The distance to the space object under study is one of the most important characteristics that are determined from astronomical observations. At the same time, there is no universal method for determining distances suitable for all objects under study. Different methods are used in different distance ranges, which often provide only approximate estimates of distance values.

To measure distances between space objects, depending on the situation or problem under consideration, a number of off system units are used in modern astrophysics. This is due to the fact that the range of values under consideration differs by tens of orders of magnitude. The natural measure of distances in the Solar System is the astronomical unit (a.u.)

1 a.u. = 1.5 · 10¹³ cm,

is equal to the magnitude of the semi-major axis of the Earth’s orbit. It was measured by the daily parallax of the planets in the Solar System. The characteristic size of a planetary system is about 100 a.u.

When studying the stars of our stellar system — the Galaxy — and other even more distant objects, it is more convenient to use another unit — parsec (pc). A parsec is the distance from which a segment equal to the major semi-axis of the Earth’s orbit, located perpendicular to the beam of vision, is seen at an angle of 1» (an angular second). Due to the annual motion of the Earth around the Sun, the position of the luminary in the sky, located at a distance of 1 parsec, will shift by 1 angular second from the average position. In astronomy, this phenomenon is called annual parallax, hence the name of the unit of distance — parsec, i.e. parallax per second. Since in the radian measure 1″ ≈ 1/206265, we find that

1 pc = 206265 а.е.≈ 3.1 · 10¹⁸ cm.

Along with the parsec, another unit of distance measurement is widely used in astronomy — the light-year (ly). The light-year is the distance that light travels in one year. Since there are approximately 3.2∙10⁷ c in a year, a light-year is equal to

1 ly ≈ 9.5∙10¹⁷ cm ≈ 1/3.26 pc.

Knowing the annual parallax of the celestial object, expressed in arc seconds π, the distance to the object in parsec is determined by the obvious formula

d = 1/π.

The distances to the nearest stars are a few parsec. Direct determination of distances to stars, based on the measurement of their annual parallax, is limited by the astrometric accuracy of determining the position of stars on the celestial sphere. The maximum distance measured from parallaxes does not exceed 1 kpc.

To determine distances to more distant stars, various indirect methods, collectively known as methods for establishing the scale of distances in the Universe. Many of these methods are based on determining the photometric distance from a luminous object (e.g., a star) from a photometric value of the flux density the accepted value of the radiation energy flux density F, if the luminosity of a luminous object (the amount of energy emitted per star) is the same as that of a star (amount of energy emitted per second) of the object L is known from other considerations.
Assuming spherical symmetry of radiation, it is not difficult to establish a relationship between the energy flux density of radiation and luminosity:

F=L/4 πd² .

Hence we obtain the expression for the distance to the object

d2= L/4 πF.

An important class of objects, the luminosity of which is reliably estimated from the observations are cepheids — variable stars. For Cepheids, the dependence between the period of variability dependence between the period of variability of their luminosity and luminosity. This allows us to determine the luminosity the observed period to determine the luminosity of the Cepheids L, and the distance d by the measured flux of radiation F — distance d. By means of this method, distances as far as up to 10000000 pc.

The distance from the Sun to the center of the Galaxy is 8000 pc, the size of a typical galaxy is about 10000 pc.
of a typical galaxy is about 10000 pc. The nearest galaxies — the galactic satellites — are located at distances from 55000 pc (the Large and Small Magellanic Clouds) to 640000 pc pc (Andromeda Nebula). The distance to the center of galaxy clusters, at the edge of the galaxy. Galaxy is about 15000000 pc. Another nearby galaxy cluster is located
at a distance of 80000000 pc.

The distances r to distant galaxies are determined by the redshifts of spectral lines

z= (λ- λ₀)/ λ₀ ,

caused by galaxies scattering, i.e., moving away from each other due to the expansion of the Universe.
Here λ₀ is the wavelength of light emitted by a distant cosmic source, λ is the wavelength of light registered by an Earth observer. The rate at which is determined by Hubble’s law
v = H₀r,
where
H₀ ≈ 70 km/(s*Mpc)
— is the present day value of the Hubble parameter, v is the speed of galaxy removal at a distance r from the observer.