Magnitude of the telescope. Absolute maximum stellar magnitudes: description, scale and brightness. magnitude turned out to be a very convenient concept

Many novice amateur astronomers ask two main questions, namely: which telescope to choose and what will I see through it.

The most important parameter of a telescope is the diameter of its lens. The larger the diameter of the telescope lens, the fainter the stars we will see and the finer details we will be able to discern on the planets and the Moon, as well as separate closer double stars. The resolution of a telescope is measured in arcseconds and is calculated by the following formula 140/D, where D is the diameter of the telescope lens in mm. And the maximum accessible stellar magnitude of the telescope is calculated by the formula m = 5.5+2.5lgD+2.5lgG, where D is the diameter of the telescope in mm, G is the magnification of the telescope. The diameter of the lens also determines the maximum magnification of the telescope. It is equal to twice the diameter of the telescope lens in millimeters. For example, a telescope with a lens diameter of 150 mm has a maximum useful magnification of 300x. We will proceed from the parameter diameter of the telescope lens.

What size are planets visible through a telescope? With a magnification of 100x, one arcsecond corresponds to 0.12 mm visible from a distance of 25 cm. From here we can calculate the diameter of the planet visible in a telescope with a certain magnification. Dp=Г*0.0012*d, where Dp is the diameter of the planet in mm visible in projection onto a plane with a distance to the plane of 25 cm, G is the magnification of the telescope, d is the diameter of the planet in arc. sec. For example, the diameter of Jupiter is 46 arc. sec. and with a magnification of 100x it will look like a circle drawn on paper with a diameter of 5.5 mm from a distance of 25 cm.

The Orion Nebula is a very bright and impressive object. To the naked eye, the nebula is perceived as a vague glow; through binoculars it is visible as a bright cloud. By the way, the size of this “cloud” is such that its substance would be enough for about a thousand Suns, or more than three hundred million planets Earth.

So, on sale (you can purchase telescopes on the online store website www.4glaza.ru) there are telescopes from 50 mm to 250 mm and more. Also, penetrating power and resolution depend on the design of the telescope, in particular on the presence of central screening by the secondary mirror and its size. In refractor telescopes (lens lens) there is no central shielding, and they give a more contrasting and detailed image, although this applies to long-focus refractor telescopes and apochromats. In short-focus achromatic refractors, chromatic aberration will negate the advantages of the refractor. And such telescopes are available at low and medium magnifications.

The Pleiades star cluster is located in the constellation Taurus. There are about 1000 stars in the Pleiades, but, of course, not all are visible from Earth. The blue halo around the stars is a nebula in which a star cluster is embedded. The nebula is visible only around the brightest stars of the Pleiades.

In the topic of telescopes, only aperture and focal length are measured in centimeters. For everything else there are angular dimensions. For example: Jupiter has an apparent diameter of 40″-60″ depending on its position relative to the Earth.
An ordinary telescope with a 60mm aperture has a resolution of about 2.4″, that is, roughly speaking, Jupiter in such a telescope will have a resolution of 50/2.4 = ~20 “pixels”, but by zooming in we zoom in and out of these 20 pixels. If we zoom in too close (magnification is greater than 2*D, where D is the aperture diameter in mm 60mm*2=120x) then the image will be blurry and dark, as if we were using digital zoom on the camera. If it is too low, then the resolution of our eyes will not be enough to distinguish all 20 pixels (the planet looks like a small pea).

Lunar surface. The craters are clearly visible. The Soviet lunar rover and the American flag are not visible. To see them, you need a giant telescope with a mirror hundreds of meters in diameter - there is nothing like it on Earth yet.

The Andromeda Galaxy (or nebula) is one of the closest galaxies to us. Close is a relative concept: it is about 2.52 million light years. Because of its distance, we see this galaxy as it was 2.5 million years ago. There were no people on Earth then. It is impossible to know what the Andromeda Galaxy actually looks like now.

