Biology
How to determine apparent magnitude. Magnitude scale. Application of magnitudes

How to determine apparent magnitude. Magnitude scale. Application of magnitudes

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 number of electromagnetic waves in the body that 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 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, a more precise definition of an object of zero magnitude was outlined - its illumination should be equal to 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 such as 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 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 an image of any cosmic object, astronomers can use , which are more sensitive to the high-frequency part 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.

The unequal brightness (or shine) of various objects in the sky is probably the first thing a person notices when observing; therefore, in connection with this, long ago, the need arose to introduce a convenient value that would make it possible to classify luminaries by brightness.

Story

For the first time such a value for my observations naked eye used by the ancient Greek astronomer, author of the first European star catalogue, Hipparchus. He classified all the stars in his catalog by brightness, designating the brightest as stars of the 1st magnitude, and the dimmest as stars of the 6th magnitude. This system took root, and in the middle of the 19th century it was improved to its modern look English astronomer Norman Pogson.

Thus, we obtained dimensionless physical quantity, logarithmically related to the illumination created by the luminaries (the actual magnitude):

m1-m2 =-2.5*lg(L1/L2)

where m1 and m2 are the magnitudes of the luminaries, and L1 and L2 are the illumination in lux (lx is the SI unit of illumination) created by these objects. If you substitute it on the left side given equation value m1-m2 = 5, then after making a simple calculation, it will be found that the illumination in this case is correlated as 1/100, so that a difference in brightness of 5 magnitudes corresponds to a difference in illumination from objects of 100 times.

Continuing to solve this problem, we extract the 5th root of 100 and we get a change in illumination with a difference in brightness of one magnitude, the change in illumination will be 2.512 times.

This is the whole basic mathematical apparatus, necessary for orientation in a given brightness scale.

Magnitude scale

With the introduction of this system, it was also necessary to set the starting point for the magnitude scale. For this purpose, the brightness of the star Vega (alpha Lyrae) was initially taken as zero magnitude (0m). At present, the most accurate reference point is the brightness of the star, which is 0.03m brighter than Vega. However, the eye will not notice such a difference, so for visual observations, the brightness corresponding to zero magnitude can still be taken as Vega.

Another important thing to remember regarding this scale is that the lower the magnitude, the brighter the object. For example, the same Vega with its magnitude of +0.03m will be almost 100 times brighter than a star with a magnitude of +5m. Jupiter, with its maximum brightness of -2.94m, will be brighter than Vega at:

2.94-0.03 = -2.5*lg(L1/L2)
L1/L2 = 15.42 times

You can solve this problem in another way - simply by raising 2.512 to a power equal to the difference in the magnitudes of the objects:

2,512^(-2,94-0,03) = 15,42

Magnitude classification

Now, having finally dealt with the hardware, let’s consider the classification of stellar magnitudes used in astronomy.

The first classification is based on the spectral sensitivity of the radiation receiver. In this regard, stellar magnitude can be: visual (brightness is taken into account only in the range of the spectrum visible to the eye); bolometric (brightness is taken into account over the entire range of the spectrum, not only visible light, but also ultraviolet, infrared and other spectra combined); photographic (brightness taking into account the sensitivity to the spectrum of photocells).

This also includes stellar magnitudes in a specific part of the spectrum (for example, in the range of blue light, yellow, red or ultraviolet radiation).

Accordingly, visual magnitude is intended to assess the brightness of luminaries during visual observations; bolometric - to estimate the total flux of all radiation from the star; and photographic and narrow-band quantities - for assessing the color indicators of luminaries in any photometric system.

Apparent and absolute magnitudes

The second type of classification of stellar magnitudes is based on the number of dependent physical parameters. In this regard, stellar magnitude can be visible and absolute. Apparent magnitude is the brightness of an object that the eye (or other radiation receiver) perceives directly from its current position in space.

