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most luminous stars can be seen at great distances, whereas the intrinsically faint stars can be observed only if they are relatively close to Earth.
    The brightest and nearest stars fall roughly into three categories: (1) giant stars and supergiant stars that are tens or even hundreds of solar radii and extremely low average densities—in fact, several orders of magnitude less than that of water (one gram per cubic centimetre [1 cubic centimetre = .06 cubic inch]); (2) dwarf stars ranging from 0.1 to 5 solar radii and with masses from 0.1 to about 10 solar masses; and (3) white dwarf stars, with masses comparable to that of the Sun but dimensions appropriate to planets, meaning that their average densities are hundreds of thousands of times greater than that of water.
    These rough groupings of stars correspond to stages in their life histories. The second category is identified with what is called the main sequence and includes stars that emit energy mainly by converting hydrogen into helium in their cores. The first category comprises stars that have exhausted the hydrogen in their cores and are burning hydrogen within a shell surrounding the core. The white dwarfs represent the final stage in the life of a typical star, when most available sources of energy have been exhausted and the star has become relatively dim.
    The large number of binary stars and even multiple systems is notable. These star systems exhibit scales comparable in size to that of the solar system. Some, and perhaps many, of the nearby single stars have invisible (or very dim) companions detectable by their gravitational effects on the primary star; this orbital motion of the unseen member causes the visible star to “wobble” in its motion through space. Some of the invisible companions have been found to have masses on the order of 0.001 solar mass or less, which is in the range of planetary rather than stellar dimensions. Current observations suggest that they are genuine planets, though some are merely extremely dim stars (sometimes called brown dwarfs). Nonetheless, a reasonable inference that can be drawn from these data is that double stars and planetary systems are formed by similar evolutionary processes.

S TELLAR P OSITIONS
    Even the basic measurement of where a star is in the sky can yield much useful information. Such observations can tell if a star is related to its neighbours and how it moves through the Galaxy.
B ASIC M EASUREMENTS
    Accurate observations of stellar positions are essential to many problems of astronomy. Positions of the brighter stars can be measured very accurately in the equatorial system (the coordinates of which are called right ascension [α, or RA] and declination [δ, or DEC] and are given for some epoch—for example, 1950.0 or, currently, 2000.0). Fainter stars are measured by using photographic plates or electronic imaging devices (e.g., a charge-coupled device, or CCD) with respect to the brighter stars, and finally the entire group is referred to the positions of known external galaxies. These distant galaxies are far enough away to define an essentially fixed, or immovable, system, whereas positions of both the bright and faint stars are affected over relatively short periods of time by galactic rotation and by their own motions through the Galaxy.
S TELLAR M OTIONS
    Accurate measurements of position make it possible to determine the movement of a star across the line of sight (i.e., perpendicular to the observer)—its proper motion. The amount of proper motion, denoted by μ (in arc seconds per year), divided by the parallax of the star and multiplied by a factor of 4.74 equals the tangential velocity,
V T
, in kilometres per second in the plane of the celestial sphere.
    The motion along the line of sight (i.e., toward the observer), called radial velocity, is obtained directly from spectroscopic observations. If λ is the wavelength of a characteristic spectral line of some atom or