Before the star 20 light years. Determination of distances to the nearest stars. Down the stairs leading up

Due to the annual movement of the Earth in orbit, close stars move a little relative to the distant "fixed" stars. For the year, such a star describes a small ellipse on the heavenly sphere, the dimensions of which are less than a star further. In the angular measure, the large semi-axis of this ellipse is approximately equal to the magnitude of the maximum angle, which is visible to 1 a. e. (Big part of the earth orbit), perpendicular to the direction on the star. This angle (), called a one-year or trigonometric parallax star equal to half of its visible displacement for the year, serves to measure the distance to it on the basis of trigonometric relations between the sides and the angles of the ZSA triangle, in which the angle and the base is known - the big part of the earth orbit (see . Fig. 1).

Figure 1. Determination of the distance to the star by Parallax (A - Star, Z - Earth, C - Sun).

Distance r. To the star, determined by its trigonometric parallax, is equal to:

r. \u003d 206265 "" / (a. E.),

where Parallax is expressed in angular seconds.

For the convenience of determining the distance to stars with parallaxes in astronomy, a special unit of length is used in astronomy (PS). A star at a distance of 1 ps has a pararallax equal to 1 ". According to the above formula, 1 ps \u003d 206265 a. e. \u003d 3,086 · 10 18 cm.

Along with Parsecom, another special unit of distances is applied - the light year (i.e., the distance that the light passes in 1 year), it is 0.307 ps, or 9.46 · 10 17 cm.

The closest star to the solar system - the red dwarf of the 12th Star magnitude of the proxima Centaurs - has pararallax 0.762, i.e., the distance to it is 1.31 Ps (4.3 light years).

The lower limit for measuring trigonometric parallaxes ~ 0.01 "", therefore, with their help, you can measure distances that do not exceed 100 ps with a relative error of 50%. (With distances up to 20 ps, \u200b\u200bthe relative error does not exceed 10%.) With this method, up to date, ranges up to about 6000 stars are determined. The distances to more distant stars in astronomy are determined mainly by the photometric method.

Table 1. Twenty nearest stars.

What way can you measure the distance to stars?

Method of horizontal parallax

The globe, keeping at a distance of 149.6 million kilometers from the Sun, for the year "wings" in orbit is quite a very small distance.

However, truly gigantic distances begin outside. Only at the beginning of the 20th century, scientists managed to produce fairly accurate measurements and for the first time set the distance to some stars.

The method of determining the distance to stars consists in accurately determining the direction on them (that-is in determining their position on) from two ends of the diameter of the earth orbit and is called "Horizontal pararallax method". To do this, it is only necessary to determine the direction on the star at the moments separated from each other, since the Earth itself takes the observer with him from one side of its orbit to another.

The offset of the star (of course, apparent), caused by the change in the position of the observer in space, is extremely few, barely catchy. But it was measured up to 0 ", 01. Is there a lot or a little? Judge for yourself - it is like to consider from Ryazan the edge of the coin abandoned passers-by in Moscow on Red Square.

It is clear that at such distances and distances, the familiar meters and kilometers do not go anywhere. Truly large, that is, cosmic distances, it is more convenient to express not in kilometers, but in light years, that is, at those distances that light, spreading at a speed of 300,000 km / s, runs over the year.

With the help of the described method, you can determine the distances to stars, which are much farther than three hundred years. The light of stars of some distant star systems comes to us for hundreds of millions of light years.

It does not mean at all how often they think that we are watching the stars, there may be no longer existing now in reality. Do not say that "we see in the sky what is really no." In fact, the overwhelming majority of stars change as slowly that millions of years ago they were the same as now, and even visible places of them in the sky are changing extremely slowly, although in the star space moving quickly. Thus, the stars that we see them, in general, are the same and now.

Pararallax principle on a simple example.

The method of determining the distance to the stars by measuring the angle of visible displacement (parallax).

Thomas Henderson, Vasily Yakovlevich Struve and Friedrich Bessel first measured distances to stars by parallaxes.

Scheme of the location of the stars within the radius of 14 light years from the sun. Including the sun, in this area there are 32 famous starry systems (InductiveLoad / Wikipedia.org).

