The stars

When we look at the clear, moonless night sky, we can see thousands of small dots of light, almost all of which are stars. The few bright objects that are not stars are the planets of the solar system. There are, however, easily observable differences between the planets and true stars: all stars twinkle, whereas the planets do not (unless the air in the earth’s atmosphere is extremely turbulent). And, by looking at the sky on successive nights, the planets can be seen to have moved by a relatively large amount when compared with the apparently stationary background of stars. In addition, most of the planets are close enough to earth to appear as disks (or sometimes crescents, depending on their phase) when viewed even with low-powered binoculars. A more fundamental difference is that stars, unlike the planets, generate their own energy (emitted in the form of light and other radiation) by nuclear fusion. Planets are visible only because they reflect sunlight.
The sun is our nearest star, situated at an average distance from the earth of about 92,960,000 miles (149,600,000 kilometers) or one astronomical unit. The next nearest star is Proxima Centauri, slightly more than 25 million million miles (40 million million kilometers).
Despite the immense distances to the stars, and the fact that we cannot see the surface of any star except the sun, we can nevertheless determine some of their individual characteristics. These would be temperature, size, chemical composition, brightness (luminosity), and their groupings. Some stars, such as the sun, are solitary, whereas others may be part of multiple star systems, associations, or stellar clusters.

Stellar parallax can be used to determine the distances to relatively close stars. The angle to the nearby star is measured when the earth is at one extreme of its orbit, and again when the earth is at its other orbital extreme. Since the distance between these orbital extremes is known, the distance to the star can be calculated by trigonometry.

Distances to the stars

It is very difficult to measure accurately the distances to stars. This is partly because they are so large and partly because of the apparent smallness of the stars when observed from earth. Moreover, the observed brightness of a star is not in itself a reliable indicator of distance. Stars that appear to be equally bright seem also to be equally distant. Thus, an extremely remote, but intrinsically very bright, star may seem to be the same distance from earth as a much closer, but fainter star.
Despite these difficulties, stellar distances can be measured. There are two main ways of doing this. One is by using the stellar parallax effect, the other by comparing the unknown star with a nearer one whose distance is known. The stellar parallax method relies on the effect whereby a relatively near object appears to move in relation to a distant background as the observer moves. In astronomy, the relatively close object is a “nearby” star (whose distance is to be found), which is observed in relation to the background of more distant stars. The observer uses the movement of the earth in its orbit as a known, sufficiently large change in position. When the earth is at one side of its orbit, the angle to the nearby star is measured. This measurement is repeated six months later, when the earth is on the other side of its orbit. The distance to the nearby star can then be calculated by simple trigonometry.
But the angular changes for even nearby stars are minute. Proxima Centauri, for example, has a parallax angle of only 0.75 of a second of arc, equivalent to the angle subtended by a small coin at a distance of about 2,000 yards (1,800 meters). This parallax method is practicable only for those stars that are less than about 300 parsecs (978 light-years) away. For this reason, distances to more remote stars—by far the majority—are determined using the comparative method.
Analysis of the light from stars enables them to be classified into several different types. The unknown star is first classified and is then compared with a nearby star of the same type. This second star’s intrinsic brightness and distance has previously been determined by means of stellar parallax. Working from the assumption that stars of the same type have the same intrinsic brightness, the distance to the unknown star can be determined from the difference between its intrinsic brightness and its apparent brightness.
Another method of assessing stellar distances is to study the periodic variations in brightness of variable stars (such as Cepheid variables) or, more rarely, the brightness of exploding stars (supernovae).

The Big Dipper is a familiar star pattern in the Northern Hemisphere, being visible throughout the year. To the naked eye its individual stars appear to be equally— and infinitely—distant. In fact, the farthest star Alcaid (tj Ursa Major) is 210 light-years away from the earth, more than 3 times the distance to the nearest star Megrez (8 Ursa Major), which is 70 to 80 light-years away.

