Atmospheric refraction is the deviation of light rays from a straight line as they pass through the atmosphere due to changes in air density with height. Atmospheric refraction near the Earth's surface creates mirages and can cause distant objects to appear to flicker, quiver, or appear above or below their true position. In addition, the shape of objects may be distorted - they may appear flattened or stretched. Term "refraction" The same applies to the refraction of sound.
Atmospheric refraction is the reason that astronomical objects rise above the horizon somewhat higher than they actually are. Refraction affects not only light rays but also all electromagnetic radiation, although to varying degrees. For example, in visible light, blue is more affected by refraction than red. This can cause astronomical objects to blur into the spectrum in high-resolution images.
If possible, astronomers plan their observations when the celestial body passes the upper culmination point, when it is highest above the horizon. Also, when determining the coordinates of a ship, sailors will never use a luminary whose height is less than 20° above the horizon. If observing a star close to the horizon cannot be avoided, then the telescope can be equipped with control systems to compensate for the displacement caused by the refraction of light in the atmosphere. If dispersion is also an issue (in the case of using a broadband camera for high-resolution observations), then correction for light refraction in the atmosphere (using a pair of rotating glass prisms) can be used. But since the degree of atmospheric refraction depends on temperature and pressure, as well as humidity (the amount of water vapor, which is especially important when observing in the mid-infrared region of the spectrum), the amount of effort required for successful compensation can be prohibitive.
Atmospheric refraction interferes with observations most strongly when it is not uniform, for example, in the presence of turbulence in the air. This is the reason for the twinkling of stars and the deformation of the visible shape of the sun at sunset and sunrise.
Atmospheric refraction values
Atmospheric refraction equal to zero at zenith, less than 1" (one minute of arc) at an apparent altitude of 45° above the horizon, and reaching a value of 5.3" at 10° altitude; refraction increases rapidly with decreasing altitude, reaching 9.9" at 5° altitude, 18.4" at 2° altitude, and 35.4" at the horizon (1976 Allen, 125); all values obtained at 10°C and atmospheric pressure 101.3 kPa.
At the horizon, the value of atmospheric refraction is slightly greater than the apparent diameter of the Sun. Therefore, when the full disk of the sun is visible just above the horizon, it is visible only due to refraction, since if there were no atmosphere, then not a single part of the solar disk would be visible.
According to the accepted convention, the time of sunrise and sunset is referred to as the time when the upper edge of the Sun appears or disappears above the horizon; the standard value for the true height of the Sun is -50"...-34" for refraction and -16" for the half-diameter of the Sun (the height of a celestial body is usually given for the center of its disk). In the case of the Moon, additional corrections are necessary to take into account the horizontal parallax of the Moon and its apparent half-diameter, which varies depending on the distance of the Earth-Moon system.
Daily weather changes affect the exact times of sunrise and sunset of the sun and moon (), and for this reason it makes no sense to give the time of apparent sunset and sunrise of luminaries with an accuracy greater than a minute of arc (this is described in more detail in the book “Astronomical Algorithms”, Jean Meeus , 1991, p. 103). More accurate calculations can be useful for determining day-to-day changes in sunrise and sunset times when using standard refractive index values, since it is clear that actual changes may differ due to unpredictable changes in refractive index.
Due to the fact that atmospheric refraction is 34" at the horizon, and only 29 minutes of arc at an altitude of 0.5° above the horizon, then at sunset or sunrise it appears to be flattened by about 5" (which is about 1/6 of its apparent diameter).
Calculation of atmospheric refraction
Rigorous calculation of refraction requires numerical integration using this method described in the paper by Auer and Standish Astronomical refraction: calculation for all zenith angles, 2000. Bennett (1982), in his article “Calculation of astronomical refraction for use in marine navigation,” derived a simple empirical formula for determining the value of refraction depending on the apparent height of the luminaries, using Garfinkel’s algorithm (1967) as a reference, if h a- this is the apparent height of the luminary in degrees, then refraction R in arc minutes will be equal to
The accuracy of the formula is up to 0.07" for altitudes from 0° to -90° (Meeus 1991, 102). Smardson (1986) derived a formula for determining refraction relative to the true height of the luminaries; if h- this is the true altitude of the luminary in degrees, then the refraction R in arc minutes will be
the formula agrees with the Bennett formula with an accuracy of 0.1". Both formulas will be correct at an atmospheric pressure of 101.0 kPa and a temperature of 10 ° C; for different pressure values R and temperature T the result of calculating refraction made using these formulas should be multiplied by
(according to Meeus 1991, 103). Refraction increases by approximately 1% for every 0.9 kPa increase in pressure and decreases by approximately 1% for every 0.9 kPa decrease in pressure. Similarly, refraction increases by about 1% for every 3°C decrease in temperature and refraction decreases by about 1% for every 3°C increase in temperature.
