Observations have confirmed this and a number of other conclusions of the theory of relativity.

= a ” x Dpc, or Aa. e. = a "/ p",

since Dpk = 1 / p ".

Comparing the motion of the star’s satellite with the Earth’s motion around the Sun (for which the period of rotation Tl = 1 year, and the major half-axis of the orbit – a.o.), according to Kepler’s third law we can write:

where m1 and m2 are the masses of the components in the pair of stars, M © and MÅ are the masses of the Sun and the Earth, and T is the period of rotation of the pair in years. Neglecting the mass of the Earth compared to the mass of the Sun, we obtain the sum of the masses of stars that make up the pair, in the masses of the Sun:

m1 + m2 = A3: T2

To determine the mass of each star, it is necessary to study the motion of the components relative to the surrounding stars and calculate their distances A1 and A2 from the common center of mass. Then we have the second equation:

m1 + m2 = A2: A1

and from the system of two equations we find both masses separately.

In the telescope, double stars are often a beautiful sight: the main star is yellow or orange, and the satellite is white or blue.

If the components of a double star in close rotation are close to each other, then even in the strongest telescope they can not be seen separately. In this case, the duality can be detected by the spectrum. Such stars will be called spectral-binary.

Due to the Doppler effect, the lines in the spectra of the stars will shift in opposite directions (when one star moves away from us, the other approaches). The offset of the lines changes with a period equal to the period of rotation of the pair. If the brightness and spectra of the stars that make up the pair are similar, then in the spectrum of the double star there is a periodically repeated bifurcation of spectral hoarfrost.

Let the components occupy positions A1, and B1, and A3 and B3, then one of them moves to the observer, and the other – from him. In this case, the separation of the spectral lines is observed. In an approaching star, the spectral lines are shifted to the blue end of the spectrum, and in the receding one. – to red. But if the components of double vision occupy positions A2 and B2 or A4 and B4, then they both move at right angles to the line of sight and bifurcated spectral lines will not be.

If one of the stars glows faintly, you will see only the lines of the second star, which are periodically shifted.

In mutual rotation, the components of the spectral-double Jurassic can alternately overlap. Such stars are called obscure-double or algols, after the name of their typical representative p Perseus. During eclipses, the overall brightness of the vapor, the components of which we do not see separately, will weaken. The rest of the time between eclipses, it almost became (positions A and C) and the longer, the shorter the duration of the eclipses and the greater the radius of the orbit. If the satellite is large, but itself gives little light, the total brightness of the system decreases only slightly when a bright star replaces the satellite.

The ancient Arabs called Perseus Algol (twisted el gul), which means "devil". Perhaps they noticed his strange behavior: for 2 days 11 hours. the brightness of Algol became, then in 5 hours. it weakens from 2.3 to 3.5 magnitude, then for 5 hours. the brightness returns to the previous value.

Analysis of the curve of change of the visible stellar magnitude as a function of time makes it possible to determine the size and brightness of stars, the size of the orbit, its shape and inclination to the ray of vision, as well as the mass of stars. Thus, obscure binary stars, which are also observed as spectral binaries, are the most thoroughly studied systems. Unfortunately, relatively few such systems are known.

The periods of known spectral binary stars and algols are mostly short – about a few days.

In general, the duality of vision is a very common phenomenon. Statistics show that about 30% of all stars are obviously double.

The masses of stars determined by the described methods differ much less than their luminosities: from about 0.1 to 100 masses of the Sun. Very large masses are too rare. Usually the stars have a mass less than five masses of the Sun.

It is the mass of stars that determines their existence and nature as a special type of celestial bodies, which are characterized by high subsoil temperatures (over 107 K). Nuclear reactions to convert hydrogen to helium, which occur at this temperature, are the source of the energy they emit in most stars. At lower masses, the temperature inside celestial bodies does not reach the values ​​required for thermonuclear reactions.

The evolution of the chemical composition of matter in the universe has taken place and is taking place mainly due to the stars. It is in their bowels that the irreversible process of synthesis of heavier chemical elements from hydrogen takes place.

Dimensions of vision. The density of their substance. Let’s show by a simple example how it is possible to compare the sizes of stars of identical temperature, for example the Sun and Capella (and the Chariot). These stars have the same spectra, color and temperature, but the luminosity of the Capella is 120 times the luminosity of the Sun.

Since at the same temperature the brightness of a unit of the surface of stars is also the same, it means that the surface of the Capella is 120 times larger than the surface of the Sun, and its diameter and radius are 11 times larger than that of the Sun. Knowing the laws of radiation makes it possible to determine the dimensions of other stars.