Jupiter - it can also be seen through a telescope. Like Venus, Saturn, Uranus and Neptune, and many other space objects.

What can we see in telescopes of different diameters:

Refractor 60-70 mm, reflector 70-80 mm.

• Double stars with separation greater than 2” - Albireo, Mizar, etc.
• Faint stars up to 11.5m.
• Sunspots (with aperture filter only).
• Phases of Venus.
• There are craters on the Moon with a diameter of 8 km.
• Polar ice caps and seas on Mars during the Great Confrontation.
• Belts on Jupiter and ideal conditions The Great Red Spot (GRS), four moons of Jupiter.
• The rings of Saturn, the Cassini slit under excellent visibility conditions, the pink belt on the disk of Saturn.
• Uranus and Neptune in the form of stars.
• Large globular (for example M13) and open clusters.
• Almost all Messier catalog objects have no details in them.

Refractor 80-90 mm, reflector 100-120 mm, catadioptric 90-125 mm.

• Double stars with a separation of 1.5″ or more, faint stars up to 12 stars. quantities.
• Sunspot structure, granulation and flare fields (with aperture filter only).
• Phases of Mercury.
• Lunar Craters are about 5 km in size.
• Polar ice caps and seas on Mars during oppositions.
• Several additional belts on Jupiter and the BKP. Shadows from Jupiter's satellites on the planet's disk.
• The Cassini gap in the rings of Saturn and 4-5 satellites.
• Uranus and Neptune as small disks with no details on them.
• Dozens of globular clusters, bright globular clusters will break up into stardust at the edges.
• Dozens of planetary and diffuse nebulae and all the objects of the Messier catalog.
• The brightest objects from the NGC catalog (some details can be discerned in the brightest and largest objects, but galaxies for the most part remain hazy spots without details).

Refractor 100-130 mm, reflector or catadioptric 130-150 mm.

• Double stars with a separation of 1″ or more, faint stars up to 13 stars. quantities.
• Details of the Lunar mountains and craters measuring 3-4 km.
• You can try to see spots in the clouds on Venus with a blue filter.
• Numerous details on Mars during oppositions.
• Details in the belts of Jupiter.
• Cloud belts on Saturn.
• Many faint asteroids and comets.
• Hundreds star clusters, nebulae and galaxies (in the brightest galaxies you can see traces of a spiral structure (M33, M51)).
• A large number of NGC catalog objects (many objects have interesting details).

Refractor 150-180 mm, reflector or catadioptric 175-200 mm.

• Double stars with a separation of less than 1″, faint stars up to 14 stars. quantities.
• Lunar formations measuring 2 km.
• Clouds and dust storms on Mars.
• 6-7 satellites of Saturn, you can try to see the disk of Titan.
• Spokes in the rings of Saturn at their maximum opening.
• Galilean satellites in the form of small disks.
• The detail of an image with such apertures is determined not by the capabilities of the optics, but by the state of the atmosphere.
• Some globular clusters resolve into stars almost to the very center.
• Details of the structure of many nebulae and galaxies are visible when observed from city illumination.

Refractor 200 mm or more, reflector or catadioptric 250 mm or more.

• Double stars with separation up to 0.5″ under ideal conditions, stars up to 15 stars. magnitude and weaker.
• Lunar formations less than 1.5 km in size.
• Small clouds and small structures on Mars, in rare cases Phobos and Deimos.
• A large amount of detail in the atmosphere of Jupiter.
• Encke division in the rings of Saturn, disk of Titan.
• Neptune's moon Triton.
• Pluto as a faint star.
• The maximum detail of the images is determined by the state of the atmosphere.
• Thousands of galaxies, star clusters and nebulae.
• Virtually all of the objects in the NGC catalog, many of which show details not visible in smaller telescopes.
• The brightest nebulae exhibit subtle colors.

