The task of measuring cosmic distances has confronted astronomers since ancient times. In one of the tasks, we have already discussed modern methods for measuring distances to distant galaxies. But this whole epic with measuring distances began with the objects of the solar system closest to us.

Here we apply the parallax method, which is based on the fact that a particular celestial object is located not too much far away, and its position in the sky depends on where you look at it from. By the way, the stereoscopic perception of our eyes works in a similar way, with the help of which the brain determines the approximate distance to objects: the left and right eyes see the object at different (albeit close) angles. Knowing the angles and distances between the eyes - the so-called base length - one can fairly accurately estimate the distance to the object (Fig. 1).

In geodesy, this method of measuring distances is called triangulation. Well, in astronomy, through parallaxes, you can most accurately calculate the distances to the stars closest to us. In this case, the semiaxis of the Earth's orbit is taken as a base, and the angular position of the star is determined twice with an interval of six months. But how did it all start? How do we know the size of the Earth's orbit?

The astronomical unit (mean distance from the Earth to the Sun) - one of the main standards for distances in space - was adopted after Kepler proposed and justified the heliocentric system in which the Earth revolves around the Sun in a (nearly) circular orbit. The natural decision was to take the radius of this orbit as a unit of measurement.

Now the parameters of the earth's orbit are measured with great accuracy, but then, in the XVIII century, astronomy ran into a dead end. Scientists by that time were able to determine the distances to many planets in the solar system, expressing them in astronomical units. But the very value of the astronomical unit in units familiar to man (for example, kilometers) was not exactly known.

At the same time, the radius of the Earth has already been measured quite accurately. Thus, the value of the base was reliably known, and all that was required was to measure the parallactic angle to any of the objects in the solar system, to which the relative distance in astronomical units was known.

Therefore, astronomers around the world placed great hopes on the passage of Venus across the disk of the Sun in 1761 and 1769. A properly organized observation of this phenomenon would potentially make it possible to measure the parallax of Venus relative to the parallax of the Sun (more precisely, their difference), and, knowing the radius of the Earth (base length), to find out the astronomical unit.

The fact is that from different points of the Earth, the passage of Venus across the disk of the Sun looks different (Fig. 2). If it were possible to measure these trajectories at different points, then the problem would be solved, because then you can either find the angular dimensions of these trajectories directly, or the transit time, and from it find the required one. And so it happened: as a result of observations that took place in different parts of the globe, scientists were able to determine the value of the astronomical unit with a fairly high accuracy.

In particular, Thomas Hornsby obtained a value for the distance from the Earth to the Sun of approximately 93,726,900 English miles (150,838,449 km), which is very close to the truth.

In this problem, it is proposed to make similar measurements of the parallax of Venus.

Task

Two photographs of the transit of Venus are given, taken simultaneously at 22:25:52 UTC on June 5, 2012 (Fig. 4). On the left is a photo taken in Princeton, New Jersey. On the right is a photo taken from the top of the Haleakala volcano on the island of Maui, Hawaii.

Differences in the location of the disk of Venus are associated with parallax. It is known that the distance from the Earth to Venus at the time of the picture was 0.2887 AU. e., the distance to the Sun is 1.0147 AU. e. the angular size of the Sun is 31.57 arc minutes, and the effective radius of the Earth can be taken as 6378.1 km. Venus was almost exactly at its zenith in Hawaii when the photographs were taken. Determine according to these data and photographs, the distance from the Earth to the Sun.

Hint 1

Determining the length of the base in the general case is a rather complicated issue. However, at the time of the picture, the Sun on the island of Maui was almost exactly at the zenith. This can be verified using the Stellarium program by setting the current position in Hawaii and the time at 12 hours 25 minutes on June 5, 2012.

In this case, the length of the base is easily determined (Fig. 5).

Hint 2

Before you measure anything, you need to consider that the photos were taken with a random camera orientation, so you need to correctly match them in order to measure the real displacement of Venus. This can be done using the Sun as a background, or rather, sunspots. True, then the measured parallax will be relative, since the Sun also has its own parallax.

