What is the safe distance between us and the supernova? Light year and cosmic scales Annual parallax and distance to stars.

Parallax principle using a simple example.

A method for determining the distance to stars by measuring the angle of apparent displacement (parallax).

Thomas Henderson, Vasily Yakovlevich Struve and Friedrich Bessel were the first to measure distances to stars using the parallax method.

The layout of the stars within a radius of 14 light years from the Sun. Including the Sun, this region contains 32 known star systems (Inductiveload / wikipedia.org).

Next discovery (30th years XIX century) - determination of stellar parallaxes. Scientists have long suspected that stars might look like distant suns. However, it was still a hypothesis, and, I would say, until that time, practically not based on anything. It was important to learn how to directly measure the distance to the stars. How to do this, people understood for a long time. The earth revolves around the sun, and if, for example, today we make an accurate sketch starry sky(in the 19th century, it was still impossible to take a photograph), wait six months and re-sketch the sky, you can see that some of the stars have shifted relative to other, distant objects. The reason is simple - we are now looking at the stars from the opposite edge of the earth's orbit. There is a displacement of close objects against the background of distant ones. It is exactly the same as if we first look at the finger with one eye and then with the other. We will notice that the finger is displaced against the background of distant objects (or distant objects are displaced relative to the finger, depending on which frame of reference we choose). Tycho Brahe, the best astronomer-observer of the pre-telescope era, tried to measure these parallaxes, but did not find them. In fact, he just gave the lower limit of the distance to the stars. He said that the stars are at least farther than, about a light month (although, of course, there could not be such a term then). And in the 1930s, the development of telescopic observation technology made it possible to more accurately measure distances to stars. And it is not surprising that there are three people in different parts The globe made such observations for three different stars.

The first to formally correctly measure the distance to the stars was Thomas Henderson. He observed Alpha Centauri in the Southern Hemisphere. He was lucky, he almost accidentally chose the closest star from those visible to the naked eye in the Southern Hemisphere. But Henderson believed that he lacked the accuracy of the observations, although he received the correct value. Errors, in his opinion, were large, and he did not immediately publish his result. Vasily Yakovlevich Struve observed in Europe and chose the bright star of the northern sky - Vega. He was also lucky - he could have chosen, for example, Arcturus, which is much further. Struve determined the distance to Vega and even published the result (which, as it later turned out, was very close to the truth). However, he clarified it several times, changed it, and therefore many felt that it was impossible to believe this result, since the author himself constantly changes it. Friedrich Bessel acted differently. He chose not a bright star, but one that moves quickly across the sky - 61 Swans (the name itself says that it is probably not very bright). The stars move slightly relative to each other, and, naturally, the closer the stars are to us, the more noticeable this effect is. In the same way as on a train, roadside poles flicker very quickly outside the window, the forest only slowly moves, and the Sun actually stands still. In 1838 he published the very reliable parallax of 61 Cygnus and measured the distance correctly. These measurements proved for the first time that stars are distant suns, and it became clear that the luminosities of all these objects correspond to solar values. Determination of parallaxes for the first tens of stars made it possible to construct a three-dimensional map of the solar environs. After all, it has always been very important for a person to build maps. This made the world kind of a little more controllable. Here is a map, and already a foreign area does not seem so mysterious, probably dragons do not live there, but just some kind of dark forest. The advent of the measurement of distances to stars has indeed made the nearest solar neighborhood, a few light years away, any more friendly.

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How to determine the distance to the stars? How is it known that Alpha Centauri is about 4 light years away? Indeed, by the brightness of a star, as such, there is little to determine - the brightness of a dim close and bright distant stars can be the same. And yet there are many fairly reliable ways to determine the distance from the Earth to the farthest corners of the universe. Astrometric satellite "Hipparchus" for 4 years of work determined the distance to 118 thousand stars SPL

Whatever physicists say about three-dimensional, six-dimensional or even eleven-dimensional space, for an astronomer the observable Universe is always two-dimensional. What is happening in the Cosmos is seen by us as a projection onto the celestial sphere, just as in a movie the entire complexity of life is projected onto a flat screen. On the screen, we can easily distinguish far from close thanks to our acquaintance with the volumetric original, but in the two-dimensional scattering of stars there is no visual clue that allows us to turn it into a three-dimensional map suitable for plotting the course of an interstellar ship. Meanwhile, distances are the key to almost half of all astrophysics. How to distinguish a nearby dim star from a distant but bright quasar without them? Only knowing the distance to the object, you can estimate its energy, and hence the direct road to understanding its physical nature.

A recent example of the uncertainty of cosmic distances is the problem of sources of gamma-ray bursts, short pulses of hard radiation, arriving to Earth from different directions about once a day. Initial estimates of their distance ranged from hundreds of astronomical units (tens of light hours) to hundreds of millions of light years. Accordingly, the spread in the models was also impressive - from annihilation of comets from antimatter on the outskirts of the Solar System to explosions of neutron stars shaking the entire Universe and the birth of white holes. By the mid-1990s, more than a hundred different explanations for the nature of gamma-ray bursts had been proposed. Now that we have been able to estimate the distances to their sources, there are only two models left.

But how to measure the distance if you cannot reach the object with either a ruler or a locator beam? The triangulation method, widely used in conventional earth geodesy, comes to the rescue. We select a segment of a known length - a base, measure from its ends the angles at which a point inaccessible for one reason or another is visible, and then simple trigonometric formulas give the desired distance. When we move from one end of the base to the other, the apparent direction to the point changes, it shifts against the background of distant objects. This is called parallax offset, or parallax. Its magnitude is the smaller, the further the object is, and the larger, the longer the base.