Graph of refraction versus height (Bennett, 1982)
Random atmospheric effects caused by refraction
Atmospheric turbulence increases and decreases the apparent brightness of stars, making them brighter or fainter in milliseconds. The slow components of these oscillations are visible to us as flickering.
In addition, turbulence causes small random movements in the visible image of the star, and also produces rapid changes in its structure. These effects are not visible to the naked eye, but are easy to see even with a small telescope.
Astronomical refraction (atmospheric refraction) - refraction in the atmosphere of light rays from celestial bodies. Since the density of planetary atmospheres decreases with altitude, the refraction of light occurs in such a way that its convexity of the curved beam is always directed towards the zenith. In this regard, refraction always “raises” the images of celestial bodies above their true position. Another visible consequence of refraction (more precisely, the difference in its values at different heights) is the flattening of the visible disk of the Sun or Moon on the horizon.
Refraction values
The magnitude of refraction strongly depends on the height of the observed object above the horizon and varies from 0 at the zenith to about 35 minutes of arc at the horizon. In addition, there is a dependence on atmospheric pressure and temperature: an increase in refraction value by 1% can be caused by an increase in pressure by 0.01 atm or a decrease in temperature by 3 degrees Celsius. There is also a dependence of the magnitude of refraction on the wavelength of light (atmospheric dispersion): short-wave (blue) light is refracted more strongly than long-wave (red), and at the horizon this difference reaches about 0.5 arc minutes.
The value of refraction at some altitudes (at a temperature of 10 ° C and a pressure of 760 mm Hg):
| visible (distorted by refraction) altitude, degrees |
refraction value, minutes of arc: |
|---|---|
| 90 | 0 |
| 70 | 0,4 |
| 50 | 0,8 |
| 30 | 1,7 |
| 20 | 2,6 |
| 10 | 5,3 |
| 5 | 9,9 |
| 4 | 11,8 |
| 3 | 14,4 |
| 2 | 18,4 |
| 1 | 24,7 |
| 0 | 35,4 |
Thus, the refraction at the horizon is slightly greater than the apparent angular diameter of the Sun. Therefore, at the moment when it touches the horizon with the lower edge of the disk, we see it only thanks to refraction: if it were not there, the solar disk would already be entirely below the horizon. The same applies to the Moon.
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Notes
Literature
Zharov V. E. . . "Astronet" (2002). Retrieved October 18, 2012. .
An excerpt characterizing astronomical refraction
- Well? - said Pierre, looking with surprise at the strange animation of his friend and noticing the look that he cast at Natasha as he stood up.“I need, I need to talk to you,” said Prince Andrei. – You know our women’s gloves (he was talking about those Masonic gloves that were given to a newly elected brother to give to his beloved woman). “I... But no, I’ll talk to you later...” And with a strange sparkle in his eyes and anxiety in his movements, Prince Andrei approached Natasha and sat down next to her. Pierre saw Prince Andrei ask her something, and she flushed and answered him.
But at this time Berg approached Pierre, urgently asking him to take part in the dispute between the general and the colonel about Spanish affairs.
Berg was pleased and happy. The smile of joy did not leave his face. The evening was very good and exactly like other evenings he had seen. Everything was similar. And ladies', delicate conversations, and cards, and a general at cards, raising his voice, and a samovar, and cookies; but one thing was still missing, something that he always saw at the evenings, which he wanted to imitate.
There was a lack of loud conversation between men and an argument about something important and smart. The general started this conversation and Berg attracted Pierre to him.
