CHAPTER III.
HOW THE POSITIONS OF THE HEAVENLY BODIES ARE DEFINED.
TWO MEASUREMENTS REQUISITE.—In order to make a more precise study of the movements of the heavenly bodies, it is essential that we should have some very definite means of specifying their positions upon the celestial sphere. To define the position of any object, at least two measurements are required. If, for example, one wishes to draw attention to a particular letter on the page of a book, it is only necessary to say that it is so many lines from the top, and a certain number of letters from the end of the particular line on which it lies. In the same way, latitude and longitude sufficiently indicate the situation of a place on the surface of the earth, and similar measures can be employed to indicate the places of the heavenly bodies.
ALTITUDE AND AZIMUTH.—The horizon and zenith at any place—being in a constant position with reference to the earth—may be utilised for indicating the positions of external bodies. We may say, for instance, that at noon on June 24, the sun, as seen from London, is 62° above the horizon, or 28° from the zenith. Technically, the former is called the _altitude_ of the sun, being the angular distance above the horizon, while the latter measure is called the _zenith distance_.
[Illustration:
FIG. 11.—_Altitude and Azimuth._ ]
We may next note that an object, besides having a certain altitude, is a certain number of degrees from the north, south, east, or west points, measured horizontally; if we reckon from the north point through E, S, and W, from 0° to 360°, such a horizontal measurement is called _azimuth_; if reckoned north or south of the east or west points it is called the _amplitude_ of the body. Fig. 11 illustrates these terms. In this diagram the observer is placed at O, N S and E W respectively representing a north and south, and an east and west line in the horizon; the point Z is the zenith, and S a heavenly body. A vertical circle drawn from Z through S will meet the horizon at a point A. The azimuth of S is thus the angle N O A, and its amplitude is the angle E O A, while the altitude of S is simply the angle A O S. Measurements of altitude and azimuth are made by means of an instrument called the altazimuth, an account of which will be found on page 202.
DECLINATION.—Altitude and azimuth only specify the position of a star for a particular place at a particular time. A better system is evidently one which is independent of the observer’s situation on the earth. Of the two measurements required, one is readily decided upon; we can say that the sun, or star, or other heavenly body is a certain number of degrees from the north celestial pole; or, what is just as good, we can state the number of degrees north or south of the celestial equator, which lies midway between the poles. The former measurement gives what is called the _north polar distance_ of the star, and the latter its _declination_.
RIGHT ASCENSION.—Just as the latitude of a place on the earth does not tell whether it is in Europe or North America, so declination alone fails to locate a heavenly body. We must have some measurement equivalent to terrestrial longitude, and it is therefore necessary in the first instance to select a start-point, which shall do for stars what Greenwich does for our geographical maps. By universal consent the fundamental point for the stars is a point situated on the celestial equator where it is crossed by that part of the ecliptic occupied by the sun at the vernal equinox. This zero mark is called the _First Point of Aries_, and is frequently denoted by the symbol ♈︎ identical with that employed for the corresponding sign of the zodiac.
The location of this reference point being thus determined, the _right ascension_ of a celestial body may be defined as its angular distance from the First Point of Aries, as measured along the celestial equator. Like terrestrial longitude, it may be stated in degrees, but it is more usually expressed in hours, minutes, and seconds of time, for the reason that in general the measurement of a right ascension consists of an observation of the time at which the body in question comes to a certain position.
The right ascensions and declinations of stars are best determined when they are on the meridian of the place of observation, and such measurements are made by means of a transit instrument. When a star is on the meridian, its declination is estimated by the angle at which the instrument is inclined to the celestial equator when directed to the star. The fact that the earth is turning on its axis furnishes us with a simple method of finding the right ascensions of the heavenly bodies. Imagine a plane passing through the observers position on the earth and through the earth’s axis. This, prolonged indefinitely, cuts the celestial sphere in his meridian, and it is evident that on account of the earth’s rotation it will turn completely round every twenty-four hours. It may therefore be regarded as the hour-hand of a clock, which is provided with figures ranging from I. to XXIV. When this gigantic clock hand sweeps past the First Point of Aries, all stars then seen in the plane—that is, all stars which are on the meridian—will have zero right ascension. After a complete rotation it will again sweep through the First Point of Aries.
USE OF STAR TIME.—Meanwhile, suppose we have a clock regulated so that it marks twenty-four hours between these two meridian passages of the First Point of Aries. Evidently, then, the time by this clock at which any object in the sky is seen on the meridian will depend upon its angular distance from the celestial meridian passing through the First Point of Aries. As the earth is rotating through 360° in twenty-four hours, reckoned by our clock, the meridian plane will travel at the rate of 15° per hour, so that, for example, a star 60° from the celestial meridian passing through the First Point of Aries, will appear to cross the observer’s meridian at IV. hours by the clock. A clock so regulated to keep time with the stars is called a sidereal clock, and the sidereal time at which a celestial body crosses the meridian, or “souths,” is the right ascension of that object. Such a time measurement can be converted into angular measure by allowing 15° per hour, 15′ per minute, and 15″ per second of time.