Solution

Having fiddled around, you can compare the two proposed images of Venus on the solar disk in a graphical editor. Since the boundaries of the Sun are quite blurry due to clouds and darkening towards the edge, you can focus on sunspots. It is enough to combine three pairs of spots. Here is the result (photos slightly processed to highlight the edges):

Then we find the centers of two silhouettes of Venus (Fig. 7). Since we are still working with images, we can measure distances in pixels, but then, of course, we will have to convert everything into “normal” units of length. The coordinates of the centers are obtained as follows: C 1 (red center in Fig. 7) - X: 624.5px Y: 317px, C 2 - X: 631.5px Y: 324.5px.

Now we calculate the relative parallax of Venus (also in pixels):

\[ p=\sqrt((624(,)5-631(,)5)^2+(317-324(,)5)^2)=10(,)3\pm0(,)25~\text (px). \]

You could get a different number, but this is normal, because these values ​​\u200b\u200bare relative, and their specific values ​​\u200b\u200bdepend on the size and resolution of the photos.

The diameter of the Sun can also be measured in pixels (Fig. 8), and this will give a translation scale. Our pictures show that Ds\u003d 936 ± 1 px, which corresponds to a value of 31.57 ± 0.005 arc minutes or 1894.2 ± 0.3 arc seconds. Hence 1 px = 2.024±0.002 arcseconds.

We get that the parallax of Venus (relative to the Sun) is equal to

pvs\u003d 10.3 2.024 \u003d 20.9 ± 0.5 arc seconds.

Since we want to find the absolute value of the astronomical unit, we are interested in the absolute parallax of Venus. Pay attention to fig. 9. On it p v And ps are the real parallaxes of Venus and the Sun, and pvs- the parallax of Venus relative to the Sun (what we calculated above). From the figure it is clear that pvs = p v − ps.

Since the angles are small, we will use approximate equalities for small angles: sin φ ≈ tg φ ≈ φ in radians. Then in the notation of Fig. 9: d ⊥ /EV ≈ p v, d ⊥ /ES ≈ ps, Where EV And ES are the distances from the Earth to Venus and the Sun, respectively. From here we find the real parallax:

\[ p_v=\frac(p_(vs))(1-\frac(EV)(ES))=29(,)2\pm 0(,)7~\text(arcseconds). \]

With the help of any mapping service with the function of measuring distances on the Earth's surface (or in some other way), we determine that the shortest distance between two observation points is 7834 km (Fig. 10). This is the length of arc AB in fig. 9. Then α ≈ 1.2282 radians, and you can find the length of the base: d⊥ ≈ 6007.6 km.

Remains the simplest. Knowing the base length and parallax, you can find the distance to Venus: d v = d ⊥ /p v=42±1 million km. And since it is known that the relative distance to Venus in astronomical units is 0.2887 AU. e., we get that 1 a. e. = 147 ± 3 million km. The accuracy of these calculations could be greatly improved with higher resolution images.

Afterword

It is not surprising that the first more or less accurate measurements of the value of the astronomical unit were made precisely with the help of the transit of Venus. The Sun itself was a rather poor candidate for such observations, since it is not a point object, and besides, angle measurements in the 18th century were rather inaccurate. For the same reason, it was quite difficult to measure the parallax of Mars.

Venus itself, which is closer to Earth than Mars in inferior conjunction, is also not very convenient. The fact is that in this position, Venus is located directly between the Earth and the Sun and therefore is a thin strip of a halo. And the Sun itself in this case makes it very difficult to measure the angular position of Venus relative to the background stars. Therefore, the paired passage of Venus across the disk of the Sun in 1761 and 1769 was a truly grandiose event in the world of science at that time.

Parallax and the astronomical unit are associated with another measure of length, often found in astrophysics and cosmology. As noted above, using the parallax method, astronomers today measure the distances to the nearest objects outside the solar system (Fig. 11)

Due to the revolution of the Earth around the Sun, the image of a star against the background of distant stars that are not subject (or much less susceptible) to the parallax effect will shift slightly (by a parallactic angle). By definition, if the parallax of a star is 1 arc second, then the star is at a distance of 1 parsec (abbreviated pc), which is approximately 3.26 light years. In other words, 1 parsec is the distance from which the Earth-Sun system has an angular size of only 1 arc second.

The distance to our nearest star, Proxima Centauri, is 1.301 parsecs. The center of our Galaxy is 8000 parsecs (8 kiloparsecs). The closest large galaxy to us, Andromeda, is 778 kpc.