As you can see, even modest astronomical instrument will allow you to enjoy the many beauties of the night sky. So don’t immediately go after a large instrument; start with a small telescope. And don’t be afraid that it will soon exhaust its resource. Believe me, he will delight you with new objects and new details on them for many years. You will become an increasingly experienced observer, your eyes will learn to sense fainter objects, and you yourself will learn to apply various techniques from the observer’s arsenal, use special filters, etc.

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Many novice amateur astronomers ask themselves two main questions, namely: which telescope to choose and what will I see through it. The most important parameter of a telescope is the diameter of its lens. The larger the diameter of the telescope lens, the fainter the stars we will see and the finer details we will be able to discern on the planets and...

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Each of these stars has a certain magnitude that allows them to be seen

Stellar magnitude is a numerical dimensionless quantity that characterizes the brightness of a star or other cosmic body in relation to the visible area. In other words, this value reflects the amount electromagnetic waves, body, which are registered by the observer. Therefore, this value depends on the characteristics of the observed object and the distance from the observer to it. The term covers only the visible, infrared and ultraviolet spectra of electromagnetic radiation.

The term “gloss” is also used to refer to point light sources, and “brightness” to extended ones.

An ancient Greek scientist who lived in Turkey in the 2nd century BC. e., is considered one of the most influential astronomers of antiquity. He compiled a volumetric one, the first in Europe, describing the locations of more than a thousand celestial bodies. Hipparchus also introduced such a characteristic as stellar magnitude. Observing the stars with the naked eye, the astronomer decided to divide them by brightness into six magnitudes, where the first magnitude is the brightest object, and the sixth is the dimmest.

In the 19th century, British astronomer Norman Pogson improved the scale for measuring stellar magnitudes. He expanded the range of its values ​​and introduced a logarithmic dependence. That is, with an increase in magnitude by one, the brightness of the object decreases by 2.512 times. Then a star of 1st magnitude (1 m) is a hundred times brighter than a star of 6th magnitude (6 m).

Magnitude standard

The standard of a celestial body with zero magnitude was initially taken to be the brightness of the brightest point in . Somewhat later it was stated more precise definition an object of zero magnitude - its illumination should be 2.54·10 −6 lux, and the luminous flux in the visible range should be 10 6 quanta/(cm²·s).

Apparent magnitude

The characteristic described above, which was defined by Hipparchus of Nicea, subsequently began to be called “visible” or “visual”. This means that it can be observed both with the help of human eyes in the visible range, and using various instruments like a telescope, including ultraviolet and infrared ranges. The magnitude of the constellation is 2 m. However, we know that Vega with zero magnitude (0 m) is not the brightest star in the sky (fifth in brightness, third for observers from the CIS). Therefore, brighter stars may have a negative magnitude, for example (-1.5 m). It is also known today that among the celestial bodies there can be not only stars, but also bodies that reflect the light of stars - planets, comets or asteroids. The total magnitude is −12.7 m.

Absolute magnitude and luminosity

In order to be able to compare the true brightness of cosmic bodies, such a characteristic as absolute stellar magnitude was developed. According to it, the value of the apparent magnitude of an object is calculated if this object were located 10 (32.62) from the Earth. In this case, there is no dependence on the distance to the observer when comparing different stars.

Absolute magnitude for space objects c uses a different distance from the body to the observer. Namely, 1 astronomical unit, while, in theory, the observer should be at the center of the Sun.

A more modern and useful quantity in astronomy has become “luminosity”. This characteristic determines the total radiation emitted by a cosmic body over a certain period of time. The absolute magnitude is used to calculate it.

Spectral dependence

As stated earlier, magnitude can be measured for various types electromagnetic radiation, and therefore has different meanings for each spectrum range. To obtain a picture of any space object Astronomers can use , which are more sensitive to the high-frequency portion of visible light, and the stars appear blue in the image. This magnitude is called “photographic”, m Pv. To obtain a value close to visual (“photovisual”, m P), the photographic plate is coated with a special orthochromatic emulsion and a yellow filter is used.