This brightness depends on two parameters at once - the power of the luminary’s radiation and the distance to it. The absolute magnitude depends only on the radiation power and does not depend on the distance to the object, since the latter is assumed to be general for a specific class of objects.

The absolute magnitude for stars is defined as their apparent magnitude if the distance to the star were 10 parsecs (32.616 light years). Absolute magnitude for objects solar system is defined as their apparent magnitude if they were at a distance of 1 AU. from the Sun and would show its full phase to the observer, and the observer himself would also be at 1 AU. (149.6 million km) from the object (i.e. at the center of the Sun).

The absolute magnitude of meteors is defined as their apparent magnitude if they were located at a distance of 100 km from the observer and at the zenith point.

Application of magnitudes

These classifications can be used together. For example, the absolute visual magnitude of the Sun is M(v) = +4.83. and the absolute bolometric M(bol) = +4.75, since the Sun shines not only in the visible range of the spectrum. Depending on the temperature of the photosphere (visible surface) of the star, as well as its luminosity class ( main sequence, giant, supergiant, etc.).

There are differences between visual and bolometric absolute magnitudes of a star. For example, hot stars (spectral classes B and O) shine mainly in the ultraviolet range, which is invisible to the eye. So their bolometric brilliance is much stronger than their visual one. The same applies to cool stars (spectral classes K and M), which shine predominantly in the infrared range.

The absolute visual magnitude of the most powerful stars (hypergiants and Wolf-Rayet stars) is of the order of -8, -9. The absolute bolometric can reach -11, -12 (which corresponds to the apparent magnitude full moon).

The radiation power (luminosity) is millions of times higher than the radiation power of the Sun. The apparent visual magnitude of the Sun from Earth's orbit is -26.74m; in the area of Neptune's orbit it will be -19.36m. The apparent visual magnitude of the brightest star, Sirius, is -1.5m, and the absolute visual magnitude of this star is +1.44, i.e. Sirius is almost 23 times brighter than the Sun in the visible spectrum.

The planet Venus in the sky is always brighter than all the stars (its visible brightness ranges from -3.8m to -4.9m); Jupiter is somewhat less bright (from -1.6m to -2.94m); During oppositions, Mars has an apparent magnitude of about -2m or brighter. In general, most planets are the most bright objects sky after the Sun and Moon. Because there are no stars with high luminosity in the vicinity of the Sun.

If you raise your head up on a clear, cloudless night, you can see many stars. So many that it seems impossible to count at all. It turns out that the celestial bodies visible to the eye are still counted. There are about 6 thousand of them. This is the total number for both the northern and southern hemispheres of our planet. Ideally, you and I, being, for example, in the northern hemisphere, should see approximately half of them total number, namely about 3 thousand stars.

Myriads of winter stars

Unfortunately, it is almost impossible to consider all the available stars, because this would require conditions with a perfectly transparent atmosphere and the complete absence of any light sources. Even if you find yourself in an open field far from city light on a deep winter night. Why in winter? Yes, because summer nights are much lighter! This is due to the fact that the sun does not set far below the horizon. But even in this case, no more than 2.5-3 thousand stars will be available to our eyes. Why is this so?

The thing is that the pupil of the human eye, if imagined as collecting a certain amount of light from different sources. In our case, the light sources are stars. How many of them we see directly depends on the diameter of the lens of the optical device. Naturally, the lens glass of a binocular or telescope has a larger diameter than the pupil of the eye. Therefore, it will collect more light. As a result, a much larger number of stars can be seen using astronomical instruments.

The starry sky through the eyes of Hipparchus

Of course, you have noticed that stars differ in brightness, or, as astronomers say, in apparent brightness. In the distant past, people also paid attention to this. The ancient Greek astronomer Hipparchus divided all visible celestial bodies into stellar magnitudes of VI classes. The brightest of them “earned” I, and he characterized the most inexpressive as category VI stars. The rest were divided into intermediate classes.

