Atmospheric refraction

Astronomical refraction is the change in direction of a falling of the outside on the ground the light beam by refraction of the atmosphere. The cause of the astronomical refraction is the increase of the refractive index of n = 1 in the vacuum of space to about n = 1.00029 at the ground.

The curvature of the beam is controlled convex downward - in the same sense as the Earth's curvature, but much less. The greatest curvature occurs near the ground and makes for very shallow sightings maximum of 10-15% of the earth's curvature (see also terrestrial refraction).

In the sea level ( at the geoid ) and expressed in degrees is the astronomical refraction depending on the temperature

• About 0.6 degrees ( 34 ' to 39 ') for horizontally incident light rays - so when loading or demise of a star
• About 29 ' at a half degrees to the horizon,
• About 5 ' at an elevation angle of 10 °,
• About 1 " (55 " to 65 " ) in an elevation angle of 45 °
• And zero at normal incidence angle - that is in the zenith.
• It follows a complicated formula with several atmospheric parameters and trigonometric functions of the zenith distance (z = 90 ° minus altitude angle). For zenith distances z <70 ° one can write approximately for the refraction r at sea level and at an average air pressure:

Raised as asterisks

The astronomical refraction turn each light beam down - all the stars appear to an observer on Earth therefore higher than would be the case without the Earth's atmosphere. Their value depends mainly on the tangent of the zenith distance as well as temperature and air pressure at the location of the observer. In 5 km altitude it drops to about 50 % of their value from sea level.

The cause of the astronomical refraction, the refraction for Lot experienced by each beam of light when it passes from an optically less dense medium into a denser. It enters into differentially small steps between adjacent air layers ( Snell's law ), and must be integrated over the entire light path.

For this purpose, an appropriate approach of the temperature and pressure, is according to the level required - a so-called normal or standard atmosphere ( at ground level: 15 ° C temperature and 1013.25 hPa air pressure, vertical temperature gradient from -6 to 7 K / km). Approached one can calculate by tackling the atmosphere as 8 km thick plane- parallel plate of air (" height of the homogeneous atmosphere ").

Indeed, the astronomical refraction from this default value will be different, if the layers are not stored normally. If they are slightly inclined - what about each mountain range is the case because of the sunny and shady side - occurs at the zenith instead of the value 0 to the so-called Zenitrefraktion.

Such anomalies may 0.2 " and longer reach and are the reason why sophisticated measurement techniques are required in astronomy and geodesy, where an accuracy of better than 1 " is desired. They are also a key reason why can be carried as astrometric Hipparcos increase the accuracy of the astrometry from 0.01 " to 0.1 " to 0.001 ".

Small temperature changes within the optical system of the telescope, dome of the observatory or camera or sensor or by cooling during the night also cause minor anomalies. To keep them under the measuring accuracy, you have to adjust the instruments before use on the ambient temperature and model the Saalrefraktion the dome or the telescope aperture. This is more possible if the light is reduced, for example by a white coating of the dome or by temperature control in the interior of the telescope or satellite.

Terrestrial and satellite refraction

Passing a beam of light entirely within the atmosphere, it is called " terrestrial refraction ". It occurs in every geodetic measurement on the earth's surface and affects the curvature of the earth by about one-seventh contrary. This factor is called refraction coefficient (usual symbols k) and has already been determined in 1800 by Carl Friedrich Gauss exactly. When Hannover'schen land surveying Gauss received as an average 13% of the earth's curvature (k = 0.13 ).

One can model the terrestrial refraction in a similar way or calculate how the astronomical refraction, but playing local temperature changes in the air a greater role. If the air temperature up not as in the normal atmosphere at 0.6 ° C per 100 meters away, a light beam bends stronger or weaker than normal. Is known of the mirroring effect on hot asphalt, if you - it looks at a shallow angle - such as on the highway. Here is the refraction coefficient of the near-surface air layers even negative ( refraction coefficient to -2.0 ). Extend the measurement beams at a greater height above the terrain can vary k still 0.10 to 0.15. These anomalies ( deviations of the air layers from the spherical shape ) limit the accuracy with which the height can be determined from survey points to a few millimeters to centimeters.

In the measurement to satellites in turn begins or ends of the light beam is not in complete vacuum, and the goal is not "infinitely " far away as a star. This occurs on a parallax effect, which can make up a few percent of the astronomical refraction ( small angle s in the above picture), with satellites in very low orbits (English Low Earth Orbit LEO) but also more.

Effect on distance measurements

Sometimes the term refraction is also used for the atmospheric effects of the distance measurement, where the angle does not change, but the wavelength is essential. Again, for a precise reduction of measured values ​​relatively complicated formulas necessary, the most famous of which is that of the Finnish geodesics Juhani Saastamoinen (1972 ) for modification of an EDM measurement path through the atmosphere:

Z is in the zenith distance, the latitude, the mean height H of the points, P is the average pressure, T is the integral air temperature ( in Kelvin) and the vapor pressure e, and the other parameters B and δ.

Random refraction effects in the atmosphere

Enlarge turbulence in the Earth's atmosphere and reduce the image of a star, so it several times brighter and paler appears in the second. This perceived by the eye blinking is called scintillation.

In addition, image blurring and image motion occurs. All three effects are summarized under the term seeing.