The next day, Prince Andrei went to the Rostovs for dinner, as Count Ilya Andreich called him, and spent the whole day with them.
Everyone in the house felt for whom Prince Andrei was traveling, and he, without hiding, tried to be with Natasha all day. Not only in Natasha’s frightened, but happy and enthusiastic soul, but throughout the whole house there was a sense of fear of something important that was about to happen. The Countess looked at Prince Andrei with sad and seriously stern eyes when he spoke to Natasha, and timidly and feignedly began some insignificant conversation as soon as he looked back at her. Sonya was afraid to leave Natasha and was afraid to be a hindrance when she was with them. Natasha turned pale with fear of anticipation when she remained alone with him for minutes. Prince Andrei amazed her with his timidity. She felt that he needed to tell her something, but that he could not bring himself to do so.
When Prince Andrey left in the evening, the Countess came up to Natasha and said in a whisper:
- Well?
“Mom, for God’s sake don’t ask me anything now.” “You can’t say that,” Natasha said.
But despite this, that evening Natasha, sometimes excited, sometimes frightened, with fixed eyes, lay for a long time in her mother’s bed. Either she told her how he praised her, then how he said that he would go abroad, then how he asked where they would live this summer, then how he asked her about Boris.
Astronomical refraction is the phenomenon of refraction of light rays in the earth's atmosphere. Due to refraction, the observed (measured) direction to the luminary does not correspond to the actual one, which would occur in the absence of an atmosphere. The angle by which a beam is deflected in the atmosphere is also called refraction.
The structure of the atmosphere is complex and unstable. To obtain a formula that completely determines the value of refraction, it is necessary to select a model of the atmosphere.
In geodetic astronomy, a model of the normal atmosphere is adopted, which is determined by the following provisions:
The atmosphere consists of a number of layers;
The air density d in each layer is constant and decreases with height;
The normal to the boundary of the two media, drawn at the point of incidence of the beam, coincides with the plumb line.
The theory of refraction is based on the laws of refraction of light:
1. The incident ray, the refracted ray and the normal drawn at the point of incidence to the boundary of the two media lie in the same plane.
It follows from this that for a normal atmosphere the refraction of light occurs in the vertical plane, that is, refraction affects only the zenith distance, but not the azimuth of the luminary.
2. Snell's Law. Angle of incidence sine ratio i 1 to the sine of the angle of refraction i 2 for these two media there is a constant value equal to the ratio of the refractive index m 2 to the refractive index m 1:
sin i 1 /sin i 2 = m 2 / m 1.
It follows that if the density of the second layer d 2 is greater than the density of the first layer d 1, then m 2 > m 1, and i 2 < i 1, that is, the beam, getting from a less dense layer to a more dense layer, is deflected towards a plumb line.
Let's consider how astronomical refraction affects the coordinates of the star. Let us assume that the Earth’s surface is a plane at the observation point M
(Fig. 1.20). A ray falling in a vacuum from a star is refracted as it enters the earth's atmosphere. As a result, the observed direction to the star does not correspond to the actual one, which would occur in the absence of an atmosphere. In Fig. 1.20 it can be seen that the topocentric zenith distance ztop is the sum of the measured zenith distance z" and refraction r:
Z top = z" + r.
For a normal atmosphere model, astronomical refraction does not change the horizontal direction, that is, the topocentric azimuth is equal to the measured azimuth
Let us derive a formula for calculating the value of r.
According to Snell's law,
sin z top / sin z" = m/1,
from here sin z top = m sin z", or
sin(z" + r) = m sin z". (1.12)
Let's expand the left side (1.12):
sin z" cos r + sin r cos z" = m sin z".
Since the angle r is small, then
cos r ~ 1, sin r = r"/206265".
sin z" + cos z"r"/206265" = m sin z". (1.13)
Let us divide both sides of expression (1.13) by sin z" and express r":
r" = (m - 1) tg z"·206265".
Thus, astronomical refraction r depends on the zenith distance of the luminary and the refractive index of air. The refractive index m is proportional to the atmospheric density d, which in turn depends on temperature and pressure. Using the Boyle–Mariotte and Gay–Lussac laws, we can write for any state of the atmosphere:
r = 21.67′′B tg z′/(273 + t o C), (1.14)
where B is pressure, mm Hg. Art.,
t – temperature in degrees Celsius,
z" – measured zenith distance.