To measure distances to stars, one has to take the maximum base available to astronomers, equal to the diameter of the earth's orbit. The corresponding parallax displacement of stars in the sky (strictly speaking, half of it) began to be called the annual parallax. Tycho Brahe tried to measure it, who did not like Copernicus's idea of ​​the Earth's rotation around the Sun, and he decided to check it - parallaxes also prove the Earth's orbital motion. The measurements carried out had an impressive accuracy for the 16th century - about one minute of an arc, but this was completely insufficient to measure the parallaxes, which Brahe himself did not suspect and concluded that Copernicus's system was incorrect.

Distance to star clusters is determined by main sequence fitting

The next attack on parallax was undertaken in 1726 by the Englishman James Bradley, the future director of the Greenwich Observatory. At first, it seemed that luck smiled at him: the Dragon gamma star chosen for observations really fluctuated around its average position with a span of 20 arc seconds for a year. However, the direction of this displacement was different from what was expected for parallaxes, and Bradley soon found the correct explanation: the speed of the Earth's orbit adds up with the speed of light coming from the star, and changes its apparent direction. Likewise, raindrops leave inclined paths on the windows of the bus. This phenomenon, called the annual aberration, was the first direct evidence of the Earth's motion around the Sun, but had nothing to do with parallaxes.

Only a century later, the accuracy of goniometric instruments has reached the required level. In the late 1830s, as John Herschel put it, "the wall that prevented penetration into the stellar Universe was breached almost simultaneously in three places." In 1837, Vasily Yakovlevich Struve (at that time the director of the Dorpat observatory, and later the Pulkovo observatory) published the Vega parallax measured by him - 0.12 arc seconds. The following year, Friedrich Wilhelm Bessel reported that the parallax of the 61st Cygnus star is 0.3 ". And a year later, the Scottish astronomer Thomas Henderson, who worked in the Southern Hemisphere at the Cape of Good Hope, measured the parallax in the Alpha Centauri system - 1.16" ... True, later it turned out that this value was overestimated by a factor of 1.5, and in the entire sky there is not a single star with a parallax of more than 1 arc second.

For distances measured by the parallax method, a special unit of length was introduced - parsec (from parallax second, pc). One parsec contains 206,265 astronomical units, or 3.26 light years. It is from this distance that the radius of the earth's orbit (1 astronomical unit = 149.5 million kilometers) is seen at an angle of 1 second. To determine the distance to a star in parsecs, you need to divide one by its parallax in seconds. For example, to the closest star system to us, Alpha Centauri, 1 / 0.76 = 1.3 parsecs, or 270 thousand astronomical units. A thousand parsecs is called a kiloparsec (kpc), a million parsecs is a megaparsec (Mpc), and a billion is a gigaparsec (Gpc).

Measuring extremely small angles required technical sophistication and great diligence (Bessel, for example, processed more than 400 individual observations of the 61st Cygnus), but after the first breakthrough things went easier. By 1890, the parallaxes of already three dozen stars were measured, and when photography began to be widely used in astronomy, the exact measurement of parallaxes was completely put on stream. Parallax measurement is the only method direct definition distances to individual stars. However, during ground-based observations, atmospheric noise does not allow the parallax method to measure distances over 100 pc. For the Universe, this is not a very large value. (“It's not far here, there are a hundred parsecs,” as Gromozeka used to say.) Where geometric methods fail, photometric methods come to the rescue.

Geometric records

V last years the results of measuring distances to very compact sources of radio emission - masers - are being published more and more often. Their radiation falls within the radio range, which makes it possible to observe them on radio interferometers capable of measuring the coordinates of objects with a microsecond precision, unattainable in the optical range in which stars are observed. Thanks to masers, trigonometric methods can be applied not only to distant objects in our Galaxy, but also to other galaxies. For example, in 2005 Andreas Brunthaler (Germany) and his colleagues determined the distance to the M33 galaxy (730 kpc) by comparing the angular displacement of the masers with the rotation speed of this stellar system. A year later, Ye Xu (China) and his colleagues applied the classical parallax method to "local" maser sources to measure the distance (2 kpc) to one of the spiral arms of our Galaxy. Perhaps, the farthest managed to advance in 1999, J. Hernstein (USA) with colleagues. Tracking the motion of masers in the accretion disk around the black hole in the core of the active galaxy NGC 4258, astronomers have determined that this system is at a distance of 7.2 Mpc from us. Today it is an absolute record for geometric methods.

Astronomers' Standard Candles

The farther from us the radiation source is, the dimmer it is. If you know the true luminosity of an object, then by comparing it with the apparent brightness, you can find the distance. Huygens was probably the first to apply this idea to measuring distances to stars. At night he watched Sirius, and during the day he compared its brilliance with a tiny hole in the screen that covered the Sun. Having chosen the size of the hole so that both brightness coincided, and comparing the angular values ​​of the hole and the solar disk, Huygens concluded that Sirius is 27,664 times farther from us than the Sun. This is 20 times less than the real distance. Part of the error was due to the fact that Sirius is actually much brighter than the sun, and partly - by the difficulty of comparing the brilliance from memory.

A breakthrough in the field of photometric methods happened with the advent of photography in astronomy. At the beginning of the 20th century, the Harvard College Observatory carried out a large-scale work to determine the brightness of stars from photographic plates. Particular attention was paid to variable stars, whose brightness fluctuates. Studying variable stars of a special class - Cepheids - in the Small Magellanic Cloud, Henrietta Levitt noticed that the brighter they are, the longer the period of their brightness fluctuations: stars with a period of several tens of days turned out to be about 40 times brighter than stars with a period of the order of a day.

Since all Levitt Cepheids were in the same star system - the Small Magellanic Cloud - it could be assumed that they were removed from us at the same (albeit unknown) distance. This means that the difference in their apparent brightness is associated with real differences in luminosity. It remained to determine the geometrical method of the distance to one Cepheid in order to calibrate the entire dependence and to get the opportunity, by measuring the period, to determine the true luminosity of any Cepheid, and from it the distance to the star and the star system containing it.

