Atmospheric refraction
Encyclopedia
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
or other things like humanelectromagnetic wave from a straight line as it passes through the atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
due to the variation in air density as a function of altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
. Atmospheric refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
near the ground produces mirage
Mirage
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at"...
s and can make distant objects appear to shimmer or ripple, elevated or lowered, stretched or shortened
Looming and similar refraction phenomena
While mirages are the best known atmospheric refraction phenomena, looming and similar refraction phenomena do not produce mirages. Mirages show an extra image or images of the miraged object, while looming, towering, stooping, and sinking do not. No inverted image is present in those phenomena...
with no mirage involved. The term also applies to the refraction of sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
.
Atmospheric refraction causes astronomical object
Astronomical object
Astronomical objects or celestial objects are naturally occurring physical entities, associations or structures that current science has demonstrated to exist in the observable universe. The term astronomical object is sometimes used interchangeably with astronomical body...
s to appear higher in the sky than they are in reality. It affects not only lightrays but all electromagnetic radiation, although in varying degrees (see dispersion in optics
Dispersion (optics)
In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
). For example in visible light, blue is more affected than red. This may cause astronomical objects to be spread out into a spectrum in high-resolution images.
Whenever possible, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
s will schedule their observations around the time of culmination
Culmination
In astronomy, the culmination of a planet, star, constellation, etc. is the altitude reached when the object transits over an observer's meridian....
of an object when it is highest in the sky. Likewise sailors will never shoot a star which is not at least 20° or more above the horizon. If observations close to the horizon cannot be avoided, it is possible to equip a telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...
with control systems to compensate for the shift caused by the refraction. If the dispersion is a problem too, (in case of broadband high-resolution observations) atmospheric refraction correctors can be employed as well (made from pairs of rotating glass prisms). But as the amount of atmospheric refraction is a function of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
as well as humidity
Humidity
Humidity is a term for the amount of water vapor in the air, and can refer to any one of several measurements of humidity. Formally, humid air is not "moist air" but a mixture of water vapor and other constituents of air, and humidity is defined in terms of the water content of this mixture,...
(the amount of water vapour is especially important at mid-infrared wavelengths) the amount of effort needed for a successful compensation can be prohibitive.
Atmospheric refraction becomes more severe when the atmospheric refraction is not homogenous, when there is turbulence in the air for example. This is the cause of twinkling
Scintillation (astronomy)
Scintillation or twinkling are generic terms for rapid variations in apparent brightness or color of a distant luminous object viewed through a medium, most commonly the atmosphere ....
of the star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s and deformation of the shape of the sun at sunset and sunrise.
Values
Atmospheric refraction is zero in the zenithZenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
, less than 1′ (one arcminute) at 45° apparent altitude
Celestial coordinate system
In astronomy, a celestial coordinate system is a coordinate system for mapping positions on the celestial sphere.There are different celestial coordinate systems each using a system of spherical coordinates projected on the celestial sphere, in analogy to the geographic coordinate system used on...
, and still only 5.3′ at 10° altitude; it quickly increases as altitude decreases, reaching 9.9′ at 5° altitude, 18.4′ at 2° altitude, and 35.4′ at the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...
(Allen 1976, 125); all values are for 10 °C and 101.3 kPa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
.
On the horizon, refraction is slightly greater than the apparent diameter of the Sun. Therefore when it appears that the full disc of the sun is just above the horizon, if it weren't for the atmosphere, no part of the sun's disc would be visible. By convention, sunrise
Sunrise
Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Sunrise should not be confused with dawn, which is the point at which the sky begins to lighten, some time before the sun itself appears, ending twilight...
and sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...
refer to times at which the Sun’s upper limb appears on or disappears from the horizon; the standard value for the Sun’s true altitude is −50′: −34′ for the refraction and −16′ for the Sun’s semidiameter
Semidiameter
In geometry, the semidiameter or semi-diameter of a set of points may be one half of its diameter; or, sometimes, one half of its extent along a particular direction.-Special cases:...
(the altitude of a celestial body is normally given for the centre of the body’s disc). In the case of the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
, additional corrections are needed for the Moon’s horizontal parallax and its apparent semidiameter; both vary with the Earth–Moon distance.
Day-to-day variations in the weather will affect the exact times of sunrise and sunset (Schaefer and Liller 1990) as well as moonrise and moonset, and for that reason it generally is not meaningful to give rise and set times to greater precision than the nearest minute (Meeus 1991, 103). More precise calculations can be useful for determining day-to-day changes in rise and set times that would occur with the standard value for refraction (for example Meeus 2002, 315) if it is understood that actual changes may differ because of unpredictable variations in refraction.
Because atmospheric refraction is 34′ on the horizon itself, but only 29′ at 0.5° above it, the setting or rising sun seems to be flattened by about 5′ (about 1/6 of its apparent diameter).
Calculating refraction
Rigorous calculation of refraction requires numerical integration, using a method such as that of Auer and Standish (2000). Bennett (1982) developed a simple empirical formula for calculating refraction from the apparent altitude, using the algorithm of Garfinkel (1967) as the reference; if ha is the apparent altitude in degrees, refraction R in arcminutes is given by
the formula is accurate to within 0.07′ for the altitude range 0°–90° (Meeus 1991, 102). Sæmundsson (1986) developed a formula for determining refraction from true altitude; if h is the true altitude in degrees, refraction R in arcminutes is given by
the formula is consistent with Bennett’s to within 0.1′. Both formulas assume an atmospheric pressure
Atmospheric pressure
Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...
of 101.0 kPa and a temperature of 10 °C; for different pressure P and temperature T, refraction calculated from these formulas is multiplied by
(Meeus 1991, 103). Refraction increases approximately 1% for every 0.9 kPa increase in pressure, and decreases approximately 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases approximately 1% for every 3 °C decrease in temperature, and decreases approximately 1% for every 3 °C increase in temperature.
Random refraction effects
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
in the atmosphere magnifies and de-magnifies star images, making them appear brighter and fainter on a time-scale of milliseconds. The slowest components of these fluctuations are visible to the eye as twinkling (also called “scintillation”).
Turbulence also causes small random motions of the star image, and produces rapid changes in its structure. These effects are not visible to the naked eye, but are easily seen even in small telescopes. They are called “seeing”
Astronomical seeing
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...
by astronomers.