Scientists have compiled a so-called photometric system of ranges, thanks to which it is possible to determine the main characteristics of cosmic bodies, such as: surface temperature, degree of light reflection (albedo, not for stars), degree of light absorption and others. To do this, photographs are taken of the luminary in different spectra of electromagnetic radiation and subsequent comparison of the results. The most popular filters for photography are ultraviolet, blue (photographic magnitude) and yellow (close to the photovisual range).

A photograph with captured energies of all ranges of electromagnetic waves determines the so-called bolometric magnitude (mb). With its help, knowing the distance and degree of interstellar absorption, astronomers calculate the luminosity of a cosmic body.

Magnitudes of some objects

• Sun = −26.7 m
• Full Moon = −12.7 m
• Iridium flare = −9.5 m. Iridium is a system of 66 satellites that orbit the Earth and serve to transmit voice and other data. Periodically, the surface of each of the three main apparatuses glows sunlight towards the Earth, creating the brightest smooth flash in the sky for up to 10 seconds.

Or using one or another optical instrument. The concept is used in observational (including amateur) astronomy to assess the state of the sky and observation conditions, and is also one of the characteristics of telescopes and other optical astronomical instruments.

In observational astronomy

On average, under ideal observation conditions (clear sky, no light pollution), objects with a magnitude of up to 6 m are accessible to the naked eye (stellar magnitudes more than the observed object less bright). However, factors such as astroclimate, artificial (urban) or natural (for example, from the Moon in its large phase) illumination, suboptimal atmospheric conditions, high humidity make the observation of faint luminaries impossible; Therefore, in reality, the number of observed stars and other astronomical phenomena (such as meteors) almost always turns out to be less than theoretically expected.

The limiting magnitude characterizes how faint celestial objects are visible during a given observation. The higher this indicator, the weaker objects can be observed. The limiting stellar magnitude is thus a relatively simple “integral” indicator characterizing the conditions for observing starry sky, in connection with which it is often indicated in astronomical reports (for example, an indication "Lm~4.5" means that during the observation only objects with a magnitude of about 4.5 or brighter were visible). It should be noted, however, that the maximum magnitude in in this case is a subjective indicator, since it also depends on the visual acuity of the observer, his experience, etc.

An approximate estimate of the maximum magnitude during amateur observations can be made by noting the faintest visible stars and clarifying their magnitude using reference sources. For a more accurate assessment, the number of visible stars within standardized areas of the sky is counted (their boundaries are the lines between noticeable stars): the number of stars seen is matched with the corresponding limiting stellar magnitude. Determining the maximum stellar magnitude as accurately as possible during visual observations is extremely desirable, for example, when observing meteors for subsequent analysis of the activity of meteor showers.

Other than that equal conditions the maximum stellar magnitude increases (the number of observed objects becomes larger) when observing far from urban illumination, when the observer's altitude above sea level increases, and also when observing in dry weather or in a dry climate.

Characteristics of observational instruments

The use of telescopes makes it possible to observe objects less bright than visible ones naked eye. The maximum stellar magnitude of objects, observable into a telescope, is often designated as penetrating power and is its important characteristic. It is usually given in technical specifications or can be calculated using a number of formulas.

Sources

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Links

• (Russian) . imo.net. Retrieved January 2, 2015.
• (English) . cruxis.com. Retrieved January 2, 2015.