But, unfortunately, there are no Cepheids in the vicinity of the Earth. The closest one is polar Star- removed from the Sun, as we now know, by 130 pc, that is, it is out of reach for ground-based parallax measurements. This did not allow throwing the bridge directly from the parallaxes to the Cepheids, and astronomers had to erect a structure that is now figuratively called the staircase of distances.

Open star clusters, including from several tens to hundreds of stars, connected by a common time and place of birth, became an intermediate step on it. If you plot the temperature and luminosity of all the stars in the cluster, most of the points fall on one oblique line (more precisely, a strip), which is called the main sequence. Temperature is determined with high accuracy from the spectrum of a star, and luminosity is determined from apparent brightness and distance. If the distance is unknown, the fact that all the stars in the cluster are almost equally distant from us again comes to the rescue, so that within the cluster, the apparent brightness can still be used as a measure of luminosity.

Since the stars are the same everywhere, the main sequences for all clusters must be the same. The differences are only due to the fact that they are at different distances. If we determine the geometrical method the distance to one of the clusters, then we will find out what the "real" main sequence looks like, and then, by comparing the data on other clusters with it, we will determine the distances to them. This technique is called "main sequence fitting". For a long time, the Pleiades and Hyades served as a standard for him, the distances to which were determined by the method of group parallaxes.

Fortunately for astrophysics, Cepheids have been found in about two dozen open clusters. Therefore, by measuring the distances to these clusters by fitting the main sequence, it is possible to "reach the ladder" to the Cepheids, which are at its third stage.

As an indicator of distances, Cepheids are very convenient: there are relatively many of them - they can be found in any galaxy and even in any globular cluster, and being giant stars, they are bright enough to measure intergalactic distances from them. Thanks to this, they have earned many high-profile epithets, such as "beacons of the Universe" or "milestones of astrophysics." The Cepheid "ruler" stretches up to 20 Mpc, which is about a hundred times the size of our Galaxy. Then they can no longer be distinguished even in the most powerful modern instruments, and in order to climb the fourth rung of the ladder of distances, you need something brighter.

To the outskirts of the universe

One of the most powerful extragalactic distance measurements is based on a pattern known as the Tully-Fisher relationship: the brighter a spiral galaxy, the faster it spins. When a galaxy is viewed edge-on or at a significant tilt, half of its material is approaching us due to rotation, and half is receding, which leads to broadening of spectral lines due to the Doppler effect. This expansion is used to determine the speed of rotation, from it - the luminosity, and then from comparison with the apparent brightness - the distance to the galaxy. And, of course, to calibrate this method, galaxies are needed, the distances to which have already been measured by Cepheids. The Tully - Fisher method is very long-range and covers galaxies hundreds of megaparsecs distant from us, but it also has a limit, since for galaxies that are too distant and faint, it is not possible to obtain sufficiently high-quality spectra.

In a slightly wider range of distances, another "standard candle" operates - type Ia supernovae. The outbursts of such supernovae are "the same type" thermonuclear explosions of white dwarfs with a mass slightly above the critical mass (1.4 solar masses). Therefore, there is no reason for them to vary greatly in power. Observations of such supernovae in nearby galaxies, the distances to which can be determined by Cepheids, seem to confirm this constancy, and therefore cosmic thermonuclear explosions are now widely used to determine distances. They are visible even in billions of parsecs from us, but you never know the distance to which galaxy you will be able to measure, because it is not known in advance exactly where the next supernova will break out.

So far, only one method allows you to move even further - redshifts. Its history, like the history of the Cepheids, begins simultaneously with the 20th century. In 1915, the American Vesto Slipher, studying the spectra of galaxies, noticed that in most of them the lines are shifted towards the red side relative to the "laboratory" position. In 1924, the German Karl Wirtz noticed that the smaller the angular dimensions of the galaxy, the stronger this displacement. However, only Edwin Hubble in 1929 managed to bring these data into a single picture. According to the Doppler effect, the redshift of lines in the spectrum means that the object is moving away from us. Comparing the spectra of galaxies with the distances to them, determined by the Cepheids, Hubble formulated the law: the speed of a galaxy's receding is proportional to the distance to it. The proportionality coefficient in this ratio is called the Hubble constant.

Thus, the expansion of the Universe was discovered, and with it the possibility of determining the distances to galaxies from their spectra, of course, provided that the Hubble constant is tied to some other "rulers". Hubble himself performed this binding with an error of almost an order of magnitude, which was corrected only in the mid-1940s, when it became clear that Cepheids are divided into several types with different "period - luminosity" ratios. The calibration was performed anew based on the "classical" Cepheids, and only then the value of the Hubble constant became close to modern estimates: 50-100 km / s for each megaparsec of distance to the galaxy.

Now, redshifts are used to determine distances to galaxies that are thousands of megaparsecs away from us. True, in megaparsecs, these distances are indicated only in popular articles. The fact is that they depend on the model of the evolution of the Universe adopted in the calculations, and besides, in the expanding space it is not entirely clear what distance is meant: the one at which the galaxy was at the moment of emission of radiation, or the one at which it is located. at the time of its reception on Earth, or the distance traveled by light on the way from the starting point to the final one. Therefore, astronomers prefer to indicate for distant objects only the directly observed value of the redshift, without converting it into megaparsecs.

Red shifts are currently the only method for estimating "cosmological" distances comparable to the "size of the Universe", and at the same time it is, perhaps, the most widespread technique. In July 2007, a catalog of redshifts of 77 418 767 galaxies was published. True, when creating it, a somewhat simplified automatic technique for analyzing spectra was used, and therefore errors could creep into some values.