Subsequently, it turned out that different magnitudes have a certain algorithmic connection with each other. And the distortion of brightness by an equal number of times is perceived by our eye as moving away to the same distance. Thus, it became known that the radiance of a category I star is approximately 2.5 times brighter than that of category II.

The star of class II is the same number of times brighter than class III, and the celestial body of class III is, accordingly, brighter than class IV. As a result, the difference between the luminosity of stars of magnitude I and VI differs by a factor of 100. Thus, category VII celestial bodies are beyond the threshold of human vision. It is important to know that magnitude is not the size of the star, but its apparent brightness.

What is the absolute magnitude?

Stellar magnitudes are not only visible, but also absolute. This term is used when it is necessary to compare two stars by their luminosity. To do this, each star is placed at a conventional standard distance of 10 parsecs. In other words, this is the magnitude of the stellar object that it would have if it were at a distance of 10 PCs from the observer.

For example, the magnitude of our sun is -26.7. But from a distance of 10 PCs, our star would be a barely visible fifth-magnitude object. It follows: the higher the luminosity of a celestial object, or, as they also say, the energy that a star emits per unit time, the greater the likelihood that the absolute magnitude of the object will take on a negative value. And vice versa: the lower the luminosity, the higher the positive values of the object will be.

The brightest stars

All stars have different apparent brightness. Some are slightly brighter than the first magnitude, others are much fainter. In view of this, fractional values were introduced. For example, if the apparent magnitude in its brightness is somewhere between categories I and II, then it is usually considered a class 1.5 star. There are also stars with magnitudes 2.3...4.7...etc. For example, Procyon, part of the equatorial constellation Canis Minor, is best visible throughout Russia in January or February. Its visible gloss is 0.4.

It is noteworthy that magnitude I is a multiple of 0. Only one star corresponds almost exactly to it - this is Vega, the brightest luminary at its brilliance is approximately 0.03 magnitude. However, there are luminaries that are brighter than it, but their magnitude is negative character. For example, Sirius, which can be observed in two hemispheres at once. Its luminosity is -1.5 magnitude.

Negative magnitudes are assigned not only to stars, but also to other celestial objects: the Sun, Moon, some planets, comets and space stations. However, there are stars that can change their brightness. Among them there are many pulsating stars with variable brightness amplitudes, but there are also those in which several pulsations can be observed simultaneously.

Measuring magnitudes

In astronomy, almost all distances are measured by a geometric magnitude scale. The photometric measurement method is used for long distances, and also if you need to compare the luminosity of an object with its apparent brightness. Basically, the distance to the nearest stars is determined by their annual parallax - the semi-major axis of the ellipse. Space satellites launched in the future will increase the visual accuracy of images by at least several times. Unfortunately, other methods are still used for distances greater than 50-100 PCs.

As a gift you will receive a card that will show
where exactly can you see your Star in the Sky!

Magnitudes

It is immediately worth noting that the brilliance of heavenly bodies, namely stars, is still expressed in special, so to speak, historically established indicators, namely “stellar magnitudes”. The appearance and origin of this number system is directly related to the peculiarity of human vision: if the strength of the light source changes in geometric progression, then our feeling from it is only arithmetic. Several centuries ago, the Greek astronomer Hipparchus (before 161 - after 126 BC) was able to divide all stars visible to the human eye into 6 classes, distributing them by brightness. He called the brightest stars 1st magnitude stars, while the faintest stars 6th magnitude. A little later, measurements were able to show that the fluxes of light originating from 1st magnitude stars are approximately 100 times greater than the fluxes of light from 6th magnitude stars, according to the work of Hipparchus.