In astrophysics and cosmology, it is this unit of measurement of distances that is used, and not light years, as many people think. In particular, for example, according to the data of the Planck telescope, the Hubble constant is approximately equal to 68 km/s/Mpc, that is, every megaparsec (million parsecs) the “escape” velocity of galaxies due to the expansion of the Universe increases by 68 km/s.

The measurement of distances in cosmology, as mentioned above, is the most important problem that has been facing astronomers for many decades.

Basically, the parallax method measures distances up to several hundred parsecs. However, there is also a kind of record. It was put by the Hubble telescope, which was able to measure the exact parallax of stars at a distance of up to 5000 parsecs! To do this, the telescope required a resolution of 20 microarcseconds (an observational accumulation technique was used, which improved the measurement accuracy at a limited resolution). It's like reading from the Earth the inscription on a piece of paper held by an astronaut on the moon.

More distant distances are measured in other ways, for example, using standard candles (such as supernovae, RR Lyrae stars, Cepheids, etc.). The problem is that all of these measurements are model specific and therefore not independent. To do this, they must be calibrated using model independent methods such as parallax.

However, these models also have their limits of applicability, beyond which new methods are needed, which, again, need to be calibrated on the old ones. This system of methods, each of which works on more distant objects, but is calibrated on nearby objects using the previous methods, is called the cosmological "ladder" of distances (see also M. Musin's article "A Star Talks to a Star"). And this staircase originates precisely in the method studied in this problem.

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1 kilometer [km] = 6.6845871226706E-09 astronomical unit [a]. e.]

Initial value

Converted value

meter exameter petameter terameter gigameter megameter kilometer hectometer decameter decimeter centimeter millimeter micrometer micron nanometer picometer femtometer attometer megaparsec kiloparsec parsec light year astronomical unit (international) mile (statute) mile (US, geodetic) mile (Roman) 1000 yards furlong furlong (US, geodetic) chain chain (US, geodetic) rope (English rope) genus genus (US, geodetic) perch field (eng. . pole) fathom fathom (US, geodetic) cubit yard foot foot (US, geodetic) link link (US, geodetic) cubit (Brit.) hand span finger nail inch inch (US, geodetic) barleycorn (eng. barleycorn) thousandth of a microinch angstrom atomic unit of length x-unit fermi arpan ration typographic point twip cubit (Swedish) fathom (Swedish) caliber centiinch ken arshin actus (O.R.) vara de tarea vara conuquera vara castellana cubit (Greek) long reed reed long cubit palm "finger" Planck length classical electron radius Bohr radius equatorial radius of the Earth polar radius of the Earth distance from the Earth to the Sun radius of the Sun light nanosecond light microsecond light millisecond light second light hour light day light week Billion light years Distance from Earth to the Moon cables (international) cable (British) cable (US) nautical mile (US) light minute rack unit horizontal pitch cicero pixel line inch (Russian) vershok span foot fathom oblique fathom verst boundary verst

Converter feet and inches to meters and vice versa

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More about length and distance

General information

Length is the largest measurement of the body. In three dimensions, length is usually measured horizontally.

Distance is a measure of how far two bodies are from each other.

Distance and length measurement

Distance and length units

In the SI system, length is measured in meters. Derived quantities such as kilometer (1000 meters) and centimeter (1/100 meter) are also widely used in the metric system. In countries that do not use the metric system, such as the US and the UK, units such as inches, feet, and miles are used.

Distance in physics and biology

In biology and physics, lengths are often measured much less than one millimeter. For this, a special value, a micrometer, has been adopted. One micrometer is equal to 1×10⁻⁶ meters. In biology, micrometers measure the size of microorganisms and cells, and in physics, the length of infrared electromagnetic radiation. A micrometer is also called a micron and sometimes, especially in English literature, is denoted by the Greek letter µ. Other derivatives of the meter are also widely used: nanometers (1×10⁻⁹ meters), picometers (1×10⁻¹² meters), femtometers (1×10⁻¹⁵ meters), and attometers (1×10⁻¹⁸ meters).