Team play

Geometric methods for measuring distances are not limited to annual parallax, in which the apparent angular displacements of stars are compared with the displacements of the Earth in orbit. Another approach relies on the movement of the sun and stars relative to each other. Imagine a star cluster flying past the Sun. According to the laws of perspective, the visible trajectories of its stars, like rails on the horizon, converge at one point - the radiant. Its position indicates at what angle to the line of sight the cluster flies. Knowing this angle, one can decompose the motion of the cluster stars into two components - along the line of sight and perpendicular to it along the celestial sphere - and determine the proportion between them. The radial velocity of stars in kilometers per second is measured by the Doppler effect and, taking into account the found proportion, the projection of the velocity onto the sky is calculated - also in kilometers per second. It remains to compare these linear velocities of the stars with the angular ones determined from the results of many years of observations - and the distance will be known! This method works up to several hundred parsecs, but is applicable only to star clusters and is therefore called the group parallax method. This is how the distances to the Hyades and the Pleiades were first measured.

Down the stairs leading up

Building our staircase to the outskirts of the universe, we were silent about the foundation on which it rests. Meanwhile, the parallax method gives the distance not in standard meters, but in astronomical units, that is, in the radii of the earth's orbit, the value of which was also far from being determined immediately. So let's look back and go down the ladder of cosmic distances to Earth.

Probably the first to try to determine the remoteness of the Sun was Aristarchus of Samos, who proposed a heliocentric system of the world one and a half thousand years before Copernicus. He turned out that the Sun is 20 times farther from us than the Moon. This estimate, as we now know, underestimated by a factor of 20, held out until the Kepler era. Although he himself did not measure the astronomical unit, he already noted that the Sun should be much farther than Aristarchus believed (and all other astronomers behind him).

The first more or less acceptable estimate of the distance from the Earth to the Sun was obtained by Jean Dominique Cassini and Jean Richet. In 1672, during the opposition of Mars, they measured its position against the background of stars simultaneously from Paris (Cassini) and Cayenne (Richet). The distance from France to French Guiana served as the base for the parallax triangle, from which they determined the distance to Mars, and then using the equations celestial mechanics calculated the astronomical unit, getting the value of 140 million kilometers.

Over the next two centuries, the transit of Venus along the solar disk became the main tool for determining the scale of the solar system. Observing them simultaneously from different points of the globe, you can calculate the distance from Earth to Venus, and hence all other distances in the solar system. In the 18th-19th centuries, this phenomenon was observed four times: in 1761, 1769, 1874 and 1882. These observations were among the first international scientific projects. Large-scale expeditions were equipped (the English expedition of 1769 was led by the famous James Cook), special observation stations were created ... scientists have already taken an active part in research. Unfortunately, the extreme complexity of the observations has led to a significant discrepancy in the estimates of the astronomical unit - from about 147 to 153 million kilometers. A more reliable value - 149.5 million kilometers - was obtained only at the turn of the XIX-XX centuries from observations of asteroids. And, finally, it should be borne in mind that the results of all these measurements were based on knowledge of the length of the base, in the role of which, when measuring the astronomical unit, was the radius of the Earth. So ultimately the foundation of the space-distance ladder was laid by surveyors.

Only in the second half of the 20th century at the disposal of scientists appeared fundamentally new methods of determining space distances - laser and radar. They made it possible to increase the accuracy of measurements in the solar system by hundreds of thousands of times. The radar error for Mars and Venus is several meters, and the distance to the corner reflectors installed on the Moon is measured with an accuracy of centimeters. The currently accepted value of the astronomical unit is 149,597,870,691 meters.

The difficult fate of "Hipparchus"

Such a radical progress in measuring the astronomical unit has raised the question of the distances to stars in a new way. The accuracy of determining parallaxes is limited by the Earth's atmosphere. Therefore, back in the 1960s, the idea arose to take a goniometer instrument into space. It was realized in 1989 with the launch of the European astrometric satellite "Hipparchus". This name is a well-established, although formally not quite correct translation English name HIPPARCOS, which is short for High Precision Parallax Collecting Satellite and does not coincide with the English spelling of the name of the famous ancient Greek astronomer - Hipparchus, the author of the first star catalog.

The creators of the satellite set themselves a very ambitious task: to measure the parallaxes of more than 100 thousand stars with millisecond precision, that is, to "reach" the stars located hundreds of parsecs from the Earth. It was necessary to clarify the distances to several open star clusters, in particular the Hyades and the Pleiades. But most importantly, it became possible to "jump over a step" by directly measuring the distance to the Cepheids themselves.

The expedition began with trouble. Due to a failure in the upper stage, Hipparchus did not enter the calculated geostationary orbit and remained on an intermediate, highly elongated trajectory. The specialists of the European Space Agency managed to cope with the situation, and the orbiting astrometric telescope successfully worked for 4 years. The processing of the results took the same amount of time, and in 1997 a stellar catalog with parallaxes and proper motions of 118,218 luminaries, including about two hundred Cepheids, was published.

Unfortunately, on a number of issues, the desired clarity did not come. The most incomprehensible result was for the Pleiades - it was assumed that "Hipparchus" would clarify the distance, which was previously estimated at 130-135 parsecs, but in practice it turned out that "Hipparchus" corrected it, having received a value of only 118 parsecs. Acceptance of a new value would require an adjustment of both the theory of stellar evolution and the scale of intergalactic distances. This would become a serious problem for astrophysics, and the distance to the Pleiades began to be carefully checked. By 2004, several groups independently obtained estimates of the distance to the cluster in the range from 132 to 139 pc. Offensive voices began to be heard suggesting that the consequences of putting the satellite into the wrong orbit still could not be completely eliminated. Thus, in general, all parallaxes measured by him were called into question.