Magnitude

The absolute, or intrinsic, brightness of a star can be determined only when its apparent brightness and distance are known. Once this is done for a “nearby” star of one particular type, the distances to other stars of the same type (and brightness) can be calculated.
There are enormous differences in the intrinsic brightnesses of different stars—the brightest star known is about 10 billion times more luminous than the faintest. So it is more convenient to refer to the brightness of stars in terms of their apparent magnitudes—that is, their relative apparent brightness.
The ancient astronomers arranged the stars visible to the naked eye on a six-point scale of magnitude: first magnitude for the brightest stars down to sixth magnitude forthose that were only just visible. In the nineteenth century, it was discovered that the brightest stars are about 100 times brighter than the faintest stars visible to the naked eye—a difference of only 5 magnitudes on the original scale—so a new scale of magnitude was devised. On this new scale, which is the one used today, a difference of 1 magnitude between stars means that one star is 2.512 (the fifth root of 100) times brighter (or fainter) than a star of the next magnitude. The scale ranges from +28.0 for the faintest star observable with the space telescope, to —27.0 for the brightest star (which is the sun).
The absolute magnitude of a star is a measure of its intrinsic brightness and is defined as the apparent magnitude a given star would have if viewed from a distance of 10 parsecs.

The apparent magnitude of an astronomical object is a measure of how bright that object appears to be, irrespective of its intrinsic (or absolute) magnitude. On the magnitude scale, a difference of one magnitude equals a difference in brightness of 2.512 times. The brighter an object, the lower its magnitude number. For example, the sun— the brightest celestial object—has an apparent magnitude of —27.0.

Star color

Even with the naked eye it is possible to see that stars vary in color: for example, Aldebaran (Alpha Tauri) is orange; Betelgeuse (Alpha Orionis) is red; Rigel (Beta Orionis) is blue; Sirius (Alpha Canis Majoris) is white; and our sun and Capella (Alpha Aurigae) are yellow. From our experience of hot objects on earth, we know that color differences reflect differences in temperature. Because the physical laws of radiation are thought to apply to all objects, we can assume that the different colors of the stars also signify temperature differences. Thus, blue stars are hotter than white stars which, in turn, are hotter than red stars.
The subtle variations in stellar colors and, therefore, temperatures can be assessed by observing the stars through colored filters. When viewed through a red filter, for example, a red star appears bright red, whereas a blue star is barely visible. Such precise color analyses are not made visually but by using photographic plates or standard filters attached to photo-multipliers.

Thousands of stars can be seen on a clear night Most of those visible to the naked eye lie in the Milky Way, which appears as a broad, relatively faint band that divides the sky in two. Viewed through a telescope, the night sky looks even more impressive. This photograph, for instance, shows the North American Nebula as it appears through a telescope; to the naked eye, however, the nebula is only just visible.

Spectral classes

The surface temperatures of stars (ascertained from their colors) can be used to classify them into a number of spectral classes. These classes are denoted by letters of the alphabet and—from hottest to coolest—are O, B, A, F, G, K, and M. For example, O-type stars are blue and very hot, with temperatures above 37,000° F. (20,500° C); A-type stars are white and have temperatures of about 17,000° F. (9,430° C); and M-type stars are red and relatively cool, with temperatures of only about 5,500° F. (3,000° C).
Each of the spectral classes is numerically divided into ten subcategories, with zero denoting the hottest stars within the class through to nine for the coolest. Thus the hottest stars are 00, followed by 01, 02 through to 09 for the coolest stars, within class 0; the next coolest category is B0, followed by Bl, B2, and so on down through each of the lettered classes to M9, which is the coolest category of all. In this system, the sun is a G2 star; it has an effective surface temperature of about 10,000° F. (5,500° C).

rom their colors) can be used to classify them into a number of spectral classes. These classes are denoted by letters of the alphabet and—from hottest to coolest—are O, B, A, F, G, K, and M. For example, O-type stars are blue and very hot, with temperatures above 37,000° F. (20,500° C); A-type stars are white and have temperatures of about 17,000° F. (9,430° C); and M-type stars are red and relatively cool, with temperatures of only about 5,500° F. (3,000° C).
Each of the spectral classes is numerically divided into ten subcategories, with zero denoting the hottest stars within the class through to nine for the coolest. Thus the hottest stars are 00, followed by 01, 02 through to 09 for the coolest stars, within class 0; the next coolest category is B0, followed by Bl, B2, and so on down through each of the lettered classes to M9, which is the coolest category of all. In this system, the sun is a G2 star; it has an effective surface temperature of about 10,000° F. (5,500° C).