For a normal atmosphere with t o = 0 o C and B = 760 mm Hg. Art. the refraction value is r o = 60.3" tg z"; at t o = 10 o C and B = 760 mm Hg. the corresponding value r o = 58.1" tg z".
Expressions for rо are called average refraction and are used in approximate astronomical determinations with an error of more than 1".
As the zenith distance increases, the refraction value increases. At the horizon, the refraction value for a normal atmosphere reaches approximately 35¢.
To determine the correction for refraction, special tables are compiled. The Astronomical Yearbook contains several types of tables:
Table of average refraction, where r is calculated for constant temperature t = 10 o C and pressure B = 760 mm Hg. Art., as a function of the measured zenith distance, that is, r o = f(z", t 10, B 760);
Table of corrections to average refraction for temperature and pressure.
Using these tables you can obtain the refraction value with an accuracy of 1".
Refraction values with an accuracy of 0.1" are given in the logarithmic table.
Parallax
Parallax is the change in direction of an object when observing it from different points in space. The Earth participates in two movements - daily and annual, therefore observations of celestial bodies, carried out even from the same point on the earth's surface, are each time made from different points in space.
Diurnal parallax occurs due to the observation of luminaries at different times of the day. The correction for daily parallax is the reduction of observations made on the Earth's surface to the center of the Earth (transition from topocentric to geocentric coordinates).
The annual parallax is due to observations at different times of the year. Correction for annual parallax - bringing observations to the center of the Sun (barycenter of the Solar System), or transition from geocentric coordinates to heliocentric (barycentric).
Refraction astronomical
Refraction astronomical (atmospheric refraction) - refraction in the atmosphere of light rays from celestial bodies. Since the density of planetary atmospheres always decreases with height, the refraction of light occurs in such a way that its convexity of the curved beam is always directed towards the zenith. In this regard, refraction always “raises” the images of celestial bodies above their true position. Another visible consequence of refraction (more precisely, the difference in its values at different heights) is the flattening of the visible disk of the Sun or Moon on the horizon.
The actual position of the Sun below the horizon (yellow disk) and its apparent position (orange) during sunrise/sunset.
Refraction values
The magnitude of refraction strongly depends on the height of the observed object above the horizon and varies from 0 at the zenith to about 35 minutes of arc at the horizon. In addition, there is a dependence on atmospheric pressure and temperature: an increase in refraction value by 1% can be caused by an increase in pressure by 0.01 atm or a decrease in temperature by 3 degrees Celsius. There is also a dependence of the magnitude of refraction on the wavelength of light (atmospheric dispersion): short-wave (blue) light is refracted more strongly than long-wave (red), and at the horizon this difference reaches about 0.5 arc minutes.
The value of refraction at some altitudes (at a temperature of 10°C and a pressure of 760 mm Hg):
Thus, the refraction at the horizon is slightly greater than the apparent angular diameter of the Sun. Therefore, at the moment when it touches the horizon with the lower edge of the disk, we see it only thanks to refraction: if it were not there, the solar disk would already be entirely below the horizon. The same applies to the Moon.
Notes
Literature
Zharov V. E. 6.1. Refraction. Spherical astronomy. "Astronet" (2002). Archived from the original on October 27, 2012. Retrieved October 18, 2012.
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See what “Astronomical refraction” is in other dictionaries:
- (Refraction) the angle between the true and apparent directions to the celestial body, formed as a result of the refraction of a ray of light coming from the celestial body to the earth’s atmosphere. As a result of R.A., the apparent position of the luminaries is elevated above the horizon. The largest... ...Marine Dictionary
Refraction of light in the atmosphere [Late Lat. refractio - refraction, from Lat. refractus - refracted (refringo - breaking, refracting)], an atmospheric optical phenomenon caused by the refraction of light rays in the atmosphere and manifested in the apparent... ...