The next discovery (30s of the XIX century) is the definition of star parallaxes. Scientists have long suspected that the stars can be similar to the distant sun. However, it was still a hypothesis, and I would say, until that time, practically not found on anything. It was important to learn directly to measure the distance to the stars. How to do it, people understood quite a long time. The Earth rotates around the Sun, and, if, for example, today to make an accurate sketch starry sky (In the XIX century, it was still impossible to take a photo), wait half a year and re-sketching the sky, it can be noted that part 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 orbit. There is a shift of close objects against the background of distant. This is exactly the same as if we first look at your finger with one eye, and then others. We note that the finger is shifted against the background of distant objects (or distant objects are displaced relative to the finger, depending on which we choose the reference system). Quietly Brage, the best astronomer of the Dotheliescopic era, tried to measure these parallaxes, but did not find them. In fact, he gave the lower limit of the distance to the stars. He said that the stars at least further than, about, the light month (although, such a term, of course, could not be). And in the 30s, the development of telescopic observation technology made it possible to more accurate the distances to the stars. And it is not surprising that at once three people in different parts The globe conducted such observations for three different stars.

The first formally correctly the distance to the stars measured Thomas Henderson. He observed Alpha Centauro in the southern hemisphere. He was lucky, he almost accidentally chose the closest star from those who are visible non-equipped eye In the southern hemisphere. But Henderson believed that he lacks the accuracy of observations, although he received the right thing. Errors, in his opinion, were big, and he did not immediately publish his result. Vasily Yakovlevich Struve watched in Europe and chose a bright star of the Northern sky - Vehi. He was too lucky - he could choose, for example, Arcturus, which is much further. Struve determined the distance to Veks and even published the result (which, as it turned out, was very close to truth). However, he clarified him several times, changed, and therefore many considered that it is impossible to believe this result, since the author himself constantly changes him. And Friedrich Bessel came differently. He chose not a bright star, and the one that quickly moves across the sky - 61 swans (the name itself says that, probably, it is not very bright). Stars move slightly relative to each other, and naturally, the closer to us the stars, the more noticeably this effect. Just like on the train, the roadside poles flashed very quickly outside the window, the forest is only slowly shifted, and the sun actually stands in place. In 1838, he published a very reliable parallax star 61 Swan and correctly measured the distance. These measurements first proved that the stars are distant sun, and it became clear that the luminosity of all these objects correspond to the solar meaning. The definition of parallaxes for the first tens of stars made it possible to build a three-dimensional map of the sun's surroundings. Still, man has always been very important to build cards. This made the world as if a little more controlled. Here is a map, and already someone else's area does not seem so mysterious, probably do not live by dragons, but just some kind of dark forest. The emergence of measuring distances to stars really made the nearest sunshine in several light years some more or more, friendly.

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On February 22, 2017, NASA reported that 7 exoplanets were found at the single star TrapPist-1. Three of them are in the range of distances from the star, in which the planet can have liquid water, and water is a key condition for life. It is also reported that this star system is at a distance of 40 light years from the ground.

This message made a lot of noise in the media, someone even seemed that humanity was in a step from the construction of new settlements from a new star, but it is not. But 40 light years is a lot, it's a lot, it is too many kilometers, that is, it is a monstrously tremendous distance!

From the course of physics, the third cosmic speed is known - this is such a speed that the body should have the body at the surface of the earth to go beyond Solar system. The value of this speed is 16.65 km / s. Ordinary orbital spaceships Start at a speed of 7.9 km / s, and rotate around the Earth. In principle, the speed of 16-20 km / s is quite affordable in modern earth technologies, but not more!

Humanity has not yet learned to accelerate cosmic ships faster than 20 km / s.

Calculate how many years you need a starrel flying at a speed of 20 km / s to overcome 40 light years and reach the Star TrapPist-1.
One light year is the distance that goes the beam of light in vacuum, and the speed of light is approximately 300 thousand km / s.

The spacecraft made by the hands of people flies at a speed of 20 km / s, that is, 15,000 times slower speed of light. 40 light years such a ship will overcome the time equal to 40 * 15000 \u003d 600000 years!

The earth's ship (at the modern level of technology) is tensed to the Star TrapPist-1 for about 600 thousand years! The sensible man exists on Earth (according to scientists) only 35-40 thousand years, and there are as many as 600 thousand years!

In the near future, technology will not allow a person to reach the Star Trappist-1. Even promising engines (ionic, photon, cosmic sails, etc.), which are not in the earth's reality, it is estimated that they can dispersed the ship to a speed of 10,000 km / s, and therefore the flight time to the TAPPIST-1 system will be reduced to 120 years . This is already a more or less acceptable time to fly using anabiosis or for several generations of immigrants, but today all these engines are fantasy.

Even the closest stars are still too far from people, too far, not to mention the stars of our galaxy or other galaxies.