Stellar sizes

The sizes of stars vary considerably, from supergiant stars several hundred times larger than the sun, to dwarf stars that are much smaller than the earth. The sun itself is a medium-sized star, with a diameter of about 865,000 miles (1,392,000 kilometers), nearly 109 times the diameter of the earth. In contrast, Antares—one of the largest stars known—has a diameter about 330 times that of the sun, whereas van Maanen’s Star—one of the smallest stars—is only about 6,100 miles (9,800 kilometers) across, considerably less than onehundredth of the sun’s diameter.
With the exception of the sun, the diameters of stars are difficult to measure. Some can be measured by lunar occultation, which involves analyzing the light from a star in the time it takes for the star to be hidden by the moon as the moon moves across the sky. But this method can be used only for those relatively few stars that lie in the zodiac and can be obscured by the moon.
Another technique, called speckle interferometry, is more widely applicable. It involves photographing the unknown star and then subjecting the photograph to computer analysis.

The diameters of stars vary greatly, from a few thousand miles in dwarf stars to hundreds of millions of miles in super giants. So vast are the super-giants that Antares, for example, would extend as far as Jupiter if it were where our sun is. But the diameter of a star is not a reliable indication of its mass. Some extremely large stars consist mainly of gas and, therefore, have relatively low masses; some dwarf stars are very dense and are more massive than much larger stars.

The Hertzsprung-Russell diagram

The most informative way of showing differences in the brightness and surface temperatures of stars is with a special type of graphical diagram called a Hertzsprung-Russell (H-R) diagram. This method was developed independently by the Danish astronomer Ejnar Hertz-sprung in 1911 and the American astronomer Henry Russell in 1913. In the H-R diagram, the absolute magnitudes of stars are plotted against their temperatures (or spectral class or color, all of which are equivalent). When this is done, it is found that most stars lie within a wide band—called the main sequence—that runs from the upper left to the lower right of the diagram. The sun is a typical main-sequence star and lies about midway along the main sequence.
Stars can be classified into characteristic types according to their positions on the H-R diagram. For example, the stars outside the main sequence, nearest the top of the diagram, are very large; these types of stars are called super giants, in contrast, stars toward the bottom of the diagram are very small; these are called white dwarfs. Within the main sequence itself, there is a general increase in stellar mass from the lower right corner up to the top left.

Chemical composition

There is a surprisingly high degree of uniformity in the chemical composition of stars, and it is necessary to examine a great many to find any striking variations from the norm. A typical star, such as the sun, consists almost entirely of hydrogen and helium. Spectral analysis of the sun’s atmosphere shows that it comprises 75 per cent hydrogen, 25 per cent he

lium, and 1 to 2 per cent other elements. But spectral analysis can measure only the abundance of elements in the surface layers of stars, and more indirect methods must be used to determine the composition of their interiors.
Evidence about the composition of stellar interiors has come mainly from studies of the occurrence of the extremely rare element technetium in stellar atmospheres. This element is radioactive and decays rapidly, yet has been detected in the atmosphere of certain giant stars. From this it has been concluded that technetium is being continually created within these stars. Because technetium can be formed only by the nuclear transformation of other elements, there must, therefore, be a decrease in these other elements, which indicates that the stars continuously change their internal compositions.

The Hertzsprung-Russell (H-R) diagram illustrates the relationship between stars’ absolute magnitudes (a measure of their intrinsic brightness and defined as the apparent magnitude a given star would have if viewed from a distance of 10 parsecs) and their spectral classes (or temperatures). On the H-R diagram, stars can be classified into four main types: supergiants, which are extremely large and highly luminous (and therefore have low absolute magnitudes); giants, which are slightly smaller and less luminous than supergiants; main-sequence stars (by far the largest group), which are mediumsized stars of a wide range of temperatures and luminosities; and white dwarfs, which are small and dim and also tend to be relatively hot.