You are riding on a train and looking out the window... Pillars standing along the rails flash by. Buildings located a few tens of meters from the railway track run back more slowly. And very slowly, reluctantly, the houses and groves that you see in the distance, somewhere near the horizon, fall behind the train...
Why does this happen? This question is answered in Fig. 1. While the direction to the telegraph pole, when the observer moves from the first position to the second, changes by a large angle P 1, the direction to a distant tree will change by a much smaller angle P 2. The speed at which the direction of an object changes when the observer moves is less, the further away the object is from the observer. And from this it follows that the magnitude of the angular displacement of an object, which is called parallactic displacement or simply parallax, can characterize the distance to the object, which is widely used in astronomy.
Of course, it is impossible to detect the parallactic displacement of a star while moving along the earth's surface: the stars are too far away, and the parallaxes during such movements are far beyond the possibility of their measurement. But if you try to measure the parallactic displacements of stars when the Earth moves from one point in its orbit to the opposite (that is, repeat observations with an interval of six months, Fig. 2), then you can quite count on success. In any case, the parallaxes of several thousand stars closest to us were measured in this way.
Parallax displacements measured using the Earth's annual orbital motion are called annual parallaxes. The annual parallax of a star is the angle (π) by which the direction to the star will change if an imaginary observer moves away from the center solar system to the Earth's orbit (more precisely, to the average distance of the Earth from the Sun) in a direction perpendicular to the direction of the star. It is easy to understand from Fig. 2 that the annual parallax can also be defined as the angle at which the semimajor axis of the earth’s orbit, located perpendicular to the line of sight, is visible from the star.
The annual parallax is also associated with the basic unit of length adopted in astronomy for measuring distances between stars and galaxies - the parsec (see Distance units). The parallaxes of some nearby stars are given in the table.
For closer celestial bodies - the Sun, Moon, planets, comets and other bodies of the Solar System - parallactic displacement can also be detected when the observer moves in space due to the daily rotation of the Earth (Fig. 3). In this case, parallax is calculated for an imaginary observer moving from the center of the Earth to the equator point at which the star is on the horizon. To determine the distance to the star, calculate the angle at which the equatorial radius of the Earth is visible from the star, perpendicular to the line of sight. This parallax is called daily horizontal equatorial parallax or simply daily parallax. The daily parallax of the Sun at an average distance from the Earth is 8.794″; the average daily parallax of the Moon is 3422.6″, or 57.04′.
As already mentioned, annual parallaxes can be determined by direct measurement of the parallactic displacement (the so-called trigonometric parallaxes) only for the nearest stars located no further than several hundred parsecs.
However, the study of stars for which trigonometric parallaxes have been measured has revealed a statistical relationship between the type of spectrum of a star (its spectral class) and absolute magnitude (see “Spectrum-luminosity” diagram). Having extended this dependence also to stars for which the trigonometric parallax is unknown, they were able to estimate the absolute magnitudes of the stars by the type of spectrum, and then, comparing them with visible magnitudes, astronomers began to estimate the distances to the stars (parallaxes). Parallaxes determined by this method are called spectral parallaxes (see Spectral classification of stars).
There is another method for determining distances (and parallaxes) to stars, as well as star clusters and galaxies - using variable stars of the Cepheid type (this method is described in the article Cepheids); such parallaxes are sometimes called Cepheid parallaxes.
The radius of the Earth turns out to be too small to serve as a basis for measuring the parallactic displacement of stars and for determining the distances to them. Even in the time of Copernicus, it was clear that if the Earth really moves in space, revolving around the Sun, then the apparent positions of the stars in the sky should change. The Earth moves by the amount of the diameter of its orbit in six months. The directions to the star from the two ends of the diameter of this orbit must differ by the amount of parallactic displacement. In other words, the stars should have a noticeable annual parallax. The annual parallax of a star p is the angle at which the semi-major axis of the Earth's orbit (equal to 1 AU) could be seen from the star if it is perpendicular to the line of sight (Fig. 79).