The Hipparchus team was forced to admit that the measurements are generally accurate, but may need to be re-processed. The point is that parallaxes are not directly measured in space astrometry. Instead, Hipparchus measured the angles between numerous pairs of stars over the course of four years. These angles change both due to the parallax displacement and due to the proper motions of the stars in space. To "extract" the parallax values ​​from the observations, a rather complex mathematical processing is required. It was this that had to be repeated. The new results were published at the end of September 2007, but it is not yet clear how much this has improved.

But this is not the only problem of "Hipparchus". The parallaxes of the Cepheids determined by him turned out to be insufficiently accurate for reliable calibration of the "period-luminosity" relation. Thus, the satellite was unable to solve the second task before it. Therefore, several new space astrometry projects are currently being considered in the world. The closest to implementation is the European project Gaia, which is scheduled to launch in 2012. Its principle of operation is the same as that of "Hipparchus" - multiple measurements of the angles between pairs of stars. However, thanks to powerful optics, he will be able to observe much dimmer objects, and the use of the interferometry method will increase the accuracy of measuring angles to tens of microseconds of an arc. It is assumed that "Gaia" will be able to measure kiloparsec distances with an error of no more than 20% and within several years of operation will determine the positions of about a billion objects. This will build a three-dimensional map of a significant part of the Galaxy.

Aristotle's universe ended at nine distances from the Earth to the Sun. Copernicus believed that the stars are 1,000 times farther than the Sun. Parallaxes pushed even nearby stars light years away. At the very beginning of the 20th century, the American astronomer Harlow Shapley, with the help of Cepheids, determined that the diameter of the Galaxy (which he identified with the Universe) is measured in tens of thousands of light years, and thanks to Hubble, the boundaries of the Universe expanded to several gigaparsecs. How definitive are they?

Of course, at each step of the ladder of distances, its own, larger or smaller errors arise, but on the whole, the scales of the Universe are determined quite well, tested by different methods independent of each other and add up to a single consistent picture. So the modern boundaries of the universe seem to be immutable. However, this does not mean that one day we will not want to measure the distance from it to some neighboring Universe!

Surely, having heard in some fantastic action movie an expression a la “to Tatooine twenty light years”, Many asked legitimate questions. I will voice some of them:

Isn't a year a time?

Then what is it light year?

How many kilometers are there?

How much will it take light year spaceship with Of the earth?

I decided to devote today's article to explaining the meaning of this unit of measurement, comparing it with our usual kilometers and demonstrating the scales with which it operates Universe.

Virtual racer.

Imagine a person, in violation of all the rules, rushing along the highway at a speed of 250 km / h. In two hours he will overcome 500 km, and in four - as much as 1000. Unless, of course, it crashes in the process ...

It would seem that this is speed! But in order to go around the whole Earth(≈ 40,000 km), our rider will need 40 times longer. And this is already 4 x 40 = 160 hours. Or almost a whole week of continuous driving!

In the end, however, we will not say that he covered 40,000,000 meters. Since laziness has always forced us to come up with and use shorter alternative units of measurement.

Limit.

From the school physics course, everyone should know that the fastest rider in The universe- light. In one second, its beam covers a distance of about 300,000 km, and thus it will circle the globe in 0.134 seconds. That's 4,298,507 times faster than our virtual racer!

From Of the earth before Moon light reaches an average of 1.25 s, up to Suns its beam will fly in a little over 8 minutes.

Colossal, isn't it? But the existence of speeds greater than the speed of light has not yet been proven. Therefore, the scientific world decided that it would be logical to measure cosmic scales in units that a radio wave passes over certain time intervals (which light, in particular, is).

Distances.

Thus, light year- nothing more than the distance that a ray of light travels in one year. On an interstellar scale, using distance units smaller than this does not make much sense. And yet they are. Here are their approximate values:

1 light second ≈ 300,000 km;

1 light minute ≈ 18,000,000 km;

1 light hour ≈ 1,080,000,000 km;

1 light day ≈ 26,000,000,000 km;

1 light week ≈ 181,000,000,000 km;

1 light month ≈ 790,000,000,000 km.

And now, so that you understand where the numbers come from, let's calculate what one is light year.

There are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Thus, a year consists of 365 x 24 x 60 x 60 = 31,536,000 seconds. In one second, light travels 300,000 km. Consequently, in a year its ray will cover the distance of 31,536,000 x 300,000 = 9,460,800,000,000 km.

This number is read like this: NINE TRILLION, FOUR SIXTY BILLION AND EIGHT HUNDRED MILLION kilometers.

Of course the exact meaning light year slightly different from what we calculated. But when describing the distances to stars in popular science articles, the highest accuracy is, in principle, not needed, and a hundred or two million kilometers will not play a special role here.

Now let's continue our thought experiments ...

The scale.

Suppose modern spaceship leaves Solar system with the third cosmic speed (≈ 16.7 km / s). First light year it will overcome in 18,000 years!

4,36 light years to the closest star system ( Alpha Centauri, see the picture at the beginning) it will overcome in about 78 thousand years!

Our the milky way galaxy with a diameter of about 100,000 light years, it will cross in 1 billion 780 million years.

And to the nearest to us big galaxies, spaceship will come only after 36 billion years ...

These are the pies. But in theory even Universe emerged only 16 billion years ago ...

And finally ...

Cosmic scale, you can start to wonder even without going beyond Solar system, because it itself is very large. This was shown very well and clearly, for example, by the creators of the project If the moon wereonly 1 pixel (If the moon was just one pixel): http://joshworth.com/dev/pixelspace/pixelspace_solarsystem.html.

On this I, perhaps, will conclude today's article. I am glad to welcome all your questions, comments and wishes in the comments below.

Stars are the most common type celestial bodies in the Universe. There are about 6000 stars up to the 6th magnitude, about a million up to the 11th magnitude, and up to the 21st magnitude there are about 2 billion of them in the entire sky.

