Tricks of a more tolerable twilight

The Twilight of the Gods presents some dismal weather prospects

The Twilight of the Gods presents some dismal weather prospects. Wagner's Gotterdammerung is the Day of Doom, when our Earthly world will be totally annihilated by the forces of evil. And climate change, it seems, will warn us of its coming.

First, according to Scandinavian mythology, there will be a triple winter, during which snow will fall from the four corners of the heavens; the frost will be severe, the wind piercing, and the sun will impart no gladness. Three such winters will pass without being tempered by a single summer, and war and discord will spread over the whole universe.

Happily, our own diurnal twilight is somewhat easier to cope with - the gentle afterglow of a departing day, perhaps, but no Wagnerian Armageddon.

"Twilight" describes the time when the sun is just hidden from view, but light from it is still reflected or scattered by the atmosphere. It begins at sunset which, strictly speaking, occurs the instant the upper edge or "limb" of the solar disc appears to coincide with the horizon. Allowing for the effects of refraction - the bending of the rays of light from the sun by the atmosphere - sunset occurs when the sun's centre is geometrically slightly less than one degree below the horizon.

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The end of twilight, however, is less clear-cut. "Civil twilight", for example, ends when the centre of the solar disc is 6 degrees 1/8 six degrees 3/8 below the horizon, but "nautical twilight" is for many purposes a more practical definition, and ends when the sun's centre is 12 degrees below: by this time, it is for all practical purposes, completely dark, the constellations can be distinguished overhead, and a distant horizon is no longer visible, except by moonlight.

At our latitude, the length of twilight varies throughout the year, depending on the angle that the path of the setting sun makes with the horizon. At a large angle of incidence, such as occurs near the equinoxes, the sun shoots straight down behind the horizon with no nonsense, and nautical twilight lasts only for an hour or so. But at this time of year the path of the setting sun is at a relatively shallow angle to the horizon, and takes considerably longer to reach a position where it is 12 degrees below; for this reason nautical twilight lingers for well over an hour.

In the tropics, however, the path of the sun in the sky is always high, and it descends almost vertically in its journey towards, and down below, the horizon. Twilight, therefore, is always very brief and varies little with the time of year - being always just a little over 20 minutes.