The greater the distance D to the star, the less its parallax (Fig. 79). The parallactic shift in the position of a star in the sky throughout the year occurs in a small ellipse or circle if the star is at the pole of the ecliptic (see Fig. 79).
Rice. 79. Annual parallaxes of stars.
To determine the annual parallax, the direction to the star is measured at different times when the Earth is at different points in its orbit. Parallax is easiest to measure if the observation moments are separated by about six months. During this time, the Earth carries the observer to a distance equal to the diameter of its orbit.
The parallax of stars could not be discovered for a long time, and Copernicus correctly argued that the stars were too far from the Earth for the then existing instruments to detect the parallax displacement of stars with a basis equal to the diameter of the Earth's orbit. (Calculate how many times it is greater than the diameter of the Earth.) Currently, the method of determining the annual parallax is the main one in determining distances to stars, and parallaxes have already been measured for several thousand stars.
For the first time, the annual parallax of a star was reliably measured by the outstanding Russian scientist V. Ya. Struve in 1837. He measured the annual parallax of the star Vega. Almost simultaneously, other countries measured the parallaxes of two more stars. One of them was Centauri. This star of the southern hemisphere of the sky is not visible in the USSR either. It turned out to be the closest star to us with an annual parallax p = 0.75". At this angle, a wire 1 mm thick is visible to the naked eye from a distance of 280 m. It is not surprising that such small angular displacements in stars could not be noticed for so long.
Distance to star
where a is the semimajor axis of the earth's orbit. If we take a as unity and take into account that at small angles
then we get:
astronomical units.
Distance to the nearest star a Centauri D = 206,265": 0.75" = 270,000 a. e. Light travels the distance to Centauri in 4 years, while from the Sun to the Earth it travels only 8 minutes and from the Moon about 1 s.
It is convenient to express distances to stars in parsecs (pc).
Parsec- the distance from which the semi-major axis of the earth's orbit, perpendicular to the line of sight, is visible at an angle of 1". The distance in parsecs is equal to the reciprocal of the annual parallax expressed in arc seconds. For example, the distance to the star a Centauri is 0.75" (3/ 4") or 4/3 pcs.
1 parsec = 3.26 light years = 3 10 13 km.
By measuring the annual parallax, the distance to stars located no further than 100 pc, or 300 light years, can be reliably determined. Distances to more distant stars are currently determined by other methods (see § 24.1).
Parallax(parallactic displacement) in astronomy, the apparent movement of luminaries by celestial sphere, caused by the movement of the observer in space due to the rotation of the Earth (daily rotation), the rotation of the Earth around the Sun (annual rotation), and the movement of the Solar system in the Galaxy (secular rotation). Precisely measured positions of celestial bodies and groups of luminaries make it possible to determine the distances to them.
The daily angle is defined as an angle with its vertex at the center of the celestial body and with its sides directed towards the center of the Earth and to the observation point on the earth's surface. The magnitude of the daily P. depends on the zenith distance of the star and changes with the daily period. The position of a luminary located on the horizon of the observation site is called a horizontal position, and if the observation site lies on the equator, it is called a horizontal equatorial position, constant for luminaries located at a constant distance from the Earth. The horizontal equatorial position of a celestial body p o is related to its geocentric distance r by the relation
where R is the radius of the earth's equator. The distances to the Sun, Moon, and other bodies within the solar system are expressed in horizontal equatorial values. For the average distance of the Sun, the value taken is 8.79", for the average distance of the Moon 57" 2.6". Due to their great distance, the daily position of the stars has practically no effect.
Annual P. - small angle (at the luminary) in right triangle, in which the hypotenuse is the distance from the Sun to the star, and the minor leg is the semimajor axis of the earth's orbit. Annual plots are used to determine distances to stars; These parameters, due to their smallness, can be considered inversely proportional to the distances to the stars (parallax 1" corresponds to a distance of 1 parsec). The position of the nearest star - Proxima Centauri - 0.76". The parameters determined by direct measurements of the visible displacements of stars against the background of much more distant stars are called trigonometric. Trigonometric parameters, due to their smallness, could only be measured for the nearest stars. However, a comparison of the calculated ones with with their help absolute magnitudes These stars with some features of their spectra made it possible to identify dependencies used to estimate distances to other, more distant stars, for which trigonometric determination is impossible. Points calculated in this way are called spectral.
