Astronomy & Celestial Mechanics
the sky, computed
Concept

Refractive index — where it appears

The ratio of the speed of light in vacuum to its speed in a medium. For air it exceeds one by about three parts in ten thousand at sea level, falls with height as the air thins, and varies with wavelength, which is why the atmosphere both bends and disperses starlight.

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

A star drawn out into 3.0 arcseconds of spectrum. Atmospheric refraction relative to its value at 550 nanometres, against wavelength, at four zenith angles. The air's refractive index rises towards the blue, so the blue image of a star sits above the red one and the object is smeared into a short vertical spectrum. At 60 degrees from the zenith the separation across an optical band is 2.96 arcseconds — several times the size of the image at a good site, and comparable to the width of a spectrograph slit. Every curve here is the same curve multiplied by the tangent of the zenith angle, which is why one corrector with an adjustable strength works at every airmass. The practical consequences are three: a slit aligned other than vertically loses blue light or red light depending on where it was centred, a photometric aperture contains a different fraction of the light in each band, and an astrometric position depends on the colour of the star it is measured from.

The atmosphere is a prism as well as a lens

Refraction lifts a star towards the zenith, and everybody corrects for that. It lifts blue light further than red, and the difference is a short vertical spectrum a few arcseconds long — larger than the image, larger than a spectrograph's slit, and quietly present in every ground-based measurement not taken straight overhead.

sky · Refraction Rays that follow the curve of the Earth. Rays of light leaving an observer five metres above a cold surface at elevations between −0.2° and +0.45°, traced through an atmosphere whose lowest 150 metres warm upwards by 0.15 K per metre, drawn as height above the ground against distance along it — so the Earth's curvature has been removed and a ray that follows the curve runs flat. Rays that start downwards or only slightly upwards are bent back by the inversion before they can leave it, glance off the surface, and are guided along the layer in shallow hops: 5 of the 8 traced remain inside it for the whole 300 km. Only the steeper rays escape upwards. Traced backwards, the trapped rays are lines of sight: an observer inside the duct sees objects hundreds of kilometres away that lie far below the geometric horizon, lifted into view.

An atmosphere that bends light round the Earth

A horizontal ray of light curves towards denser air, and in an ordinary atmosphere it curves at a fifth of the rate the ground falls away. Put eleven degrees of warmer air above every hundred metres of cold air over sea ice and the ray curves as fast as the Earth does. It follows the curve, and a Sun five degrees below the horizon rises two weeks early.

sky · Refraction Four atmospheres, one refraction, until the last few degrees. Refraction against zenith angle, traced through the four atmospheres of the first figure. The curves lie on top of each other from the zenith to beyond 80 degrees, and separate only near the horizon, where they reach 37.3 arcminutes (isothermal), 34.0 arcminutes (standard lapse), 50.8 arcminutes (inversion), 28.7 arcminutes (hot ground). Everything above the first few hundred metres of air is different between them, and almost none of it shows.

A bend fixed by the air at the telescope

Starlight crosses fifty kilometres of air whose temperature nobody at the telescope knows, and yet the refraction it suffers can be computed to a hundredth of an arcsecond from a thermometer and a barometer on the dome. The structure of the air overhead cancels out of the first term exactly, and out of the second because of hydrostatics. It returns only within a few degrees of the horizon, and there it takes over completely.

sky · Refraction

Named alongside it

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

Atmospheric refractionTemperature inversionAirmassAtmospheric dispersionAtmospheric ductingFata morganaFlux calibrationHydrostatic equilibriumLapse rateLoomingNovaya zemlya effectParallactic angle

All concepts