An excerpt characterizing the Limiting Magnitude

Anna Pavlovna had an evening on August 26, the very day of the Battle of Borodino, the flower of which was to be the reading of the letter from the Eminence, written when sending the image of the venerable saint Sergius to the sovereign. This letter was revered as an example of patriotic spiritual eloquence. It was to be read by Prince Vasily himself, famous for his art of reading. (He also read for the Empress.) The art of reading was considered to consist in pouring out words loudly, melodiously, between a desperate howl and a gentle murmur, completely regardless of their meaning, so that, quite by chance, a howl would fall on one word, and a murmur on others. This reading, like all Anna Pavlovna’s evenings, had political significance. At this evening there were to be several important persons who had to be shamed for their trips to the French theater and encouraged into a patriotic mood. Quite a lot of people had already gathered, but Anna Pavlovna had not yet seen all the people she needed in the living room, and therefore, without starting to read yet, she started general conversations.
The news of the day that day in St. Petersburg was the illness of Countess Bezukhova. A few days ago the Countess unexpectedly fell ill, missed several meetings of which she was an adornment, and it was heard that she did not see anyone and that instead of the famous St. Petersburg doctors who usually treated her, she entrusted herself to some Italian doctor who treated her with some new and in an extraordinary way.
Everyone knew very well that the illness of the lovely countess was due to the inconvenience of marrying two husbands at once and that the Italian’s treatment consisted in eliminating this inconvenience; but in the presence of Anna Pavlovna, not only did no one dare to think about it, but it was as if no one knew it.
- On dit que la pauvre comtesse est tres mal. Le medecin dit que c"est l"angine pectorale. [They say that the poor countess is very bad. The doctor said it was a chest disease.]
- L"angine? Oh, c"est une maladie terrible! [Chest disease? Oh, this is a terrible disease!]
- On dit que les rivaux se sont reconcilies grace a l "angine... [They say that the rivals were reconciled thanks to this illness.]
The word angine was repeated with great pleasure.
– Le vieux comte est touchant a ce qu"on dit. Il a pleure comme un enfant quand le medecin lui a dit que le cas etait dangereux. [The old count is very touching, they say. He cried like a child when the doctor said that dangerous case.]
- Oh, ce serait une perte terrible. C "est une femme ravissante. [Oh, that would be a great loss. Such a lovely woman.]
“Vous parlez de la pauvre comtesse,” Anna Pavlovna said, approaching. “J"ai envoye savoir de ses nouvelles. On m"a dit qu"elle allait un peu mieux. Oh, sans doute, c"est la plus charmante femme du monde," Anna Pavlovna said with a smile at her enthusiasm. – Nous appartenons a des camps differents, mais cela ne m"empeche pas de l"estimer, comme elle le merite. Elle est bien malheureuse, [You are talking about the poor countess... I sent to find out about her health. They told me she was feeling a little better. Oh, without a doubt, this is the loveliest woman in the world. We belong to different camps, but this does not prevent me from respecting her according to her merits. She is so unhappy.] – added Anna Pavlovna.
Believing that with these words Anna Pavlovna was slightly lifting the veil of secrecy over the countess’s illness, one careless young man allowed himself to express surprise that famous doctors were not called in, but that the countess was being treated by a charlatan who could give dangerous remedies.
“Vos informations peuvent etre meilleures que les miennes,” Anna Pavlovna suddenly attacked the inexperienced man with venom. young man. – Mais je sais de bonne source que ce medecin est un homme tres savant et tres habile. C"est le medecin intime de la Reine d"Espagne. [Your news may be more accurate than mine... but I know from good sources that this doctor is a very learned and skillful person. This is the life physician of the Queen of Spain.] - And thus destroying the young man, Anna Pavlovna turned to Bilibin, who, in another circle, picked up the skin and, apparently, about to loosen it to say un mot, spoke about the Austrians.

Even people far from astronomy know that stars have different brightnesses. The brightest stars are easily visible in the overexposed city sky, while the faintest stars are barely visible under ideal viewing conditions.

To characterize the brightness of stars and other celestial bodies (for example, planets, meteors, the Sun and the Moon), scientists have developed a scale of stellar magnitudes.

Apparent magnitude(m; often called simply “magnitude”) indicates the radiation flux near the observer, i.e., the observed brightness of the celestial source, which depends not only on the actual radiation power of the object, but also on the distance to it.

This is a dimensionless astronomical quantity that characterizes the illumination created by a celestial object near the observer.

Illumination– light magnitude, equal to the ratio luminous flux incident on a small area of ​​the surface, to its area.
The unit of illumination in the International System of Units (SI) is lux (1 lux = 1 lumen per square meter), in GHS (centimeter-gram-second) – phot (one phot is equal to 10,000 lux).