Secular P. - the angular displacement of a star (per year), caused by the movement of the Solar system and related to the direction perpendicular to this movement. In contrast to the daily and annual shifts, which are associated with the periodic displacements of stars on the celestial sphere, the secular shift is determined by the parallactic displacement, which continuously increases with the passage of time. Due to proper motions of stars Secular positions are determined only statistically in relation to a sufficiently large group of stars (it is assumed that peculiar movements of stars in this group are on average zero). Secular distances are used in stellar astronomy, since with their help it is possible to estimate distances that are much greater than those obtained from measurements of annual distances. However, the corresponding distances are correct only on average for the entire group of stars covered by measurements; for individual stars they may differ significantly from actual ones.
Lit.: Parenago P. P., Course of stellar astronomy, , M., 1954.
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encyclopedic Dictionary Brockhaus and Euphron
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Great Soviet Encyclopedia
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Great Soviet Encyclopedia
- - Quadrature in astronomy, one of the characteristic configurations, i.e., mutual positions of the Sun, planets, and Moon on the celestial sphere. See Configurations in Astronomy for more details...
Great Soviet Encyclopedia
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Great Soviet Encyclopedia
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Great Soviet Encyclopedia
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Great Soviet Encyclopedia
"Parallax (in astronomy)" in books
VI. A LITTLE ASTRONOMY
From the book Nicolaus Copernicus author Revzin Grigory IsaakovichVI. A LITTLE ASTRONOMY Astronomical science was born out of practical needs: “The need to calculate the periods of the Nile flood created Egyptian astronomy, and at the same time the dominance of the priestly caste as the leaders of agriculture.” Thus, the first astronomer
II. MY WORKS ON ASTRONOMY
From the book Letters to a Grandson. Book two: Night in Emontaev. author Grebennikov Viktor StepanovichII. MY WORKS ON ASTRONOMY 9. Radiant of the Lyrid meteor shower. Astronomical Circular of the USSR Academy of Sciences, 1946, No. 56, p. Z (about meteors observed through a telescope).10. A simple device for photographing the Moon. Bulletin Vses. Astronomo-Geodesich. Islands of the USSR Academy of Sciences. M.-L., 1948, No. 3(10), p. 36–37 (astrograph from
ASTRONOMY LESSONS
From the book Gods of the New Millennium [with illustrations] by Alford AlanASTRONOMY LESSONS Very few people know that the seven days of the week - from Sunday to Sunday - were originally named according to astronomical principles. This may seem funny, but the names of the days of the week come from Ptolemy (2nd century of our faith) and his erroneous
Chapter Three Astronomy in Astronomy
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Parallax
From the book Self-Teacher on Modern Photography. Independently from Azov to Mastery author Lysov IgorParallax Until humanity invented the SLR camera, all portable cameras suffered from parallax. Even the most excellent ones, which were photographed by great photographers in the recent past. So parallax is not related to the quality itself. From the book Great Soviet Encyclopedia (PA) by the author TSB
Parallax of the Sun
From the book Great Soviet Encyclopedia (PA) by the author TSBAnnual parallax
From the book Great Soviet Encyclopedia (GO) by the author TSBGuide (in astronomy)
From the book Great Soviet Encyclopedia (GI) by the author TSBGuide (in astronomy) A guide in astronomy, an auxiliary visual optical tube mounted on a telescope so that the optical axes of the telescope and the telescope are strictly parallel. G. is used for guiding. In modern large instruments, automatic photoelectric tracking
Daily parallax
From the book Great Soviet Encyclopedia (SU) by the author TSBEquatorial parallax
From the book Great Soviet Encyclopedia (EC) by the author TSBParallax
From the book CSS3 for Web Designers by Siderholm DanParallax Looking back at the Moon example site, you can see how multiple background images are used on the body element to create a composite outer space. Instead of one flat image, four translucent PNGs are used,
The principle of parallax using a simple example.