All of them, like the Sun, are hot self-luminous balls of gas, in the depths of which enormous energy is released. However, stars, even in the strongest telescopes, are visible as luminous points, since they are very far from us.

1. Yearly parallax and distances to stars

The radius of the Earth turns out to be too small to serve as a basis for measuring the parallax displacement of stars and for determining the distances to them. Even in the days of Copernicus, it was clear that if the Earth really revolves around the Sun, then the apparent positions of the stars in the sky must change. For six months, the Earth moves by the size of the diameter of its orbit. The directions to the star from opposite points of this orbit should be different. In other words, the stars should have a noticeable annual parallax (Fig. 72).

The annual parallax of the star ρ is the angle at which from the star one could see the semi-major axis of the earth's orbit (equal to 1 AU) if it is perpendicular to the line of sight.

The greater the distance D to the star, the smaller its parallax. The parallactic displacement of the position of the star in the sky during the year occurs along a small ellipse or circle if the star is at the pole of the ecliptic (see Fig. 72).

Copernicus tried but failed to detect the parallax of the stars. He correctly asserted that the stars are too far from the Earth to be able to detect their parallax displacement with the instruments that existed at that time.

For the first time, a reliable measurement of the annual parallax of the Vega star was carried out in 1837 by the Russian academician V. Ya. Struve. Almost simultaneously with it, parallaxes were determined in other countries in two more stars, one of which was α Centauri. This star, which is not visible in the USSR, turned out to be the closest to us, its annual parallax ρ = 0.75 ". At this angle, a 1 mm thick wire is visible to the naked eye from a distance of 280 m. small angular displacements.

Distance to the star where a is the semi-major axis of the earth's orbit. At small angles if p is in arc seconds. Then, taking a = 1 a. That is, we get:

Distance to the nearest star α Centauri D = 206 265 ": 0.75" = 270 000 AU. e. Light travels this distance in 4 years, while it takes only 8 minutes from the Sun to the Earth, and about 1 second from the Moon.

The distance that light travels in a year is called a light year.... This unit is used to measure distance along with parsec (pc).

Parsec is the distance from which the semi-major axis of the earth's orbit, perpendicular to the line of sight, is seen at an angle of 1 ".

The distance in parsecs is equal to the reciprocal of the annual parallax, expressed in arc seconds. For example, the distance to the star α Centauri is 0.75 "(3/4"), or 4/3 pc.

1 parsec = 3.26 light years = 206 265 amu. e. = 3 * 10 13 km.

At present, the measurement of the annual parallax is the main method for determining the distances to stars. Parallaxes have already been measured for many stars.

By measuring the annual parallax, it is possible to reliably establish the distance to stars that are no further than 100 pc, or 300 light years.

Why is it not possible to accurately measure the annual parallax of more than o distant stars?

Distances to more distant stars are currently being determined by other methods (see §25.1).

2. Visible and absolute magnitude

The luminosity of the stars. After astronomers were able to determine the distance to stars, it was found that stars differ in apparent brightness, not only because of the difference in distance to them, but also because of their difference. luminosity.

The luminosity of a star L is the power of emission of light energy in comparison with the power of emission of light by the Sun.

If two stars have the same luminosity, then the star that is farther from us has a lower apparent brightness. It is possible to compare stars in luminosity only if their apparent brightness (magnitude) is calculated for the same standard distance. Such a distance in astronomy is considered to be 10 pc.

The apparent stellar magnitude that a star would have if it were at the standard distance D 0 = 10 pc is called the absolute stellar magnitude M.

Let us consider the quantitative ratio of the apparent and absolute stellar magnitudes of a star at a known distance D to it (or its parallax p). Let us first recall that a difference of 5 magnitudes corresponds to a brightness difference of exactly 100 times. Consequently, the difference between the apparent magnitudes of two sources is equal to unity when one of them is exactly one times brighter than the other (this value is approximately equal to 2.512). The brighter the source, the smaller its apparent magnitude is. In the general case, the ratio of the apparent brightness of any two stars I 1: I 2 is associated with the difference between their apparent magnitudes m 1 and m 2 by a simple relationship:

Let m be the apparent magnitude of a star located at a distance D. If it were observed from a distance D 0 = 10 pc, its apparent magnitude m 0, by definition, would be equal to the absolute magnitude M. Then its apparent brightness would change to

At the same time, it is known that the apparent brightness of a star changes in inverse proportion to the square of the distance to it. That's why

(2)

Hence,

(3)

Taking the logarithm of this expression, we find:

(4)

where p is in arc seconds.

These formulas give the absolute magnitude M according to the known apparent magnitude m at a real distance to the star D. Our Sun from a distance of 10 pc would look approximately like a star of the 5th apparent magnitude, i.e., M ≈ 5 for the Sun.

Knowing the absolute magnitude M of some star, it is easy to calculate its luminosity L. Taking the luminosity of the Sun L = 1, by definition of the luminosity, we can write that

The quantities M and L in different units express the radiation power of the star.

The study of stars shows that they can differ in luminosity by tens of billions of times. In magnitudes, this difference reaches 26 units.

Absolute values stars of very high luminosity are negative and reach M = -9. Such stars are called giants and supergiants. The radiation of the star S Doradus is 500,000 times more powerful than the radiation of our Sun, its luminosity is L = 500,000, the dwarfs with M = + 17 (L = 0.000013) have the lowest radiation power.

To understand the reasons for the significant differences in the luminosity of stars, it is necessary to consider their other characteristics, which can be determined based on the analysis of radiation.

3. Color, spectra and temperature of stars

During the observations, you noticed that the stars have a different color, which is clearly visible in the brightest of them. The color of the heated body, including the star, depends on its temperature. This makes it possible to determine the temperature of stars from the distribution of energy in their continuous spectrum.