Thus, in physics it is established that the total energy radiated per unit time from 1 m2 of the surface of a heated body is equal to: i = sT4, where s is the coefficient of proportionality, and T is the absolute temperature. The relative linear diameter of stars having a known temperature T is found by the formula

where r is the radius of the star, and – the radiation of a unit of the star’s surface, rÓ, iÅ, T refer to the Sun, and LÓ = 1. Hence the radii of the Sun.

 

1 The Stefan-Boltzmann law was established by the Austrian physicists J. Stefan (experimentally) and L. Boltzmann.

The results of such calculations of the sizes of luminaries were completely confirmed when it became possible to measure angular diameters of stars by means of the special optical device (stellar interferometer).

Dawns of very high luminosity are called supergiants. Red supergiants are the same in size. Betelgeuse and Antares are hundreds of times larger than the Sun in diameter. More distant from us UU Cepheus is so huge that inside it would house the solar system with the orbits of the planets to the orbit of Jupiter! However, the masses of supergiants are only 30-40 times larger than the mass of the Sun. Therefore, even the average density of red supergiants is thousands of times less than the density of room air.

At the same luminosity, the size of the stars is smaller, the hotter these stars. The smallest among ordinary stars are red dwarfs, their masses and radii are tenths of the solar, and the average density is 10-100 times higher than the density of water. Even smaller than red, white dwarfs, but these are unusual stars.

Close to us and bright Sirius (whose radius is about twice that of the sun) has a satellite orbiting it over a period of 50 years. For this binary star, distance, orbit, and mass are well known. Both stars are white, almost equally hot. Thus, the surfaces of the same area emit the same amount of energy in these stars, but the luminosity of the satellite is 10,000 times weaker than Sirius.

Hence, its radius is 100 times smaller, ie it is almost like the Earth. Meanwhile, its mass is almost the same as that of the Sun! Thus, the white dwarf has a huge density – about 109 kg / m3. The existence of a gas of this density is explained as follows: usually the density limit is the size of the atoms that make up the systems consisting of the nucleus and the electron shell.

At a very high temperature in the bowels of stars and with the complete ionization of atoms, their nuclei and electrons become independent of each other. Due to the enormous pressure of the upper layers, this "crumb" of atoms can be compressed much more strongly than neutral gas.

Theoretically, the existence of stars with a density equal to the density of atomic nuclei is allowed under certain conditions. On the example of white dwarfs, we once again see how astrophysical research expands the idea of ​​the structure of matter; so far, it is impossible to create such conditions in the laboratory as inside the stars.

Therefore, astronomical observations help to develop the most important physical ideas. For example, Einstein’s theory of relativity is of great importance for physics. It leads to several conclusions that can be verified by astronomical data.) One of the conclusions of the theory is that in a very strong gravitational field light oscillations should slow down and the spectral lines should shift to the red end, and this shift is greater the stronger the gravitational field dawn.

The redshift was detected in the first spectrum of the Sirius satellite. It is caused by the action of a strong gravitational field on its surface. Observations have confirmed this and a number of other conclusions of the theory of relativity. Such examples of the close interaction of physics and astronomy are characteristic of modern science.

08/16/2011

Astronomy in antiquity: an idea of ​​the universe. Abstract

Geocentric system of the world. Heliocentric system of the world

It is difficult to say exactly when astronomy was born: we have almost no data relating to prehistoric times. In that distant epoch, when people were completely incapable of nature, there was a belief in powerful forces that supposedly created the world and rule them, for many centuries worshiped the moon, sun, planets. We learn about this from the myths of all peoples of the world.

The first ideas about the universe were very naive, they were closely intertwined with religious beliefs, which were based on the division of the world into two parts – earthly and heavenly. If now every student knows that the Earth itself is a celestial body, then before "earthly" was opposed to "heavenly". It was thought that there was a "heavenly stronghold" to which the stars were attached, and the Earth was taken to be the fixed center of the universe.

Geocentric system of the world

Hipparchus, an Alexandrian scholar who lived in the 2nd century BC. BC, and other astronomers of his time paid much attention to observing the motion of the planets.

These movements seemed to them extremely confusing. In fact, the direction of motion of the planets in the sky as if described in the sky loops. This apparent complexity in the motion of the planets is caused by the movement of the Earth around the Sun get lab report written – because we observe planets from the Earth, which moves itself. And when the Earth "catches up" with another planet, it seems that the planet seems to stop and then move back. But ancient astronomers thought that the planets did make such complex movements around the Earth.

In the 2nd century AD. Alexandrian astronomer Ptolemy put forward his "system of the world." He tried to explain the construction of the universe given the apparent complexity of the movement of the planets.

Considering the Earth spherical, and its size insignificant in comparison with the distance to the planets and especially the stars, Ptolemy, however, after Aristotle, argued that the Earth – the fixed center of the universe.

2021-02-19T12:31:28+00:00

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