Illumination is directly proportional to the luminous intensity of the light source. As the source moves away from the illuminated surface, its illumination decreases in inverse proportion to the square of the distance (inverse square law).

Subjectively visible stellar magnitude is perceived as brightness (for point sources) or brightness (for extended sources).

In this case, the brightness of one source is indicated by comparing it with the brightness of another, taken as a standard. Such standards usually serve as specially selected fixed stars.

Magnitude was first introduced as an indicator of the visible brightness of stars in the optical range, but later extended to other radiation ranges: infrared, ultraviolet.

Thus, the apparent magnitude m or brightness is a measure of the illumination E created by the source on the surface perpendicular to its rays at the observation location.

Historically, it all began more than 2000 years ago, when the ancient Greek astronomer and mathematician Hipparchus(2nd century BC) divided the stars visible to the eye into 6 magnitudes.

Hipparchus assigned the brightest stars the first magnitude, and the dimmest, barely visible to the eye, the sixth, the rest were evenly distributed among intermediate magnitudes. Moreover, Hipparchus made the division into stellar magnitudes so that stars of the 1st magnitude seemed as much brighter than stars of the 2nd magnitude as they seemed brighter than stars of the 3rd magnitude, etc. That is, from gradation to gradation the brightness of the stars changed by one and the same size.

As it turned out later, the connection between such a scale and real physical quantities logarithmic, since the change in brightness in same number times is perceived by the eye as a change of the same amount – empirical psychophysiological law of Weber–Fechner, according to which the intensity of sensation is directly proportional to the logarithm of the intensity of the stimulus.

This is due to the peculiarities of human perception, for example, if 1, 2, 4, 8, 16 identical light bulbs are lit sequentially in a chandelier, then it seems to us that the illumination in the room is constantly increasing by the same amount. That is, the number of light bulbs turned on should increase by the same number of times (in the example, twice) so that it seems to us that the increase in brightness is constant.

The logarithmic dependence of the strength of sensation E on the physical intensity of the stimulus P is expressed by the formula:

E = k log P + a, (1)

where k and a are certain constants determined by a given sensory system.

In the middle of the 19th century. English astronomer Norman Pogson formalized the magnitude scale, which took into account the psychophysiological law of vision.

Based on real results observations, he postulated that

A STAR OF THE FIRST MAGNITUDE IS EXACTLY 100 TIMES BRIGHTER THAN A STAR OF THE SIXTH MAGNITUDE.

In this case, in accordance with expression (1), the apparent magnitude is determined by the equality:

m = -2.5 log E + a, (2)

2.5 – Pogson coefficient, minus sign – a tribute to historical tradition (brighter stars have a lower, including negative, magnitude);
a is the zero point of the magnitude scale, established by international agreement related to the choice of the base point of the measurement scale.

If E 1 and E 2 correspond to the magnitudes m 1 and m 2, then from (2) it follows that:

E 2 /E 1 = 10 0.4(m 1 - m 2) (3)

A decrease in magnitude by one m1 - m2 = 1 leads to an increase in illumination E by approximately 2.512 times. When m 1 - m 2 = 5, which corresponds to the range from the 1st to the 6th magnitude, the change in illumination will be E 2 / E 1 = 100.

Pogson's formula in its classic look establishes a relationship between visible stellar magnitudes:

m 2 - m 1 = -2.5 (logE 2 - logE 1) (4)

This formula allows you to determine the difference in stellar magnitudes, but not the magnitudes themselves.

To use it to build absolute scale, you need to set null point– brightness, which corresponds to zero magnitude (0 m). At first, the brilliance of Vega was taken as 0 m. Then the null point was redefined, but for visual observations Vega can still serve as a standard of zero apparent magnitude (according to modern system, in the V band of the UBV system, its brightness is +0.03 m, which is indistinguishable from zero by eye).

Usually, the zero point of the magnitude scale is taken conditionally based on a set of stars, careful photometry of which has been carried out using various methods.

