During the early decades of the 20th century Annie J. Cannon at Harvard University examined thousands of stellar spectra. Without concern for the actual atmospheric gases or temperatures Cannon classified each spectrum as A, B, C, . . . S, depending on the number of absorption lines. Class A has few strong lines, class F has more, and classes M to S have bands, which are many lines close together, produced by molecules.

Later studies showed that Cannon's classes are a measure of surface temperature (Ts) in the sequence O, B, A, F, G, K, M, R, N, S. This measurement is based partly on physicist Max Planck's formula, which gives the relative emissions of various colors from a hot body. A cool star emits most of its light in the red; a hot star emits most of its light in the blue. A measurement of the ratio of blue to red light coming from a star (its color index) determines its temperature. O stars are hot, with surface temperatures of 30,000 K; A stars have surface temperatures of 10,000 K; G stars, such as the Sun, have surface temperatures of of 6,000 K; and M stars have surface temperatures of 3,000 K. Other spectrographic measurements of absorption lines and emission lines help to confirm or modify this so-called color temperature.

From 1911 to 1913, Ejnar Hertzsprung and H. N. Russell first plotted the luminosity (L) versus the surface temperature (Ts) of stars, using as a measure of temperature the spectral types determined by Cannon. The Hertzsprung-Russell diagram first showed that highly luminous stars are mostly of classes O and B, with helium lines andTs=25,000 K surface temperatures of 25,000 K, whereas low-luminosity stars are mostly of class M andTs=3,000 K have surface temperatures of 3,000 K.

Size. Once the temperature and the bolometric luminosity of a star are known, its size can easily be calculated. Planck's formula gives the total emission of radiant energy per unit area of a hot body's surface at each temperature. From the bolometric luminosity, the total energy emitted is known, and from the temperature, the radiant energy emitted per square centimeter is known. The ratio gives the number of square centimeters, from which the radius of the star can be calculated. This rough calculation shows that the radii of stars vary from 1/100 of that of the Sun for white dwarfs to 400 times that of the Sun for supergiants. The radius of a nearby star can also be measured directly with an interferometer on a telescope. Astronomers theorize that brown dwarfs, objects with a starlike composition but too small to initiate nuclear reactions, may also exist in the universe. This would help to some degree to account for the missing mass of cosmology theories. Once the temperature and the bolometric luminosity of a star are known, its size can easily be calculated. Planck's formula gives the total emission of radiant energy per unit area of a hot body's surface at each temperature. From the bolometric luminosity, the total energy emitted is known, and from the temperature, the radiant energy emitted per square centimeter is known. The ratio gives the number of square centimeters, from which the radius of the star can be calculated. This rough calculation shows that the radii of stars vary from 1/100 of that of the Sun for white dwarfs to 400 times that of the Sun for supergiants. The radius of a nearby star can also be measured directly with an interferometer on a telescope. Astronomers theorize that brown dwarfs, objects with a starlike composition but too small to initiate nuclear reactions, may also exist in the universe. This would help to some degree to account for the missing mass of cosmology theories.

Mass. More than half of all stars are in binary (two-star) or multiple-star systems. About 100 orbits in such systems have been measured accurately, providing perhaps the most important characteristic of a star: its mass. Using Newton's laws of gravitation, the mass of a star in a binary system can be calculated from its orbit size and the period of the orbit. If the binary stars eclipse each other, this situation also gives estimates of each star's diameter. Orbits of the planets show that the Sun's mass is 2 X 1033 g (2 billion billion billion tons, or about 333,000 times the Earth's mass). Orbits of binary stars show that some stars (giants) are 40 times the mass of the Sun, and others (dwarfs) only 1/10 the mass of the Sun.

The mass of a star is also related to its luminosity. The mass-luminosity relation states that the luminosity is approximately proportional to mass3.5 raised to the power of 3.5. A star twice the mass of the Sun will have luminosity 23.5, or 11.3 times the Sun's luminosity. This fact, together with the temperatures and compositions of stars, is closely related to theories of stellar structure. Two systematic features in the motions of stars also relate to their masses. In many groups and clusters of stars, the stars have similar motions and similar Doppler shifts in the lines of their spectra. The smaller motions of stars within a cluster show the cluster's total mass, and the motions can also be used statistically to determine its distance.

Starspots. Starspots (cooler regions on the surface of stars, similar to the familiar sunspots) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry. The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. Astronomers have also been able to detect apparent granulation patterns on some stars. Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler materials just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations "starpatches." Starspots (cooler regions on the surface of stars, similar to the familiar sunspots) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry. The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. Astronomers have also been able to detect apparent granulation patterns on some stars. Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler materials just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations "starpatches."

More than half of all stars are in binary (two-star) or multiple-star systems. About 100 orbits in such systems have been measured accurately, providing perhaps the most important characteristic of a star: its mass. Using Newton's laws of gravitation, the mass of a star in a binary system can be calculated from its orbit size and the period of the orbit. If the binary stars eclipse each other, this situation also gives estimates of each star's diameter. Orbits of the planets show that the Sun's mass is 2 X 1033 g (2 billion billion billion tons, or about 333,000 times the Earth's mass). Orbits of binary stars show that some stars (giants) are 40 times the mass of the Sun, and others (dwarfs) only 1/10 the mass of the Sun.

Mass. More than half of all stars are in binary (two-star) or multiple-star systems. About 100 orbits in such systems have been measured accurately, providing perhaps the most important characteristic of a star: its mass. Using Newton's laws of gravitation, the mass of a star in a binary system can be calculated from its orbit size and the period of the orbit. If the binary stars eclipse each other, this situation also gives estimates of each star's diameter. Orbits of the planets show that the Sun's mass is 2 X 1033 g (2 billion billion billion tons, or about 333,000 times the Earth's mass). Orbits of binary stars show that some stars (giants) are 40 times the mass of the Sun, and others (dwarfs) only 1/10 the mass of the Sun.

The mass of a star is also related to its luminosity. The mass-luminosity relation states that the luminosity is approximately proportional to mass3.5 raised to the power of 3.5. A star twice the mass of the Sun will have luminosity 23.5, or 11.3 times the Sun's luminosity. This fact, together with the temperatures and compositions of stars, is closely related to theories of stellar structure. Two systematic features in the motions of stars also relate to their masses. In many groups and clusters of stars, the stars have similar motions and similar Doppler shifts in the lines of their spectra. The smaller motions of stars within a cluster show the cluster's total mass, and the motions can also be used statistically to determine its distance.

Starspots. Starspots (cooler regions on the surface of stars, similar to the familiar sunspots) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry. The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. Astronomers have also been able to detect apparent granulation patterns on some stars. Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler materials just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations "starpatches." Starspots (cooler regions on the surface of stars, similar to the familiar sunspots) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry. The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. Astronomers have also been able to detect apparent granulation patterns on some stars. Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler materials just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations "starpatches."

Starspots. Starspots (cooler regions on the surface of stars, similar to the familiar sunspots) are now known to exist on a number of relatively nearby stars. The disks of such stars can be mapped to some degree to show areas of differing temperature, using the technique known as speckle interferometry. The giant star Betelgeuse was observed in this manner as long ago as the mid-1970s. Astronomers have also been able to detect apparent granulation patterns on some stars. Such patterns on the Sun are produced by convection, or the rising and falling of hotter and cooler materials just below the visible surface. Analysis of stellar spectra to yield this kind of detail requires the use of supercomputers. A larger, different kind of surface variation on stars has been reported by some astronomers, who call these variations "starpatches."