The diameter of our galaxy Milky Way It is about 100 thousand light years, that is, the path from the end to the end for the modern earth ship will be 1.5 billion years old! Science assumes that our land is 4.5 billion years old, and a multileaver life is about 2 billion years. The distance to the nearest to us galaxies - Andromeda nebula - 2.5 million light years from the ground - what monstrous distances!

As can be seen from all now living people, no one will never stop foot on the ground of the planet from another star.

Stars are the most common type heavenly Tel in the Universe. Stars up to the 6th Star value there are about 6,000, up to the 11th Star magnitude about a million, and to the 21st Star magnitude of them in the whole sky about 2 billion.

All of them, like the sun, are hot self-losing gas balls, in the depths of which huge energy is distinguished. However, the stars even in the strongest telescopes are visible as glowing points, as they are very far from us.

1. One-year parallax and distances to stars

The radius of the Earth turns out to be too small to serve as a basis for measuring the parallact stars offset and to determine the distances to them. In the time of Copernicus, it was clear that if the Earth really turns around the Sun, then the visible positions of the stars in the sky should change. For six months, the land moves to the diameter of its orbit. Directions on the star from the opposite points of this orbit should differ. In other words, the stars should be noticeable to a one-year pararallax (Fig. 72).

The one-year parallax of the star ρ call the angle under which from the star could be seen a large part of the earth orbit (equal to 1 or. E.), If it is perpendicular to the beam of view.

The greater the distance D to the star, the less her parallax. The parallact displacement of the star position in the sky during the year occurs on a small ellipse or a circle if the star is in the Ecliptic Pole (see Fig. 72).

Copernicus tried, but could not detect pararallax stars. He correctly argued that the stars were too far from the ground so that the devices existed then could notice their parallact displacement.

For the first time, a reliable measurement of the one-year parallax, the stars of Veks managed to implement in 1837. Russian Academician V. Ya. Struve. Almost simultaneously with him in other countries, parallaxes were identified by two stars, one of which was α centaution. This star, which in the USSR is not visible, turned out to be closest to us, its one-year parallax ρ \u003d 0.75. "Under such an angle, the naked eye is visible with a thickness of 1 mm from a distance of 280 m. It is not surprising that so long could not see the stars so long Small angular displacements.

Distance to Star where a is a large semi-axle of earthly orbit. At small angles if P is expressed in the seconds of the arc. Then, adopting a \u003d 1 a. e., I get:

The distance to the nearest star α Centaurus d \u003d 206 265 ": 0.75" \u003d 270,000 a. e. The light passes this distance in 4 years, whereas from the sun to the ground he only goes 8 minutes, and about 1 s from the moon.

The distance that the light passes throughout the year is called the Light Year. This unit is used to measure the distance along with parcember (PC).

Parsek is the distance from which the large part of the earth's orbit, perpendicular to the beam of view, is visible at an angle of 1 ".

The distance in the parseca is equal to the inverse value of a one-year parallax, expressed in the second arc. For example, the distance to the star α Centaurion is 0.75 "(3/4"), or 4/3 of the PC.

1 parsec \u003d 3.26 light year \u003d 206 265 a. e. \u003d 3 * 10 13 km.

Currently, the measurement of the one-year parallax is the main way when determining distances to stars. Pararallaks are measured for very many stars.

Measuring the one-year parallax can be reliably set the distance to stars that are 100 pcs, or 300 light years.

Why can't accurately measure the annual parallax more than the distant stars?

The distance to more distant stars is currently determined by other methods (see §25.1).

2. Visible and absolute stellar value

The luminosity of stars. After the astronomers got the opportunity to determine distances to stars, it was found that the stars differ from the visible brightness not only due to the difference in the distance to them, but due to the difference in their lamps.

The luminosity of the star L is called the power of radiation of light energy compared to the radiation power of the sun.

If two stars have the same luminosity, the star that is further from us has a smaller visible brightness. You can compare star luminosity stars only if you calculate their visible brightness (stellar value) for the same standard distance. In such a distance in Astronomy, 10 PCs are considered.

The visible stellar value that the star had if it were from us at a standard distance D 0 \u003d 10 PC, was the name of the absolute star magnitude M.

Consider the quantitative ratio of the visible and absolute star magnitudes at a well-known distance D to it (or its parallax P). Recall first that the difference in 5 star magnitudes corresponds to the difference in brightness exactly 100 times. Consequently, the difference of visible stellar values \u200b\u200bof two sources is equal to one, when one of them brighter than another exactly at times (this value is approximately equal to 2.512). The brighter than the source, the apparent stellar value is considered to be less. In general, the relation of the visible brightness of two any stars i 1: i 2 is associated with the difference between their visible stellar magnitudes M 1 and M 2 by a simple ratio:

Let M be the visible star magnitude of the star at a distance of D. If it was observed from the distance d 0 \u003d 10 PC, its visible star value m 0 by definition would be equal to the absolute star magnitude M. Then its apparent brightness would change

At the same time, it is known that the seeming brightness of the star changes inversely proportional to the square of the distance to it. therefore

(2)

Hence,

(3)

Logarithming this expression, find:

(4)

where p is expressed in the seconds of the arc.

