the Sun in northern summer, the northern summer is brighter — and, by Kepler's second law, shorter by exactly the right amount to deliver almost the same energy. Measured by the energy it delivers above a melting threshold rather than by its brightest day, a summer barely feels the precession cycle at all and feels the tilt of the axis several times more strongly.

orbits · Orbital averages Three planes on one sky: the Milky Way crosses the celestial equator at 62.87° and its pole sits at declination 27.13°. The whole sky in equatorial coordinates — right ascension decreasing to the right, declination up — with the celestial equator (grey), the ecliptic (orange) and the galactic equator, b = 0 (blue), each a great circle drawn by rotating its own frame into the equatorial one. The north galactic pole lies at right ascension 192.86° and declination 27.13°, so the galactic plane is inclined at 62.87° to the celestial equator; the zero of galactic longitude, towards the centre, lies at 266.40°, -28.94° in Sagittarius. All three are conventions tied to physical planes — the Earth's equator, its orbit, the Galaxy's disc — and only the first two are defined by measurements that can be repeated to the precision of the coordinates themselves.

A frame fixed before its centre was found

Galactic longitude and latitude look like the Galaxy's own coordinates, and they are a convention agreed in 1958: a pole taken from the radio map of neutral hydrogen, a zero of longitude put on a radio source then catalogued in Sagittarius, an equator drawn through the Sun. The black hole at the centre was found afterwards, three arcminutes away, and nobody moved the origin. The Sun sits twenty parsecs above the disc, so latitude zero is not the Galaxy's plane except far away — and over eighty million years the Sun will swing a hundred parsecs either side of it.

sky · Celestial sphere The summer sunshine at Mars's north pole over the last million years. The sunshine reaching Mars's north pole at the summer solstice, relative to its average, over the last 1,000 thousand years (blue), from a forcing built from the main periods of Mars's recent orbit: the tilt varying by about 3.5 degrees in 120,000 years and 1 degree in 99,000, the eccentricity by 0.03 in 95,000 years and 0.02 in 2.4 million, and the perihelion going round the seasons once in 51,000 years. The part due to the tilt alone is dashed. The sunshine swings by a factor of 2.06 between its extremes: the tilt sets a slow swell with a period of 120,000 years, and the precession, whose strength the eccentricity sets, cuts a faster ripple of 51,000 years into it, strongest when the orbit is most eccentric. These two periods, and their ratio of 2.35, are what a record of the sunshine should carry.

Layers that keep the rhythm and lose the dates

Mars's polar caps are stacks of ice and dust laid down while the planet's tilt and orbit changed the summer sunshine, and the question is whether they can be read as a record of that sunshine. They can — for the rhythm. Even when the ice accumulates faster under weak sunshine than under strong, the cycles of the tilt and the precession survive in the depth of the stack in their correct proportion. What does not survive is the date of any one layer.

sky · Obliquity

Named alongside it

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

EccentricityInsolationMilankovitch cyclesObliquityCaloric half-yearCelestial sphereGalactic coordinatesGalactic planeIce agesKepler second lawLocal standard of restLongitude of perihelion

All concepts