Positions, Motions, and Distances. With the construction of larger telescopes it was found that stars are not precisely "fixed." They move at various speeds, measured as changes of direction in fractions of a second of arc per year, where one second of arc is the angular size of a pinhead 183 m (200 yd) away. For all practical purposes most of the faint stars may be regarded as truly fixed as viewed from Earth. They are used as a reference frame for the minute motions of nearby stars, known as proper motion.
Parallax is another apparent motion of nearby stars. It is caused by the Earth's orbit around the Sun. That is, a star seems to shift first one way, then the other, as the Earth moves from 150 million km (93 million mi) on one side of the Sun to 150 million km on the other side. Stellar parallax can be used to determine astronomical distance. If the shift is 1 second of arc each way, the star is about 32 million million km (20 million million mi) from an observer. This distance is called the parsec and is equal to 3.26 light-years, a light-year being the distance that light travels in one year.
Brightness and Luminosity. Star brightness was first estimated by eye, and the brightest stars in the sky were described as "stars of the first magnitude." Later the magnitude scale was defined more accurately: 6th magnitude stars are just 1/100 as bright as 1st magnitude stars; 11th magnitude stars are 1/100 as bright as 6th magnitude, and so on. The magnitude scale is logarithmic. That is, each magnitude corresponds to a factor of 1/2.54, because (1/2.54)5 = 1/100.
Photographs are also used to measure star brightness. With the emulsions available in the early 1900s a blue star that appeared to the eye to have the same brightness as a red star photographed much brighter, because the emulsions were much more sensitive to blue light than to red. Because of this variation, two magnitude scales came into use: visual magnitude (mv) and photographic magnitude (mp). The difference for any one star, of photographic magnitude minus visual magnitude mp - mv , measures the color of that star - positive for red stars, negative for blue.
By using filters and special emulsions, astronomers soon had several other magnitude scales, including ultraviolet and infrared. When photoelectric detectors were introduced, the brightnesses of stars were measured with a photoelectric photometer at the focus of a telescope. Standard colors (wavelengths) of light were adopted, and the symbols (Ts = 30,000 K mv and mp that had been used for visual magnitude and photographic magnitude were changed to V and B, with U for the ultraviolet scale and several other letters for infrared scales.
Measuring the brightness of a star on any of these scales is complicated by the Earth's atmosphere, which absorbs more light when a star is near the horizon. It also absorbs different amounts of the different colors and can change during the night because of changing dust or moisture in the air. Nevertheless, by comparing a star with a standard at the same height above the horizon, astronomers using photoelectric photometers can measure U, B, and V magnitudes with an accuracy of 0.01 magnitude.
Such photometry has provided a great deal of information regarding the temperatures and energy output of stars, but it does not give the total energy output. Each measurement (U, B, V) gives only a fraction of the star's light reaching the Earth. Even if the measurements are combined, they give only the part that is not absorbed as it passes through the Earth's atmosphere. The atmosphere absorbs all light of short wavelengths below ultraviolet and many of the long wavelengths above red. A theoretical correction can be made, based on the star's temperature, to give a "bolometric" magnitude, mb, adding the energy absorbed by the atmosphere. True bolometric magnitudes, however, are measured only from rockets and spacecraft outside the Earth's atmosphere.
From parallax-distance measurements it is possible to calculate the absolute bolometric magnitude, or luminosity, of a star, a measure of its brightness relative to the Sun if it were at the Sun's distance from Earth. It has been found that some stars (giants) are 100,000 times more luminous than the Sun, and one supergigantic star - discovered in 1997 near the center of our Galaxy - is several million times more luminous. Others ( white dwarfs) are 1,000 times less luminous.