Early astronomers and navigators, from about the seventh century A.D., used the astrolabe to find or define the positions of stars. The original instrument was designed by the Arabs, using ingenious geometry at a time when spherical trigonometry was unknown. Star positions were given in terms of altitude (angle above the horizon) and azimuth (distance around a horizon circle). The astrolabe could also be used to tell the time by the stars or the sun. It gave devout Muslims the prescribed times for prayers and provided a reliable sun or star compass for travellers and navigators.
The medieval astrolabe was, in effect, a sort of calculator for transforming the coordinates of right ascension and declination of any star at a specific time into its corresponding altitude and azimuth. This capability was of great convenience in finding out just where to look in the sky for a particular star. The circular plate representing the ecliptic was divided into 12 segments, often represented by the signs of the zodiac, which served also as calendar dates.
The modern equivalent of the astrolabe and much more convenient to use is the planisphere. The example illustrated below is designed for use in the Northern Hemisphere at latitude 51 ° N. It consists of a star chart using a polar projection, with all the dates of the year inscribed around the edge (corresponding to the zodiacal signs on an astrolabe). Computer-plotted altitude and azimuth curves, bounded by a horizon circle, are printed on a transparent overlay, which can be rotated over the star chart. All stars that fall within the horizon circle should be visible (on a clear night) at the time and date set on the outer ring. A transparent cursor is calibrated in angles of declination above and below the celestial equator.
Modern star charts are drawn with respect to coordinates of right ascension and declination. Often a computer is used to plot the star positions, using information from one of the major observatories. The charts on these pages show all stars of magnitude to 5.0 and of declination 50° and larger (with positive declination for the Northern Hemisphere and negative declination for the Southern Hemisphere). All are visible to the naked eye. An indication of magnitude is given by the size of the spot. The largest spots represent a magnitude of 0.0, and the smallest spots represent magnitude 5.0.
The charts also indicate the official boundaries of the constellations, whose names in conjunction with Greek letters or numbers are the basis of the systematic naming of the stars. Some stars also have their own names, given to them over the centuries by various astronomers since the time of the Greeks and Arabs. For example, the two “pointers” in the constellation Ursa Major (the Big Bear) are called by the names Dubhe and Merak. On a star chart they are labelled a and fi (and termed Alpha Ursae Majoris and Beta Ursae Majoris). They are located at right ascension 11 hours and declination of +62° and +56°, respectively.
The northern sky
Polaris (the polestar) lies close to the northern celestial pole and is part of the constellation Ursa Minor (the Little Bear). Its nearest prominent neighbor, Kochab (Beta Ursae Minoris), forms another point in the same constellation. Both are of second magnitude. Ursa Major contains several bright stars, the most prominent being Alcaid and Alioth, both in the “handle,” and Dubhe, the bright orange “pointer” to the polestar. Ursa Minor and Ursa Major give the most easily recognized orientation in the northern sky. From them it is easy to locate Arcturus (magnitude —0.1) in Bootes by following the curve of the “handle” of the Big Dipper. Arcturus is slightly orange in color.
Just as the two “pointers” in Ursa Major can be used to locate Polaris, so the other two stars in the quadrilateral part of the constellation point away from the polestar toward Regulus (Alpha Leonis), the blue-white first magnitude star that is the brightest star in Leo. Between Regulus and the Milky Way are the two bright stars Castor and Pollux, Alpha and Beta Geminorum respectively. Castor is of second magnitude and is a multiple star; the orange Pollux is of first magnitude. An imaginary line, drawn from Pollux through the third bright star in Gemini, the second magnitude Alhena, and across the Milky Way, will locate the giant, red variable Betelgeuse, in Orion. This is easily identified by the three stars Beta, Epsilon, and Zeta Orionis, that form Orion’s belt. The brilliant Rigel (Beta Orionis), of magnitude 0.1, is on the opposite side to Betelgeuse (Alpha Orionis).
Cassiopeia, like Ursa Major, is circumpolar in the Northern Hemisphere and so is another useful locator. The small double zig-zag of stars can be found in the Milky Way on the opposite side of Polaris to Ursa Major. If the line from Polaris is continued beyond Cassiopeia, Andromeda can be identified. This is the location of the spiral galaxy M31 (NGC 224), estimated to be more than 2 million light-years away.
Between Cassiopeia and Gemini, along the path of the Milky Way, are Perseus and Auriga. Nearer to Cassiopeia, Perseus contains an eclipsing binary star, Algol (Beta Perseii), the magnitude of which varies from 2 to 3.5. Auriga, between Perseus and Gemini, contains Capella (Alpha Aurigae), of magnitude 0.1 and one of the brightest stars in the sky. It is a giant star of the same spectral type as our sun, but 46 light-years away.