Distance in navigation

Shipping uses nautical miles. One nautical mile is equal to 1852 meters. Initially, it was measured as an arc of one minute along the meridian, that is, 1/(60 × 180) of the meridian. This made latitude calculations easier, since 60 nautical miles equaled one degree of latitude. When distance is measured in nautical miles, speed is often measured in nautical knots. One knot is equal to one nautical mile per hour.

distance in astronomy

In astronomy, long distances are measured, so special quantities are adopted to facilitate calculations.

astronomical unit(au, au) is equal to 149,597,870,700 meters. The value of one astronomical unit is a constant, that is, a constant value. It is generally accepted that the Earth is located at a distance of one astronomical unit from the Sun.

Light year equals 10,000,000,000,000 or 10¹³ kilometers. This is the distance that light travels in a vacuum in one Julian year. This value is used in popular science literature more often than in physics and astronomy.

Parsec approximately equal to 30,856,775,814,671,900 meters or approximately 3.09 × 10¹³ kilometers. One parsec is the distance from the Sun to another astronomical object, such as a planet, star, moon, or asteroid, with an angle of one arc second. One arc second is 1/3600 of a degree, or about 4.8481368 mrad in radians. Parsec can be calculated using parallax - the effect of a visible change in the position of the body, depending on the point of observation. During measurements, a segment E1A2 (in the illustration) is laid from the Earth (point E1) to a star or other astronomical object (point A2). Six months later, when the Sun is on the other side of the Earth, a new segment E2A1 is drawn from the new position of the Earth (point E2) to the new position in space of the same astronomical object (point A1). In this case, the Sun will be at the intersection of these two segments, at point S. The length of each of the segments E1S and E2S is equal to one astronomical unit. If we postpone the segment through the point S, perpendicular to E1E2, it will pass through the intersection point of the segments E1A2 and E2A1, I. The distance from the Sun to point I is the SI segment, it is equal to one parsec when the angle between the segments A1I and A2I is two arcseconds.

On the image:

• A1, A2: apparent star position
• E1, E2: Earth position
• S: position of the sun
• I: point of intersection
• IS = 1 parsec
• ∠P or ∠XIA2: parallax angle
• ∠P = 1 arc second

Other units

league- an obsolete unit of length used earlier in many countries. It is still used in some places, such as the Yucatan Peninsula and rural areas of Mexico. This is the distance a person walks in an hour. Marine League - three nautical miles, approximately 5.6 kilometers. Lie - a unit approximately equal to the league. In English, both leagues and leagues are called the same, league. In literature, the league is sometimes found in the title of books, such as "20,000 Leagues Under the Sea" - the famous novel by Jules Verne.

Elbow- an old value equal to the distance from the tip of the middle finger to the elbow. This value was widespread in the ancient world, in the Middle Ages, and until modern times.

Yard used in the British imperial system and is equal to three feet or 0.9144 meters. In some countries, such as Canada, where the metric system is adopted, yards are used to measure the fabric and length of swimming pools and sports fields and grounds, such as golf and football courses.

Meter Definition

The definition of the meter has changed several times. The meter was originally defined as 1/10,000,000 of the distance from the North Pole to the equator. Later, the meter was equal to the length of the platinum-iridium standard. Later, the meter was equated to the wavelength of the orange line of the electromagnetic spectrum of the krypton atom ⁸⁶Kr in vacuum, multiplied by 1,650,763.73. Today, a meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

Computing

In geometry, the distance between two points, A and B, with coordinates A(x₁, y₁) and B(x₂, y₂) is calculated by the formula:

Calculations for converting units in the converter " Length and distance converter' are performed using the functions of unitconversion.org .

Previous definitions

In accordance with the decision of the 10th General Assembly of the IAU in 1976, the astronomical unit was defined as the radius of the circular orbit of a test body in isotropic coordinates, the angular velocity of revolution along which, neglecting all bodies of the solar system except the Sun, would be exactly equal to 0.017 202 098 95 radians on ephemeris days. In the IERS 2003 System of Constants, the astronomical unit was assumed to be equal to 149,597,870.691 km.

Subsequently, refined measurements of the astronomical unit were carried out using the passages of Venus across the solar disk. The approach of the asteroid Eros to the Earth in 1901 and measurements of its parallax made it possible to obtain an even more accurate estimate.