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I Refraction of light in the atmosphere [Late Lat. refractio refraction, from lat. refractus refracted (refringo I break, refract)], an atmospheric optical phenomenon caused by the refraction of light rays in the atmosphere and manifested in the apparent... ... Great Soviet Encyclopedia- This term has other meanings, see Moon (meanings). Moon ... Wikipedia
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Refraction: general concepts, models of standard atmospheres - refraction for plane-parallel layers, for spherical layers. Refraction tables. The influence of refractive error anomalies on the visible coordinates of luminaries.
General concepts
The influence of refraction is an important problem for ground-based astronomy, where large angles are measured on the celestial sphere, when determining the equatorial coordinates of luminaries, and calculating the moments of their rising and setting.
astronomical (or atmospheric) refraction . Because of this, the observed (apparent) zenith distance z¢ of the luminary is less than its true (i.e., in the absence of an atmosphere) zenith distance z, and the apparent height h¢ is slightly greater than the true height h. Refraction, as it were, lifts the luminary above the horizon.
Difference r = z - z¢ = h¢ - h, is called refraction.
Rice. The phenomenon of refraction in the earth's atmosphere
Refraction only changes the zenith distances z, but does not change the hour angles. If the luminary is at its culmination, then refraction changes only its declination and by the same amount as the zenith distance, since in this case the planes of its hour and vertical circles coincide. In other cases, when these planes intersect at a certain angle, refraction changes both the declination and right ascension of the luminary.
It should be noted that refraction at the zenith takes the value r = 0, and at the horizon it reaches 0.5 - 2 degrees. Due to refraction, the disks of the Sun and Moon near the horizon appear oval, since at the lower edge of the disk the refraction is 6¢ greater than at the top and therefore the vertical diameter of the disk appears shortened in comparison with the horizontal diameter, which is not distorted by refraction.
Empirically, i.e. it was experimentally deduced from observations that riblizhennoe expression to determine general (average) refraction:
r = 60².25 ´V\760´273\(273 0 +t 0) ´ tgz¢,
where: B - atmospheric pressure, t 0 - air temperature.
Then, at a temperature equal to 0 0 and at a pressure of 760 mm Hg, the refraction for visible rays (l = 550 millimicrons) is equal to:
r =60².25 ´ tgz¢ = K´ tgz¢. Here K is the refractive constant under the above conditions.
Using the above formulas, refraction is calculated for a zenith distance of no more than 70 angular degrees with an accuracy of 0.¢¢01. Pulkovo tables (5th edition) allow one to take into account the influence of refraction up to a zenith distance z = 80 angular degrees.
For more accurate calculations, the dependence of refraction is taken into account not only on the height of the object above the horizon, but also on the state of the atmosphere, mainly on its density, which itself is a function, mainly of temperature and pressure. Corrections for refraction are calculated at pressure IN[mmHg] and temperature t° C according to the formula:
To take into account the influence of refraction with high accuracy (0.¢¢01 and higher), the theory of refraction is quite complex and is discussed in special courses (Yatsenko, Nefedeva A.I., etc.). Functionally, the value of refraction depends on many parameters: height (H), latitude (j), also air temperature (t), atmospheric pressure (p), atmospheric pressure (B) along the path of a light beam from the celestial body to the observer and is different for different wavelengths of the electromagnetic spectrum (l) and each zenith distance (z). Modern refraction calculations are performed on a computer.
It should also be noted that refraction, according to the degree of its influence and consideration, is divided into normal (tabular) and abnormal. The accuracy of taking into account normal refraction is determined by the quality of the standard atmosphere model and reaches 0.¢¢01 and higher up to zenith distances of no more than 70 degrees. The choice of observation site is of great importance here - highlands, with good astroclimate and regular terrain, ensuring the absence of inclined layers of air. With differential measurements with a sufficient number of reference stars on CCD frames, the influence of refractive variations such as daily and annual refraction variations can be taken into account.