These formulas give an absolute stellar value of M according to the known visible star magnitudem at a real distance to the star D. Our sun from a distance of 10 PCs would look approximately as a star of the 5th visible star magnitude, i.e. for the sun M ≈5.

Knowing an absolute star magnitude of a star, it is easy to calculate its luminosity L. Taking the luminosity of the Sun L \u003d 1, by definition of luminosity it can be written that

The values \u200b\u200bof M and L in different units express the power of the star radiation.

Study stars shows that they may differ in tens of billion times. In stellar values, this distinction reaches 26 units.

Absolute valuesstars of very high luminosity are negative and reached M \u003d -9. Such stars are called giants and supergiants. The radiation of the star S gold fish is more powerful than the radiation of our Sun 500,000 times, its luminosity L \u003d 500,000, the smallest radiation power has dwarfs with m \u003d + 17 (L \u003d 0.000013).

In order to understand the causes of significant differences in the luminosity of stars, it is necessary to consider the other characteristics that can be determined based on the radiation analysis.

3. Color, spectra and temperatures

During the observations, you drew attention to the fact that the stars have a different color, the most bright of them. The color of the heated body, including the stars, depends on its temperature. This makes it possible to determine the temperature of the energy distribution in their continuous spectrum.

Color and range of stars are associated with their temperature. In relatively cold stars, radiation in the Red Spectrum region, which is why they have a reddish color. Temperature of red stars low. It grows consistently when moving from red stars to orange, then to yellow, yellowish, white and bluish. The spectra of the stars are extremely diverse. They are divided into classes, denoted by Latin letters and numbers (see the rear forced). In the spectra of cold red stars class Mwith a temperature of about 3000 K, the absorption bands of the simplest diatomic molecules are visible, most often titanium oxide. In the spectra of other red stars, carbon or zirconium oxides are dominated. Red stars of the first size of class M - Antares, Bethelgeuse.

In spectra yellow star Class G.To which the sun (with a temperature of 6000 K on the surface belongs), thin metal lines dominate: iron, calcium, sodium, etc. The Sun type star along the spectrum, color and temperature is a bright chapel in the constellation of the erection.

In the spectra of white stars class Alike Sirius, Vega and Denget, the most strong line of hydrogen. There are many weak lines of ionized metals. The temperature of these stars is about 10,000 K.

In the spectra of the hottest, bluish starswith a temperature of about 30,000 K visible line of neutral and ionized helium.

The temperatures of most stars are in the range from 3000 to 30,000 K. Few temperatures of about 100,000 K.

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

The differences in the star spectra are explained not so much a variety of them. chemical compositionHow much difference in temperature and other physical conditions in the star atmospheres. At high temperatures, molecules are destroyed to atoms. With an even higher temperature, less durable atoms are destroyed, they turn into ions, losing electrons. Ionized atoms of many chemical elements, as well as neutral atoms, emit and absorb the energy of certain wavelengths. By comparing the intensity of the absorption lines of atoms and the ions of the same chemical element Theoretically determine their relative amount. It is a function of temperature. Thus, on the dark lines of the spectra of stars, the temperature of their atmospheres can be determined.

The stars of the same temperature and color, but the difference luminosity spectra are generally the same, however, it can be seen 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 stars-giants, the pressure is less, they are rapid. If you express this dependence graphically, then on the intensity of the lines you can find the absolute value of the star, and then by formula (4) determine the distance to it.

An example of solving the problem

A task. What is the luminosity of the star ζ scorpion, if its visible stellar value 3, and the distance to it 7500 sv. years?

Exercise 20.

1. How many times is Sirius brighter than Aldebaran? Sun brighter than Sirius?

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

3. Pararallax vegue 0.11 ". How long is the light from it goes to the ground?

4. How many years should it be to fly towards the constellation of the Lyra at a speed of 30 km / s, so that Vega is twice as close?

5. How many times the star is 3.4 star magnitude weaker than Sirius having a visible stellar value -1.6? What is equal absolute values These stars, if the distance to both is 3 pcs?

6. Name the color of each of the IV application stars by their spectral class.