Also, a well-defined illumination is taken as 0 m, equal to the energy value E = 2.48 * 10 -8 W/m². Actually, it is the illumination that astronomers determine during observations, and only then it is specially converted into stellar magnitudes.

They do this not only because “it’s more common,” but also because magnitude turned out to be a very convenient concept.

magnitude turned out to be a very convenient concept

Measuring illumination in watts per square meter is extremely cumbersome: for the Sun the value is large, and for faint telescopic stars it is very small. At the same time, it is much easier to operate with stellar magnitudes, since the logarithmic scale is extremely convenient for displaying very large ranges of magnitude values.

The Pogson formalization subsequently became the standard method for estimating stellar magnitude.

True, the modern scale is no longer limited to six magnitudes or only visible light. Very bright objects can have a negative magnitude. For example, Sirius brightest star celestial sphere, has a magnitude of minus 1.47 m. The modern scale also allows us to obtain values ​​for the Moon and the Sun: the full moon has a magnitude of -12.6 m, and the Sun -26.8 m. The Hubble orbital telescope can observe objects whose brightness is up to approximately 31.5 m.

Magnitude scale
(the scale is reversed: lower values ​​correspond to brighter objects)

Apparent magnitudes of some celestial bodies

Sun: -26.73
Moon (full moon): -12.74
Venus (at maximum brightness): -4.67
Jupiter (at maximum brightness): -2.91
Sirius: -1.44
Vega: 0.03
Faintest stars visible to the naked eye: about 6.0
Sun from 100 light years away: 7.30
Proxima Centauri: 11.05
Brightest quasar: 12.9
The faintest objects photographed by the Hubble telescope: 31.5

A celestial object (corresponding to the faintest visible objects), accessible to observation with the naked eye or using one or another optical instrument. The concept is used in observational (including amateur) astronomy to assess the state of the sky and observation conditions, and is also one of the characteristics of telescopes and other optical astronomical instruments.

In observational astronomy

On average, under ideal observation conditions (clear sky, no light illumination), objects with magnitudes up to 6 m are accessible to the naked eye (magnitudes more than the observed object less bright). However, factors such as astroclimate, artificial (urban) or natural (for example, from the Moon in its large phase) illumination, suboptimal atmospheric conditions, high humidity make the observation of faint luminaries impossible; Therefore, in reality, the number of observed stars and other astronomical phenomena (such as meteors) almost always turns out to be less than theoretically expected.

The limiting magnitude characterizes how faint celestial objects are visible during a given observation. The higher this indicator, the weaker objects can be observed. The limiting stellar magnitude is thus a relatively simple “integral” indicator characterizing the conditions for observing the starry sky, and therefore it is often indicated in astronomical reports (for example, an indication "Lm~4.5" means that during the observation only objects with a magnitude of about 4.5 or brighter were visible). It should, however, be noted that the maximum stellar magnitude in this case is a subjective indicator, since it also depends on the visual acuity of the observer, his experience, etc. .

An approximate estimate of the maximum magnitude during amateur observations can be made by noting the faintest visible stars and clarifying their magnitude using reference sources. For a more accurate assessment, the number of visible stars within standardized areas of the sky is counted (their boundaries are the lines between noticeable stars): the number of stars seen is matched with the corresponding limiting stellar magnitude. Determining the limiting stellar magnitude as accurately as possible during visual observations is extremely desirable, for example, when observing meteors for subsequent analysis of the activity of meteor showers.

All other things being equal, the maximum stellar magnitude increases (the number of observed objects becomes larger) when observing far from urban illumination, when the observer's altitude above sea level increases, and also when observing in dry weather or in a dry climate.

Characteristics of observational instruments

The use of telescopes makes it possible to observe objects that are less bright than those visible to the naked eye. The maximum stellar magnitude of objects accessible to observation through a telescope is often referred to as penetrating power and is its important characteristic. It is usually given in technical specifications or can be calculated using a number of formulas.