For a more accurate determination, it was assumed that the difference of 5 magnitudes exactly corresponds to the ratio of light fluxes at a ratio of 1:100. Now we can say with confidence that the difference in brightness by 1 magnitude fully corresponds to the brightness ratio. To date this system classification of celestial bodies was significantly improved, after which a number of changes were made to it, thereby finalizing the works of the ancient scientist. For example: a star of the first magnitude is 2.512 times brighter than a star of the 2nd magnitude, which in turn is 2.512 times brighter than a star of the 3rd magnitude, and so on. This scale is very universal; it can be used to express the illumination created on the surface of the Earth by any type of light source.

But for a full comparison of stars, according to their true “luminosity”, the “absolute stellar magnitude” is used, which is the visible stellar magnitude that would have this star, if placed at a standard distance from the Earth of 10 pc. If a star has parallax p and apparent magnitude m, then its absolute magnitude M will be calculated by the formula. It is also worth noting that we can even describe the radiation of our star using stellar magnitudes, and in different ranges of its spectrum. For example, visual magnitude (mv) will express the brightness of a star in the yellow-green region of its spectrum, photographic magnitude (mp) - in blue, etc. The variation between visual and photographic color values is called the “color index,” which is directly related to the temperature and spectrum of the star.

Apparent magnitude, (hereinafter referred to as m; very often it is simply called “stellar magnitude”) this indicator determines the flux of radiation near the object we are observing, that is, the observed brightness of our celestial source, which directly depends not only on the real radiation power , our object, but also on the distance to its location. It is also worth noting that the scale of visible stellar magnitudes originates from the first star catalog of Hipparchus (before 161 c. 126 BC), in which all stars visible to the human eye were taken into account, after which they were divided into six classes according to their brightness

For example, the brightness of the stars of the Ursa Major Dipper is about 2m, while the stars of Vega are about 0m. But that’s not all, for particularly bright celestial bodies, the magnitude value can be negative, for example: Sirius is about -1.5m (which means that the flux of light emanating from it is 4 times greater than from Vega), while while the brightness of Venus for several days a year can reach up to -5m (light fluxes are almost 100 times greater than that of Vega). It is worth emphasizing that the visible magnitude can be measured not only with a telescope, but also with the naked eye, in the visual range of the spectrum and in others (photographic, UV, IR). In this case, the apparent magnitude will not have any relation specifically to the human gaze.

A star - in which thermonuclear reactions take place or will take place. BUT most often, stars are called those celestial bodies, in which thermonuclear reactions are already taking place.
For example, we can take our Sun, which is a typical star of spectral class G. The stars are massive luminous plasma-gas balls. It is also worth noting that they are formed from a gas-dust environment, which arises as a result of gravitational compression. Scientists claim that the temperature of matter in the interior of a star can be measured in millions of kelvins, while on their surface it can be measured in thousands of kelvins, which is several tens of times lower. The energy of the vast majority of stars is released as a result thermonuclear reactions the transformation of hydrogen into helium, which occurs at the highest temperatures, in the inner regions of stars. It is also worth noting that scientists often call stars the main bodies of our Universe, since they contain the entire bulk of luminous matter in nature. It is also noteworthy that stars have negative heat capacity. The closest star to the Sun is a little known star, Proxima Centauri. Which is at 4.2 light years from the center of the Solar System (4.2 light years = 39 PM = 39 trillion km = 3.9 1013 km).

Let's continue our algebraic excursion to the heavenly bodies. In the scale that is used to assess the brightness of stars, they can, in addition to fixed stars; find a place for yourself and other luminaries - planets, Sun, Moon. We will talk specifically about the brightness of the planets; Here we also indicate the magnitude of the Sun and Moon. The stellar magnitude of the Sun is expressed by the number minus 26.8, and the full1) Moon – minus 12.6. Why both numbers are negative, the reader should think, is clear after everything that was said earlier. But perhaps he will be puzzled by the insufficiently large difference between the magnitudes of the Sun and the Moon: the first is “only twice as large as the second.”

