Astronomy & Celestial Mechanics
the sky, computed
Concept

Solar depression — where it appears

How far the Sun has sunk below the horizon, the quantity in which twilight is defined. Civil, nautical and astronomical twilight end at 6, 12 and 18 degrees, and the height of the Earth's shadow overhead grows with its square.

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

The zenith sky after sunset, with light scattered twice. The brightness of the zenith sky at 550 nm in magnitudes per square arcsecond, brighter upward, against the Sun's depression: light scattered once (dashed), light scattered twice (dash-dot), and their sum (solid), in a spherical atmosphere with US Standard densities, Rayleigh scattering and 300 Dobson units of ozone. The dashed horizontal line is the natural night sky, 21.9 magnitudes per square arcsecond. Once-scattered light reaches it at 9.2°; the sum, dominated beyond about seven degrees by light scattered twice, reaches it at 13.2°, and it falls to a hundredth of the night sky — five magnitudes fainter, about the smallest excess a careful measurement of the sky can detect — at 17.5°, where once-scattered light alone would have reached that level at 11.9°. The second order falls more slowly than the first because it can reach the zenith by two grazing hops — sunlight to the lit air low towards the Sun, and that air to the shadowed air overhead — each of which needs only part of the depression a single hop would. Orders beyond the second are left out, so the solid curve is a lower bound on the sky.

The night is late because the light bounces twice

Light scattered once can reach the zenith only while the Earth's shadow over the observer is still low in the air, and by that reckoning the sky should reach the darkness of night about nine degrees after sunset. It does not until eighteen. The difference is light scattered twice — first by the sunlit air hundreds of kilometres towards the sunset, then again by the shadowed air overhead — and adding it to the calculation moves the end of twilight almost exactly to where observers have always put it.

sky · Twilight Where in the sky satellites still shine. The whole sky above the horizon seen from below, zenith at the centre, north at the top and the Sun 20° below the western horizon. Shaded: directions in which a satellite at 550 km is sunlit — 71 per cent of the sky by solid angle. The lit region is a cap pressed against the western horizon and reaching up past the zenith, because satellites seen low in the west are far away and high above the shadow; the eastern sky is dark. Ignoring the penumbra moves its edge by under a degree.

The shadow that also switches off the satellites

After sunset the sky overhead darkens as the Earth's shadow climbs through the air, and the same shadow, climbing on past the top of the atmosphere, decides which satellites still catch sunlight. For a satellite five hundred and fifty kilometres up the zenith stays lit until the Sun is twenty-three degrees down — five degrees past the end of astronomical twilight — and at the latitudes of most large observatories' summers there is no hour of the night when it is not.

sky · Twilight

Named alongside it

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

Astronomical twilightSky brightnessTwilightEarth shadowEarths shadowLatitudeLow earth orbitMultiple scatteringObserving conditionsOptical depthRayleigh scatteringSatellite constellations

All concepts