Adjoining Auriga is Taurus, in which the central star is the orange, first magnitude Al-debaran (Alpha Tauri). Close to Aldebaran is the open cluster of the Hyades and, beyond this, the bright open cluster of the Pleiades.
On the opposite side of Cassiopeia to Perseus and Auriga is Cygnus, a beautiful constellation in the shape of an X. The leading star is Deneb (magnitude 1.3), which, with Altair in Aquila, and Vega in Lyra, makes up the so-called Summer Triangle. Vega (magnitude 0) has a blue color that can be observed with the naked eye. First magnitude Altair can be identified by its brightness and also by the two less bright stars beside it.
The southern sky
Crux Australis, the Southern Cross, is the orientation point in the southern sky, although it is not in fact at the southern pole, it is a small constellation, more kite-shaped than cruciform, of four stars all of first or second magnitude. Alpha Crucis is a binary, and Gamma Crucis is a red giant
Adjacent to Crux are three constellations that were formerly one: Carina (keel), Puppis (poop), and Vela (sail) of the Argo. Carina stretches away from Crux to its largest star, Canopus, a supergiant of magnitude —0.7. Beyond Puppis, and close to the Milky Way, can be seen Sirius, the Dog Star, brilliant leader of Canis Major, with a magnitude of —1.4.
Close to Crux is one of the most brilliant constellations, Centaurus, the leader of which is the binary Alpha Centauri (magnitude —0.3), the nearest bright star to earth, only 4.3 light-years away. Also associated with Centaurus is the outstanding globular cluster Omega Centauri (NGC 5139). On the other side of Alpha Centauri is the easily identified Southern Triangle, with its bright orange leader. Farther along the Milky Way, moving away from Crux, is Scorpius, with the enormous red giant Antares at its heart. A diameter of 300 million miles (480 million kilometers) has been calculated for this star.
Most remarkable of the “Southern Birds” is Grus, the Crane, with its bluish Alpha and orange Beta, both of second magnitude. The sweep of the body of Grus points toward the spectacular Small and Large Magellanic clouds (Nebecula Minor and Major), some 200,000 light-years from earth. Apart from the spiral nebula in Andromeda, these are the most distant heavenly bodies that can be seen by the unaided eye. Also near the imagined flight path of Grus is the brilliant star Achernar (magnitude 0.5), in Eridanus.
Distances of stars
Early astronomers found it extremely difficult to estimate the distances to the stars. Some stars (those nearest the earth) have different angles with distant stars when they are measured on two occasions, six months apart (when the earth is on opposite sides of its orbit around the sun). Thus, the angles are measured from each end of a baseline approximately 190 million miles (300 million kilometers) long. This phenomenon, in which relatively near stars appear to move in relation to the background of more distant stars, is called parallax. For example, a star with a parallax of 1 second of arc is 3.26 light-years away, a distance known in astronomy as 1 parsec. A light-year is the distance light travels in one year, equal to 5.88 trillion miles (9.46 trillion kilometers).
Most stars are too far away to exhibit detectable parallax, and at least for the purposes of amateur astronomy, their positions can be regarded as fixed. But modern sophisticated instruments in major observatories are capable of measuring star distances with increasing accuracy. They are sufficient to reveal that, over the years, some stars do show a very small proper motion. For this reason, star atlases and catalogues have to be updated every few years. This real movement of the stars in our galaxy (their proper motion) is quite separate from the apparent small changes in position that result from the procession (“wobble”) of the earth’s axis and the recession of the First Point in Aries (the vernal equinox).
Star positions were well and accurately known before the invention of the telescope. But the orbits and positions of the planets, or “wanderers” as they were once called, could not be accurately accounted for. Therefore, they could not be inscribed on an astrolabe or plotted on a star chart. Understanding came with the revolutionary work of Galileo, Brahe, and Kepler which, together with Newton’s contribution, finally swept away the Greek idea of an earth-centered universe and established the present model of the solar system.
Kepler worked out that the orbits of the planets are elliptical (and from this assumption derived his laws of planetary motion), but had no knowledge of gravity and the physical basis for the orbits. He assumed that some mystical force or “magnetic threads” held the planets in their orbits.
Then, in 1687, with remarkable intuition, Newton postulated the existence of a universal force of gravity. He explained how gravity not only attracts all objects toward the earth, but also exists between the sun and the planets; between the earth and the moon; and indeed between any two masses. The Greeks had simplified celestial mechanics according to the simple doctrine that “matter behaves according to nature.” This view was unarguable, but it stifled scientific inquiry. Newton was able to formulate, in mathematical terms, the basic laws of motion. With these, he was able to verify Kepler’s laws mathematically and to apply them to the orbits of planets and their moons, all using the single law of gravitational attraction. This fundamental law states that the gravitational attractive force between any two objects is proportional to the product of their masses, and inversely proportional to the square of the distance between them. The same law governs the orbits of artificial satellites and space probes, which are so much a part of the twentieth century.