Let us not forget, however, that the designation of magnitude is, in essence, a certain logarithm (based on 2.5). And just as it is impossible, when comparing numbers, to divide their logarithms by one another, it makes no sense, when comparing stellar magnitudes, to divide one number by another. The result of a correct comparison is shown by the following calculation.

If the magnitude of the Sun is “minus 26.8”, then this means that the Sun is brighter than a star of the first magnitude

2.527.8 times. The moon is brighter than a star of the first magnitude

2.513.6 times.

This means that the brightness of the Sun is greater than the brightness of the full Moon at

2.5 27.8 2.5 14.2 times. 2.5 13.6

Having calculated this value (using tables of logarithms), we get 447,000. This is, therefore, the correct ratio of the brightnesses of the Sun and the Moon: the daylight in clear weather illuminates the Earth 447,000 times stronger than the full Moon on a cloudless night.

Considering that the amount of heat emitted by the Moon is proportional to the amount of light it scatters - and this is probably close to the truth - we must admit that the Moon sends us 447,000 times less heat than the Sun. It is known that every square centimeter at the boundary of the earth's atmosphere receives from the Sun about 2 small calories of heat per minute. This means that the Moon sends no more than 225,000th of a small calorie to 1 cm2 of the Earth every minute (that is, it can heat 1 g of water in 1 minute by 225,000th of a degree). This shows how unfounded are all attempts to attribute any influence on the earth’s weather to moonlight2).

1) In the first and last quarters, the magnitude of the Moon is minus 9.

2) The question of whether the Moon can influence the weather through its gravity will be discussed at the end of the book (see “The Moon and Weather”).

The widespread belief that clouds often melt under the influence of the rays of the full Moon is a gross misconception, explained by the fact that the disappearance of clouds at night (due to other reasons) becomes noticeable only under moonlight.

Let us now leave the Moon and calculate how many times the Sun is brighter than the most brilliant star in the entire sky - Sirius. Reasoning in the same way as before, we obtain the ratio of their brilliance:

2,5 27,8	2,5 25,2
2,52,6

i.e. The Sun is 10 billion times brighter than Sirius.

The following calculation is also very interesting: how many times is the illumination given by the full Moon brighter than the total illumination of the entire starry sky, i.e. all the stars visible to the naked eye on one celestial hemisphere? We have already calculated that stars from the first to the sixth magnitude, inclusive, shine together as much as a hundred stars of the first magnitude. The problem, therefore, comes down to calculating how many times the Moon is brighter than a hundred stars of the first magnitude.

This ratio is equal

2,5 13,6

100 2700.

So, on a clear moonless night we receive from the starry sky only 2700th of the light that the full Moon sends, and 2700x447,000, i.e. 1200 million times less than the Sun gives on a cloudless day.

Let us also add that the magnitude of the normal international

“candles” at a distance of 1 m is equal to minus 14.2, which means that a candle at the specified distance illuminates brighter than the full Moon by 2.514.2-12.6, i.e. four times.

It may also be interesting to note that the searchlight of an aircraft beacon with a power of 2 billion candles would be visible from the distance of the Moon as a 4½th magnitude star, i.e. could be distinguished by the naked eye.

The true brilliance of the stars and the Sun

All the gloss estimates we have made so far have referred only to their apparent brightness. The given numbers express the brilliance of the luminaries at the distances at which each of them is actually located. But we know well that the stars are not equally distant from us; The visible brightness of the stars therefore tells us both about their true brightness and about their distance from us - or rather, about neither one nor the other, until we separate both factors. Meanwhile, it is important to know what the comparative brightness or, as they say, “luminosity” of various stars would be if they were at the same distance from us.

By posing the question this way, astronomers introduce the concept of the “absolute” magnitude of stars. The absolute magnitude of a star is the one that the star would have if it were located at a distance from us.

standing 10 "parsecs". Parsec is a special measure of length used for stellar distances; We will talk about its origin separately later, here we will only say that one parsec is about 30,800,000,000,000 km. It is not difficult to calculate the absolute magnitude of the star if you know the distance of the star and take into account that the brightness should decrease in proportion to the square of the distance1).