A method for determining the distance to stars by measuring the angle of apparent displacement (parallax).
Thomas Henderson, Vasily Yakovlevich Struve and Friedrich Bessel were the first to measure distances to stars using the parallax method.
Diagram of the location of stars within a radius of 14 light years from the Sun. Including the Sun, there are 32 known star systems in this region (Inductiveload / wikipedia.org).
The next discovery (30s of the 19th century) is the determination of stellar parallaxes. Scientists have long suspected that stars could be similar to distant suns. However, it was still a hypothesis, and, I would say, until that time it was based on practically nothing. It was important to learn how to directly measure the distance to the stars. People have understood how to do this for a long time. The Earth revolves around the Sun, and if, for example, today you make an accurate sketch of the starry sky (in the 19th century it was still impossible to take a photograph), wait six months and re-sketch the sky, you will notice that some of the stars have shifted relative to other, distant objects. The reason is simple - we are now looking at the stars from the opposite edge of the earth's orbit. There is a displacement of close objects against the background of distant ones. This is exactly the same as if we first look at a finger with one eye and then with the other. We will notice that the finger is displaced against the background of distant objects (or distant objects are displaced relative to the finger, depending on which frame of reference we choose). Tycho Brahe, the best observational astronomer of the pre-telescoping era, tried to measure these parallaxes but did not detect them. In fact, he simply gave a lower limit on the distance to the stars. He said that the stars are at least further away than about a light month (although such a term, of course, could not yet exist). And in the 30s, the development of telescopic observation technology made it possible to more accurately measure distances to stars. And it is not surprising that three people at once different parts The globe made such observations for three different stars.
Thomas Henderson was the first to formally correctly measure the distance to the stars. He observed Alpha Centauri in the Southern Hemisphere. He was lucky, he almost accidentally chose the closest star of those visible to the naked eye in the Southern Hemisphere. But Henderson believed that he lacked the accuracy of his observations, although he got the correct value. The mistakes, in his opinion, were big, and he did not immediately publish his results. Vasily Yakovlevich Struve observed in Europe and chose the bright star of the northern sky - Vega. He was also lucky - he could have chosen, for example, Arcturus, which is much further away. Struve determined the distance to Vega and even published the result (which, as it turned out later, was very close to the truth). However, he clarified it several times, changed it, and therefore many felt that this result could not be trusted, since the author himself was constantly changing it. But Friedrich Bessel acted differently. He chose not a bright star, but one that moves quickly across the sky - 61 Cygni (the name itself says that it is probably not very bright). The stars move a little relative to each other, and, naturally, the closer the stars are to us, the more noticeable this effect is. Just as on a train, roadside pillars flash very quickly outside the window, the forest only slowly moves, and the Sun actually stands still. In 1838 he published a very reliable parallax of the star 61 Cygni and correctly measured the distance. These measurements proved for the first time that the stars were distant suns, and it became clear that the luminosity of all these objects corresponded to the solar value. Determining the parallaxes for the first tens of stars made it possible to construct a three-dimensional map of the solar neighborhood. After all, it has always been very important for a person to build maps. It made the world seem a little more controlled. Here is a map, and the foreign area no longer seems so mysterious, probably dragons don’t live there, but just some kind of dark forest. The advent of measuring distances to stars has indeed made the nearest solar neighborhood, several light years away, somewhat more, well, friendly.
The release material was kindly provided by Sergei Borisovich Popov - astrophysicist, Doctor of Physical and Mathematical Sciences, Professor Russian Academy Sciences, leading researcher at the State Astronomical Institute named after. Sternberg of Moscow state university, winner of several prestigious awards in the field of science and education. We hope that getting acquainted with the issue will be useful for schoolchildren, parents, and teachers - especially now that astronomy is again included in the list of compulsory school subjects (order No. 506 of the Ministry of Education and Science of June 7, 2017).