The color and spectrum of stars are related to their temperature. Relatively cool stars are dominated by radiation in the red region of the spectrum, which is why they have a reddish color. The temperature of the red stars is low. It grows sequentially from red stars to orange, then to yellow, yellowish, white and bluish. The spectra of stars are extremely diverse. They are divided into classes denoted by Latin letters and numbers (see back endpaper). In the spectra of cool red M class stars with a temperature of about 3000 K, absorption bands of the simplest diatomic molecules, most often titanium oxide, are visible. The spectra of other red stars are dominated by oxides of carbon or zirconium. Red stars of the first magnitude class M - Antares, Betelgeuse.

In the spectra of yellow class G stars, to which the Sun belongs (with a temperature of 6000 K on the surface), thin lines of metals predominate: iron, calcium, sodium, etc. A star of the Sun-type in spectrum, color and temperature is the bright Capella in the constellation Auriga.

In the spectra of class A white stars like Sirius, Vega and Deneb, the hydrogen lines are strongest. There are many weak lines of ionized metals. The temperature of such stars is about 10,000 K.

In the spectra of the hottest, bluish stars with a temperature of about 30,000 K, lines of neutral and ionized helium are visible.

Most stars have temperatures ranging from 3,000 to 30,000 K. Few stars have temperatures around 100,000 K.

Thus, the spectra of stars are very different from each other and from them it is possible to determine the chemical composition and temperature of the atmospheres of stars. The study of the spectra showed that hydrogen and helium are predominant in the atmospheres of all stars.

The differences in stellar spectra are explained not so much by the diversity of their chemical composition as by the difference in temperature and other physical conditions in stellar atmospheres. At high temperatures, molecules are broken down into atoms. At an even higher temperature, less durable atoms are destroyed, they turn into ions, losing electrons. Ionized atoms of many chemical elements, like neutral atoms, emit and absorb energy at specific wavelengths. By comparing the intensities of the absorption lines of atoms and ions of the same chemical element their relative amount is theoretically determined. It is a function of temperature. Thus, the dark lines of the spectra of stars can be used to determine the temperature of their atmospheres.

Stars have the same temperature and color, but different luminosities, the spectra are generally the same, but you can notice differences in the relative intensities of some lines. This is due to the fact that at the same temperature, the pressure in their atmospheres is different. For example, in the atmospheres of giant stars, the pressure is less, they are more rarefied. If we express this dependence graphically, then the intensity of the lines can be used to find the absolute magnitude of the star, and then, using formula (4), determine the distance to it.

An example of solving the problem

Task. What is the luminosity of the star ζ Scorpio, if its apparent magnitude is 3, and the distance to it is 7500 ns. years?

Exercise # 20

1. How many times is Sirius brighter than Aldebaran? Is the sun brighter than Sirius?

2. One star is 16 times brighter than the other. What is the difference between their magnitudes?

3. Parallax Vega 0.11 ". How long does the light travel from it to the Earth?

4. How many years would it take to fly towards the constellation Lyra at a speed of 30 km / s for Vega to become twice as close?

5. How many times is a star of magnitude 3.4 fainter than Sirius, which has an apparent magnitude of -1.6? What are the absolute magnitudes of these stars if the distance to both is 3 pc?

6. Name the color of each of the stars in Appendix IV according to their spectral class.

Looking out of the train window

The calculation of the distance to the stars did not really bother the ancient people, because in their opinion they were attached to the celestial sphere and were at the same distance from the Earth, which a person could never measure. Where are we, and where are these divine domes?

It took many, many centuries for people to understand that the universe is a little more complicated. To understand the world in which we live, it was required to build a spatial model in which each star is at a certain distance from us, just as a tourist needs a map to complete a route, not a panoramic photograph of the area.

The first assistant in this complex undertaking was parallax, familiar to us from travel by train or by car. Have you noticed how quickly the roadside pillars flicker against the backdrop of distant mountains? If you noticed, then you can be congratulated: you, unwittingly, discovered an important feature of parallax displacement - for close objects it is much larger and more noticeable. And vice versa.

What is Parallax?

In practice, parallax began to work for a person in geodesy and (where can we go without it ?!) in military affairs. Indeed, who, if not artillerymen, needs to measure distances to distant objects with the highest possible accuracy? Moreover, the triangulation method is simple, logical and does not require the use of any complex devices. All that is required is to measure two angles and one distance, the so-called base, with acceptable accuracy, and then, using elementary trigonometry, determine the length of one of the legs right triangle.

Triangulation in practice

Imagine that you need to determine the distance (d) from one coast to an inaccessible point on a ship. Below we will give an algorithm of the actions required for this.

1. Mark two points on the bank (A) and (B), the distance between which you know (l).
2. Measure the angles α and β.
3. Calculate d by the formula:

Parallactic displacement of loved onesstars against the background of distant

Obviously, the accuracy directly depends on the size of the base: the longer it is, the correspondingly greater will be the parallax displacements and angles. For a terrestrial observer, the maximum possible base is the diameter of the Earth's orbit around the Sun, that is, measurements must be taken at intervals of six months, when our planet is at the diametrically opposite point of the orbit. Such parallax is called annual, and the first astronomer who tried to measure it was the famous Dane Tycho Brahe, famous for his exceptional scientific pedantry and rejection of the Copernican system.

Perhaps Brahe's adherence to the idea of ​​geocentrism played a cruel joke with him: the measured annual parallaxes did not exceed an angular minute and could well be attributed to instrumental errors. An astronomer with a clear conscience was convinced of the "correctness" of the Ptolemaic system - the Earth is not moving anywhere and is located in the center of a small cozy Universe, in which the Sun and other stars are literally a stone's throw, only 15–20 times farther than the Moon. However, the works of Tycho Brahe were not in vain, becoming the foundation for the discovery of Kepler's laws, which finally put an end to the outdated theories of the solar system.