The astronomical unit was also refined using planetary radar. The location of Venus in 1961 established that the astronomical unit is 149,599,300 km. Possible error did not exceed 2000 km. The re-radaring of Venus in 1962 made it possible to reduce this uncertainty and clarify the value of the astronomical unit: it turned out to be 149 598 100 ± 750 km. It turned out that before the 1961 location, the value of a. e. was known with an accuracy of 0.1%.

Long-term measurements of the astronomical unit (in its definition of 1976) recorded its slow increase at a rate of about 15 centimeters per year (which is an order of magnitude higher than the accuracy of modern measurements). One of the reasons may be the loss of mass by the Sun (due to the solar wind), however, the observed effect significantly exceeds the calculated values.

see also

Notes

Wikimedia Foundation. 2010 .

• List of nearby stars
• McJob

See what the "Astronomical unit" is in other dictionaries:

ASTRONOMIC UNIT- ASTRONOMIC UNIT, a unit of length used in astronomy (mainly for measuring distances within the solar system). Equal to the average distance from the Earth to the Sun; 1 astronomical unit = 149.6 million km ... Modern Encyclopedia

astronomical unit- ASTRONOMIC UNIT, a unit of length used in astronomy (mainly for measuring distances within the solar system). Equal to the average distance from the Earth to the Sun; 1 astronomical unit = 149.6 million km. … Illustrated Encyclopedic Dictionary

ASTRONOMIC UNIT- length (AU) unit of distances in astronomy, equal to the average distance of the Earth from the Sun. 1 a. e. = 149.6 million km ... Big Encyclopedic Dictionary

ASTRONOMIC UNIT- (abbreviation AU), the average distance from the Earth to the Sun, used as a basic unit of distance, especially for measurements within the solar system. 1 a.u. equals 149,598,000 km ... Scientific and technical encyclopedic dictionary

ASTRONOMIC UNIT- length (a. e., AE), equal to cf. the distance from the Earth to the Sun, 1 AU. e. = 1.49600 1011 m. Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1983... Physical Encyclopedia

ASTRONOMIC UNIT- the average distance from the Earth to the Sun (or the semi-major axis of the Earth's orbit), equal to 149,500,000 km. Used to measure distances within the solar system. Samoilov K.I. Marine Dictionary. M. L .: State Naval ... ... Marine Dictionary

astronomical unit- (au), a unit of length in astronomy, equal to the average distance from the Earth to the Sun. 1 a. e.; 149.6 million km. * * * ASTRONOMICAL UNIT ASTRONOMICAL UNIT of length (AU), unit of distances in astronomy, equal to the average distance of the Earth from ... ... encyclopedic Dictionary

astronomical unit- astronominis vienetas statusas T sritis Standartizacija ir metrologija apibrėžtis Apibrėžtį žr. priede. priedas(ai) Grafinis formatas atitikmenys: engl. astronomical unit vok. astronomische Einheit, f rus. astronomical unit, f pranc. unité … Penkiakalbis aiskinamasis metrologijos terminų žodynas

astronomical unit- astronominis vienetas statusas T sritis fizika atitikmenys: angl. astronomical unit vok. Astronomische Einheit, f rus. astronomical unit, fpranc. unité astronomique, f … Fizikos terminų žodynas

astronomical unit- (AU unit of distances in astronomy, equal to the average distance of the Earth from the Sun. According to the list of fundamental constants of astronomy recommended in 1964 by the International Astronomical Union for astronomical research, 1 a ... Great Soviet Encyclopedia

The James Clark Maxwell Telescope (JCMT) located on Mauna Kea in the Hawaiian Islands. The comet at that moment was at a distance of 1.07 astronomical units from the sun ( astronomical unit equal to the mean radius of the earth's orbit). According to the calculations of scientists, the comet ejects about 1.5 to 10 to the 25th degree of hydrocyanic acid molecules in ... calculations, the Elenin comet on October 16, 2011 will approach the Earth at a minimum distance of 34.9 million kilometers (0.23 astronomical units).

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Detect a dense cloud of gas approximately 23,000 light-years from Earth. The mass of the cloud is 120 solar, and the diameter is less than 50 thousand astronomical units(one astronomical unit is equal to the average distance from the Earth to the Sun). The temperature of the cloud is about 18 degrees Kelvin. Currently, no thermonuclear processes are taking place inside the cluster, however...