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Material from Wikipedia - the free encyclopedia
Astronomy
Daily parallax
Daily parallax (geocentric parallax) is the difference in directions to the same body from the Earth’s center of mass (geocentric direction) and from a given point on the Earth’s surface (topocentric direction).
This angle depends on the height of the luminary above the horizon; its maximum value is achieved at zero altitude (when the luminary is observed directly on the horizon). This quantity is called horizontal parallax. The parallax base is equal to the radius of the Earth (about 6400 km).
Due to the rotation of the Earth around its axis, the position of the observer relative to the center of the Earth and, accordingly, the parallax angle change cyclically.
The daily parallax of the planets is quite small (for Mars 24″ during the great opposition), but nevertheless it was the only way to measure absolute distances in the Solar system before the advent of radar: the most convenient for this were the passages of Venus across the disk of the Sun and asteroids coming close to the Earth ( relative distances are easily determined on the basis of Kepler's laws, so that the absolute measurement of any one distance is sufficient to determine everything).
Annual parallax
Annual parallax is a change in direction to an object (for example, a star) associated with the movement of the Earth around the Sun. The magnitude of parallax is equal to the angle at which the semimajor axis of the earth's orbit is visible from the star (perpendicular to the line of sight).
Annual parallaxes are indicators of distances to stars. The distance to an object whose annual parallax is 1 arc second is called a parsec (1 parsec = 3.085678·10 16 m). The closest star to us, Proxima Centauri, has a parallax of 0.7687±0.0003″, therefore, the distance to it is 1.3009±0.00015 pc.
Secular parallax
Secular parallax is usually the change in the apparent position of an object on the celestial sphere as a result of combinations of the proper motions of that object and the Solar System in the galaxy.
Parallax in photography
Viewfinder parallax
Time parallax
Temporal parallax is a distortion of the shape of an object by parallax that occurs when shooting with a camera with a curtain shutter. Since exposure does not occur simultaneously over the entire area of the photosensitive element, but sequentially as the slit moves, when shooting fast moving objects their shape may be distorted. For example, if an object moves in the same direction as the shutter slit, its image will be stretched, and if in the opposite direction, it will be narrowed.
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Literature
- Yashtold-Govorko V. A. Photography and processing. Photography, formulas, terms, recipes. Ed. 4th, abbr. - M.: “Art”, 1977.
Notes
Links
- - a review of measuring distances to astronomical objects.
An excerpt characterizing Parallax
“And if I want...” said Natasha.“Stop talking nonsense,” said the Countess.
- And if I want...
- Natasha, I'm serious...
Natasha didn’t let her finish, she pulled the countess’s big hand towards her and kissed it on top, then on the palm, then turned it again and began kissing her on the bone of the upper joint of the finger, then in between, then again on the bone, saying in a whisper: “January, February , March April May".
- Speak, mother, why are you silent? “Speak,” she said, looking back at the mother, who was looking at her daughter with a tender gaze and, because of this contemplation, seemed to have forgotten everything she wanted to say.
- This is no good, my soul. Not everyone will understand your childhood connection, and seeing him so close to you can harm you in the eyes of other young people who come to us, and, most importantly, it tortures him in vain. He may have found a match for himself, a rich one; and now he's going crazy.
- Does it work? – Natasha repeated.
– I’ll tell you about myself. I had one cousin...
- I know - Kirilla Matveich, but he’s an old man?
– It wasn’t always an old man. But here’s what, Natasha, I’ll talk to Borya. He doesn't need to travel so often...
- Why shouldn’t he, if he wants to?
- Because I know that this will not end in anything.
- Why do you know? No, mom, you don't tell him. What nonsense! - Natasha said in the tone of a person from whom they want to take away his property.