Star cartographers

Space "ruler"

It should be noted that triangulation did a great job in our cosmic home before we seriously tackle distant stars. The main task was to determine the distance to the Sun, the very astronomical unit, without exact knowledge of which measurements of stellar parallaxes become meaningless. The first person in the world to set himself such a task was the ancient Greek philosopher Aristarchus of Samos, who proposed a heliocentric system of the world 1,500 years before Copernicus. After doing complex calculations based on rather rough knowledge of that era, he found that the Sun was 20 times farther than the Moon. For many centuries this value was accepted as true, becoming one of the basic axioms of the theories of Aristotle and Ptolemy.

Only Kepler, coming close to building a model of the solar system, subjected this value to a serious reassessment. On this scale, it was in no way possible to connect real astronomical data and the laws of motion of celestial bodies discovered by him. Intuitively, Kepler believed that the sun was much farther from the Earth, but as a theorist, he could not find a way to confirm (or refute) his guess.

It is curious that the correct estimate of the size of the astronomical unit became possible precisely on the basis of Kepler's laws, which set the "rigid" spatial structure of the solar system. Astronomers had it accurate and detailed map, on which it only remained to determine the scale. This was done by the French Jean Dominique Cassini and Jean Richet, who measured the position of Mars against the background of distant stars during opposition (in this position, Mars, Earth and the Sun are located on one straight line, and the distance between the planets is minimal).

The measurement points were Paris and the capital of French Guiana, Cayenne, which is located a good 7 thousand kilometers away. Young Richet went to the South American colony, and the venerable Cassini remained "musketeer" in Paris. Upon the return of a young colleague, the scientists sat down to calculations, and at the end of 1672 they presented the results of their research - according to their calculations, the astronomical unit was equal to 140 million kilometers. Later, to clarify the scale of the solar system, astronomers used the transit of Venus across the solar disk, which occurred four times in the 18th-19th centuries. And, perhaps, these studies can be called the first international scientific projects: in addition to England, Germany and France, Russia has become an active participant in them. By the beginning of the 20th century, the scale of the solar system was finally established, and the modern value of the astronomical unit was adopted - 149.5 million kilometers.

1. Aristarchus suggested that the moon has the shape of a ball and is illuminated by the sun. Therefore, if the Moon looks "split" in half, then the Earth-Moon-Sun angle is right.
2. Next, Aristarchus calculated the Sun-Earth-Moon angle by direct observation.
3. Using the rule "the sum of the angles of a triangle is 180 degrees," Aristarchus calculated the Earth-Sun-Moon angle.
4. Using the aspect ratio of a right-angled triangle, Aristarchus calculated that the Earth-Moon distance is 20 times greater than the Earth-Sun distance. Note! Aristarchus did not calculate the exact distance.

Parsecs, parsecs

Cassini and Richet calculated the position of Mars relative to distant stars

And with these initial data, it was already possible to claim the accuracy of measurements. In addition, the goniometric instruments have reached the required level. Russian astronomer Vasily Struve, director of the university observatory in the city of Dorpat (now Tartu in Estonia), published the results of measuring Vega's annual parallax in 1837. It turned out to be equal to 0.12 arc seconds. The baton was picked up by the German Friedrich Wilhelm Bessel, a student of the great Gauss, who a year later measured the parallax of the star 61 in the constellation Cygnus - 0.30 arc seconds, and the Scotsman Thomas Henderson, who “caught” the famous Alpha Centauri with a parallax of 1.2 ”. Later, however, it turned out that the latter overdid it a little and in fact the star is displaced by only 0.7 arc seconds per year.

The accumulated data have shown that the annual parallax of stars does not exceed one arc second. It was accepted by scientists for the introduction of a new unit of measurement - parsec ("parallax second" in abbreviation). From such a crazy distance by conventional standards, the radius of the earth's orbit is visible at an angle of 1 second. In order to more clearly represent the cosmic scale, let us assume that the astronomical unit (and this is the radius of the Earth's orbit, equal to 150 million kilometers) "compressed" into 2 tetrad cells (1 cm). So: you can "see" them at an angle of 1 second ... from two kilometers!

For cosmic depths, parsecs are not a distance, although even light will take three and a quarter years to overcome it. Within just a dozen parsecs of our stellar neighbors, you can literally count on one hand. When it comes to galactic scales, it is just right to operate with kilo- (thousand units) and megaparsecs (respectively, a million), which in our "tetrad" model can already climb into other countries.

The real boom in ultra-precise astronomical measurements began with the advent of photography. "Big-eyed" telescopes with 1-meter lenses, sensitive photographic plates designed for many-hour exposure, precision clock mechanisms that rotate the telescope synchronously with the Earth's rotation - all this made it possible to confidently record annual parallaxes with an accuracy of 0.05 arc seconds and, thus, determine distances up to 100 parsecs. For more (or rather, for less) terrestrial technology is incapable: the capricious and restless terrestrial atmosphere interferes.

If measurements are taken in orbit, then the accuracy can be significantly improved. It was for this purpose that in 1989 the astrometric satellite "Hipparchus" (HIPPARCOS, from the English High Precision Parallax Collecting Satellite), developed by the European Space Agency, was launched into near-earth orbit.

1. As a result of work orbiting telescope Hipparchus compiled a fundamental astrometric catalog.
2. With the help of Gaia, a three-dimensional map of part of our Galaxy has been compiled, indicating the coordinates, direction of movement and color of about a billion stars.

The result of his work is a catalog of 120 thousand stellar objects with annual parallaxes determined with an accuracy of 0.01 arc seconds. And its successor, the satellite Gaia (Global Astrometric Interferometer for Astrophysics), launched on December 19, 2013, draws a spatial map of the nearest galactic environs with a billion (!) Objects. And who knows, maybe it will be very useful for our grandchildren.