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The presence of dark matter, but also the fulfillment of a number of complex conditions. Some of them contradict modern views on the nature of dark matter. Gradual increase in length astronomical units astronomical unit(a.u.) - one of units length measurements for cosmic distances. A.e. corresponds to the average distance between the centers of mass of the Earth and the Sun, which is approximately equal to the semi-major axis of the Earth's orbit...

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Rotation of the Earth by 0.000017 seconds, moving away from our planet by four centimeters. The average distance from the Earth to the Sun is important astronomical parameter called astronomical units. According to the latest data, one astronomical unit is equal to 149597870.696 kilometers. In 2004, Russian astronomers Grigory Krasinsky and Viktor Brumberg found that this parameter...

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From Earth and orbiting a sun-like yellow dwarf. HD209458b, which is about half the mass of Jupiter, is only 0.05 astronomical units(one astronomical unit corresponds to the distance from the Earth to the Sun), so the surface temperature on the side facing the star reaches thousands of degrees Celsius. Since the planet is always "looking" at the star...

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One piece of evidence is that massive stars form in the same way as their lighter sisters. "Our images show an elongated object measuring approximately 13 by 19 astronomical units(one astronomical unit is equal to the distance from the Earth to the Sun, that is, approximately 149.6 million kilometers), which corresponds to a disk seen at an angle of inclination of 45 degrees.

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Five "reliable" planets range from 13 to 25 Earth masses (for comparison, the mass of Neptune is 17.2 times the mass of the Earth), they are removed from HD 10180 at a distance of 0.06 to 1.4 astronomical units(one astronomical unit corresponds to the distance from the Earth to the Sun). Depending on the distance to the star, the planets make one revolution around it in a period of 6 to 600 days. As for the two "doubtful...

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I tested the LORRI camera on Neptune and its satellite Triton. The photos were taken in June 2010 (however, they were published only now) from a distance of approximately 23.2 astronomical units from Neptune (one astronomical unit equal to the average distance from the Earth to the Sun, that is, 149 million 597 thousand 870 kilometers). In this case, the angle apparatus-Neptune-Sun ...

An astronomical unit is a measure by which anyone can visualize the distance to many objects in the solar system.

An astronomical unit is a value with which each person will be able to visualize at what distance from our planet this or that space object is located.

The reason is simple. In fact, the astronomical unit is the average length of the radius of the earth's orbit, or the distance from the earth to the sun. Agree, it is difficult to imagine the distance from the Earth to the star system, if you are told that it is 1.3. But if you are told that this distance is 270 thousand astronomical units, then you immediately imagine the segment between the Sun and the Earth and mentally increase it by 270 thousand times. This will allow you to visualize this distance more vividly and appreciate its enormous length.

Despite all its clarity, the astronomical unit as a measure of measurement is practically not used in professional astronomy. The fact is that with its help it is convenient to calculate distances only to the objects closest to us in the Universe, for example, the planets of the solar system. If we take very distant objects and try to determine the distance to them in astronomical units, the number will turn out to be so large that it will be inconvenient for them to operate when performing mathematical calculations. To determine the distances to distant space objects in the observable universe, another value is used - parsec, as well as its derivatives.

Discovery history

The prerequisite for the discovery of the astronomical unit was the discovery that the Earth revolves around the Sun, as well as Keplerian celestial mechanics, with the help of which a fairly accurate distance from the Earth to many planets in the solar system, including the Sun, was obtained. Further research by astronomers in the period from the 17th to the 20th century made it possible to correct the first figures and obtain even more accurate data on the location of the above bodies. During this period, the horizontal parallax method, which is still widely used in astronomy and geometry, played a significant role in determining distances.

In 1962, using radar signals, astronomers were able to determine the exact distance from the Earth to the Sun. The average value was taken as the standard, which is equal to 149597870.7 km. This is the astronomical unit. It is this definition that is indicated in the International System of Units SI.

In recent years, scientists have discovered that the astronomical unit is a number that is not a constant. Every year it gets a little bigger. Scientists have recorded that every 7 years the length of the astronomical unit increases by a meter. It turns out that in 100 years the Earth moves away from the Sun by 15 meters. There are several theories that can explain this phenomenon. The most popular of these is that the Sun is gradually losing its mass due to the solar wind.