“Well, I won’t get married, so let him go, if he’s having fun and I’m having fun.” – Natasha smiled and looked at her mother.
“Not married, just like that,” she repeated.
- How is this, my friend?
- Yes, yes. Well, it’s very necessary that I don’t get married, but... so.
“Yes, yes,” the countess repeated and, shaking her whole body, laughed with a kind, unexpected old woman’s laugh.
“Stop laughing, stop,” Natasha shouted, “you’re shaking the whole bed.” You look terribly like me, the same laugher... Wait... - She grabbed both hands of the countess, kissed the little finger bone on one - June, and continued to kiss July, August on the other hand. - Mom, is he very much in love? How about your eyes? Were you so in love? And very sweet, very, very sweet! But it’s not quite to my taste - it’s narrow, like a table clock... Don’t you understand?... Narrow, you know, gray, light...
- Why are you lying! - said the countess.
Natasha continued:
- Do you really not understand? Nikolenka would understand... The earless one is blue, dark blue with red, and he is quadrangular.
“You flirt with him too,” said the countess, laughing.
- No, he is a Freemason, I found out. It’s nice, dark blue and red, how can I explain it to you...
“Countess,” the count’s voice was heard from behind the door. -Are you awake? – Natasha jumped up barefoot, grabbed her shoes and ran into her room.
She couldn't sleep for a long time. She kept thinking that no one could understand everything that she understood and that was in her.
"Sonya?" she thought, looking at the sleeping, curled up cat with her huge braid. “No, where should she go!” She is virtuous. She fell in love with Nikolenka and doesn’t want to know anything else. Mom doesn’t understand either. It’s amazing how smart I am and how... she’s sweet,” she continued, speaking to herself in the third person and imagining that some very smart, smartest and nicest man was talking about her... “Everything, everything is in her.” , - continued this man, - she is unusually smart, sweet and then good, unusually good, dexterous, swims, rides excellently, and has a voice! One might say, an amazing voice!” She sang her favorite musical phrase from the Cherubini Opera, threw herself on the bed, laughed with the joyful thought that she was about to fall asleep, shouted to Dunyasha to put out the candle, and before Dunyasha had time to leave the room, she had already passed into another, even happier world of dreams , where everything was as easy and wonderful as in reality, but it was only even better, because it was different.
The next day, the countess, inviting Boris to her place, spoke with him, and from that day he stopped visiting the Rostovs.
On December 31, on New Year's Eve 1810, le reveillon [night supper], there was a ball at Catherine's nobleman's house. The diplomatic corps and the sovereign were supposed to be at the ball.
On Promenade des Anglais the famous house of the nobleman glowed with countless lights of illumination. At the illuminated entrance with a red cloth stood the police, and not only gendarmes, but the police chief at the entrance and dozens of police officers. The carriages drove off, and new ones drove up with red footmen and footmen with feathered hats. Men in uniforms, stars and ribbons came out of the carriages; ladies in satin and ermine carefully stepped down the noisily laid down steps, and hurriedly and silently walked along the cloth of the entrance.
Almost every time a new carriage arrived, there was a murmur in the crowd and hats were taken off.
“Sovereign?... No, minister... prince... envoy... Don’t you see the feathers?...” said from the crowd. One of the crowd, better dressed than the others, seemed to know everyone, and called by name the most noble nobles of that time.
Already one third of the guests had arrived at this ball, and the Rostovs, who were supposed to be at this ball, were still hastily preparing to dress.
There was a lot of talk and preparation for this ball in the Rostov family, a lot of fears that the invitation would not be received, the dress would not be ready, and everything would not work out as needed.
Along with the Rostovs, Marya Ignatievna Peronskaya, a friend and relative of the countess, a thin and yellow maid of honor of the old court, leading the provincial Rostovs in the highest St. Petersburg society, went to the ball.
At 10 o'clock in the evening the Rostovs were supposed to pick up the maid of honor at the Tauride Garden; and yet it was already five minutes to ten, and the young ladies were not yet dressed.
