The distance of a star can be found by measuring its parallax, a small change in the position of the star when viewed from opposite sides of the Earth's orbit. If the distance to a star (d) is given in parsecs and parallax (p) is measured in seconds of arc, then d = 1/p.
The motions of the stars through space cause their positions in the sky to change slowly with time. The proper motion of a star is the rate at which a star's position changes. The motion of the Sun relative to the other stars causes stars to move apart in the direction toward which the Sun is moving and to converge in the opposite direction.
The apparent brightnesses of stars are described by the magnitude system, in which increasingly fainter stars are assigned increasingly larger apparent magnitudes. Each increase of one magnitude corresponds to a decrease in brightness of 2.512 times.
Absolute magnitude describes the intrinsic brightness of a star. The absolute magnitude of a star does not depend on the star's distance, but its apparent magnitude does. Apparent magnitude (m) and absolute magnitude (M) are related to each other and distance by
m = M + 5 log (d/10).
Atoms produce dark-line spectra by absorbing radiation from a continuous source. This happens when an electron in an atom absorbs a photon and jumps to a higher energy level. When electrons jump to lower energy levels, they emit photons and produce bright-line spectra.
The appearance of the spectrum of a star is determined mostly by the star's temperature. Temperature controls the numbers of atoms with electrons in various energy levels and thus the strengths of absorption lines arising from those energy levels. In order of descending temperature, the stellar spectral classes are O, B, A, F, G, K, and M.
Because of the Doppler effect, the observed wavelengths of emission and absorption lines in a stellar spectrum depend on the motion of the star relative to the Earth. The Doppler effect makes it possible to use the observed wavelengths of spectral lines to determine how fast a star is moving toward or away from the Earth.
An H-R diagram is a plot of the luminosities of stars against their temperatures. In an H-R diagram the points representing stars tend to be concentrated in the main sequence, giant, supergiant, and white dwarf regions. These regions correspond to long-lived stages in the evolution of stars.
The masses of stars can be found by determining the orbital motion of two stars about each other in a binary system. For stars, luminosity (L) increases with mass (M) according to the massluminosity relation, L = M3.5, where L and M are expressed in terms of the luminosity and mass of the Sun.