We will introduce the reader to the results of only two such calculations: for Sirius and for our Sun. The absolute magnitude of Sirius is +1.3, the Sun is +4.8. This means that from a distance of 30,800,000,000,000 km, Sirius would shine for us as a star of 1.3 magnitude, and our Sun would be of 4.8 magnitude, i.e., weaker than Sirius in

2.5 3.8 2.53.5 25 times,

2,50,3

although the visible brilliance of the Sun is 10,000,000,000 times greater than the brilliance of Sirius.

We are convinced that the Sun is far from the brightest star in the sky. However, we should not consider our Sun to be a complete pygmy among the stars around it: its luminosity is still above average. According to stellar statistics, the average luminosity of stars surrounding the Sun up to a distance of 10 parsecs are stars of the ninth absolute magnitude. Because absolute value The Sun is 4.8, then it is brighter than the average of the “neighboring” stars, in

2,58	2,54,2	50 times.
2,53,8

Although 25 times absolutely dimmer than Sirius, the Sun is still 50 times brighter than the average stars around it.

The brightest star known

The highest luminosity is possessed by an eighth-magnitude star inaccessible to the naked eye in the constellation Doradus, designated

1) The calculation can be performed using the following formula, the origin of which will become clear to the reader when a little later he becomes more familiar with “parsec” and “parallax”:

Here M is the absolute magnitude of the star, m is its apparent magnitude, π is the parallax of the star in

seconds. Consecutive transformations are as follows: 2.5M = 2.5m 100π 2,

M lg 2.5 = m lg 2.5 + 2 + 2 lg π, 0.4M = 0.4m +2 + 2 lg π,

M = m + 5 + 5 log π .

For Sirius, for example, m = –1.6π = 0",38. Therefore, its absolute value

M = –l.6 + 5 + 5 log 0.38 = 1.3.

Latin letter S. The constellation Dorado is located in the southern hemisphere of the sky and is not visible in the temperate zone of our hemisphere. The mentioned star is part of the one next to us star system– The Small Magellanic Cloud, whose distance from us is estimated to be about 12,000 times greater than the distance to Sirius. At such a great distance, a star must have an absolutely exceptional luminosity to appear even of the eighth magnitude. Sirius, thrown just as deep into space, would shine as a 17th magnitude star, that is, it would be barely visible through the most powerful telescope.

What is the luminosity of this wonderful star? The calculation gives the following result: minus the eighth value. This means that our star is absolutely: 400,000 times (approximately) brighter than the Sun! With such exceptional brightness, this star, if placed at the distance of Sirius, would appear nine magnitudes brighter than it, i.e., would have approximately the brightness of the Moon in the quarter phase! A star that, from the distance of Sirius, could flood the Earth with such bright light has an undeniable right to be considered the brightest star known to us.

The magnitude of the planets in the earthly and alien skies

Let us now return to the mental journey to other planets (which we made in the section “Alien Skies”) and more accurately evaluate the brilliance of the stars shining there. First of all, we indicate the stellar magnitudes of the planets at their maximum brightness in the earth’s sky. Here's the sign.

In the sky of the Earth:

Venus.............................		Saturn..............................
Mars..................................		Uranus..................................
Jupiter...........................		Neptune.............................
Mercury......................

Looking through it, we see that Venus is brighter than Jupiter by almost two magnitudes, i.e. 2.52 = 6.25 times, and Sirius 2.5-2.7 = 13 times

(the magnitude of Sirius is 1.6). From the same tablet it is clear that the dim planet Saturn is still brighter than all the fixed stars except Sirius and Canopus. Here we find an explanation for the fact that the planets (Venus, Jupiter) are sometimes visible to the naked eye during the day, while stars in daylight are completely inaccessible to the naked eye.