Abnormal refraction, such as instrumental and pavilion ones are usually taken into account quite well using weather data collection systems. In the ground layer of the atmosphere (up to 50 meters), methods such as placing weather sensors on masts and sounding are used. In all of these cases, it is possible to achieve an accuracy of accounting for refractive anomalies of no worse than 0.²01. It is more difficult to eliminate the influence of refractive fluctuations caused by high-frequency atmospheric turbulence, which have a dominant influence. The power spectrum of the vibrations shows that their amplitude is significant in the range from 15Hz to 0.02Hz. It follows that the optimal time for registering celestial objects should be at least 50 seconds. Empirical formulas derived by E. Hegh (e =± 0.²33(T+0.65) - 0.25,
where T is the registration time) and I.G. Kolchinsky (e =1\Ön(± 0.²33(secz) 0.5, where n is the number of registration moments) show that with such a registration time for a zenith distance (z) equal to zero , the accuracy of the position (e) of the star is about 0.²06-0.²10.
According to other estimates, this type of refraction can be taken into account through measurements within one to two minutes with an accuracy of 0.03 (A. Yatsenko), up to 0.03-0.06 for stars in the range of 9-16 magnitudes (I .Reqiume) or up to 0."05 (E.Hog). Calculations carried out at the US Observatory USNO by Stone and Dun showed that with CCD recording on an automatic meridian telescope (field of view 30" x 30" and exposure time 100 seconds), it is possible to determine the positions of stars differentially with an accuracy of 0.²04. A prospective assessment carried out by American astronomers Colavita, Zacharias and others (see Table 7.1) for wide-angle observations in the visible wavelength range shows that using the two-color technique it is possible to achieve the atmospheric accuracy limit of about 0.²01.
For advanced telescopes with a CCD field of view of the order of 60"x60", using multi-color observation techniques, reflective optics, and finally using differential methods of high-density and accurate reference catalogs at the level of space catalogs such as HC and TC
It is quite possible to achieve an accuracy of the order of several milliseconds (0.²005).
Refraction
The apparent position of the star above the horizon, strictly speaking, differs from that calculated by formula (1.37). The fact is that rays of light from a celestial body, before entering the observer’s eye, pass through the Earth’s atmosphere and are refracted in it, and since the density of the atmosphere increases towards the Earth’s surface, the light ray (Fig. 19) is more and more deflected in the same direction along a curved line, so that the direction OM 1 , according to which the observer ABOUT sees the luminary, turns out to be deflected towards the zenith and does not coincide with the direction OM 2 (parallel VM), by which he would see the luminary in the absence of an atmosphere.
The phenomenon of refraction of light rays as they pass through the earth's atmosphere is called astronomical refraction.
Corner M 1 OM 2 is called refractive angle or refraction r. Corner ZOM 1 is called visible zenith distance of the luminary z", and the angle ZOM 2 - true zenith distance z.
Directly from Fig. 19 follows
z - z"= r or z = z" + r ,
those. the true zenith distance of the luminary is greater than the visible one by the amount of refraction r . Refraction, as it were, lifts the luminary above the horizon.
According to the laws of light refraction, the incident beam and the refracted beam lie in the same plane. Therefore, the ray trajectory MVO and directions OM 2 and OM 1 lie in the same vertical plane. Therefore, refraction does not change the azimuth of the luminary, and, in addition, is equal to zero if the luminary is at the zenith.
If the luminary is at its culmination, then refraction changes only its declination and by the same amount as the zenith distance, since in this case the planes of its hour and vertical circles coincide. In other cases, when these planes intersect at a certain angle, refraction changes both the declination and right ascension of the luminary.
The exact theory of refraction is very complex and is covered in special courses. Refraction depends not only on the height of the star above the horizon, but also on the state of the atmosphere, mainly on its density, which itself is a function, mainly of temperature and pressure. Under pressure IN mm . rt. Art. and temperature t° C approximate refraction value
Using formulas (1.38) and (1.39), refraction is calculated in cases where the apparent zenith distance z" < 70°. При z" > 70° formulas (1.38) and (1.39) give an error of more than 1", increasing with further approach to the horizon to infinity, while the actual value of refraction at the horizon is about 35" . Therefore, for zenith distances z"> The 70° refraction is determined by combining theory with special observations.
Due to refraction, a change in the shape of the disks of the Sun and Moon is observed when they rise or set. The refraction of the lower edges of the disks of these luminaries at the horizon is almost 6" greater than the refraction of the upper edges, and since the horizontal diameters do not change by refraction, the visible disks of the Sun and Moon take on an oval shape.