CELESTIAL LATITUDE AND LONGITUDE.—In some astronomical questions it is often convenient to adopt a different system of co-ordinates to indicate the situation of a celestial body. Just as the earth’s equatorial plane serves as a basis for the measurement of declination, the earth’s plane of revolution—that is, the plane of the ecliptic—is used as the term of reference for _celestial latitude_, which may be defined as the angular distance of an object above or below the plane of the ecliptic. _Celestial longitude_ is the angular distance from the First Point of Aries measured along the ecliptic.
A diagram such as that in Fig. 12 may assist the comprehension of these co-ordinates. Here the observer is supposed to be situated at the point O, at the centre of the celestial sphere. To him the north and south celestial poles will appear in some such positions as N and S, and the celestial equator will be represented by a great circle at right angles to the line joining these two points. The apparent path of the sun—the ecliptic—will be indicated by another great circle, which is inclined to the Equator; and the poles of the ecliptic will be represented by P and P′.
The Equator crosses the ecliptic at the First Point of Aries, marked ♈︎. Considering now a star which the observer sees in the direction of the line O S, its position would be reckoned as follows in the two systems:—
Right Ascension = Angle ♈︎ O R } Declination = „ S O R }
Celestial Longitude = Angle ♈︎ O L } „ Latitude = „ S O L }
Either pair of co-ordinates can, by a mathematical process, be expressed in terms of the other.
[Illustration:
FIG. 12.—_Right Ascension, Declination, Celestial Latitude, and Celestial Longitude._ ]
PRECESSION OF THE EQUINOXES.—It is not too early to remark that the First Point of Aries is not absolutely a fixed point on the celestial equator. This is on account of the precession of the equinoxes, which consists of a backward movement of the First Point, due to a change in the position of the earth’s equator. As a point common to the ecliptic and equator, it is conveniently retained as the starting-point of right ascensions and celestial longitudes, but in consequence of precession, these co-ordinates are subject to a constant change. The amount of precession for a point on the Equator is 50″·2 per annum, and this movement requires 25,800 years for a complete revolution.
GEOCENTRIC AND HELIOCENTRIC POSITIONS.—When observing objects at a very great distance, they will appear in the same direction to a spectator on the earth as they would if he could by some means be transferred so as to be able to see them from the sun. If, for instance, one sees the Peak of Teneriffe from a distant ship, its apparent direction will be very slightly affected by a change of a mile in the ship’s position. But a similar change of place would produce a greater difference of direction when a nearer body was under observation. If an object is relatively near to the sun and earth, its direction, and, therefore, its apparent position on the celestial sphere, will be different, as seen from the earth and sun. Such will be the case with planets and other bodies which lie in our immediate neighbourhood, speaking astronomically. Hence, it is often convenient to distinguish between the _geocentric_ position of a celestial body—referring it to the position it would occupy if it could be seen from the centre of the earth—and the _heliocentric_ position, representing it as it would appear to an observer occupying the centre of the sun. We thus have geocentric and heliocentric latitudes and longitudes of the nearer heavenly bodies.
STAR CATALOGUES.—The problem of constructing catalogues showing the positions of the stars is one of considerable practical value, as well as one of great scientific importance. In the first instance, such catalogues were of necessity compiled from data acquired by naked eye observations, so that the ancient catalogues comprise only a small number of stars.
As far back as 295 B.C., the positions of stars were determined by Timocharis with sufficient accuracy to lead Hipparchus to his great discovery of the precession of the equinoxes about 170 years later. From observations at Rhodes, Hipparchus drew up a catalogue of 1,022 stars, giving their latitudes and longitudes; this is preserved for us in Ptolemy’s “Almagest,” where the positions are corrected for precession, and reduced to the epoch 150 A.D. The next catalogue of importance was due to the industry of Tycho Brahé (1546–1601), who gave the positions of 1,005 stars with greater accuracy than had been previously obtained; indeed, notwithstanding his want of optical aid, it has been estimated that the probable errors of his measures were not more than 24″ and 25″ in right ascension and declination respectively. The last of the naked eye catalogues is that of Hevelius, giving the positions of 1,553 stars.
Coming to more recent times, in which the employment of telescopes has vastly increased the power of accurate observation, there are the catalogues of Flamsteed, Halley, Lacaille, Lalande, Argelander, the British Association, and catalogues of the stars in particular parts of the sky which have been published by all the leading national observatories. Eighteen observatories are now taking part in the construction of an international star catalogue by means of photography, and this is intended to record with great accuracy the positions of nearly 3,000,000 stars. A modern star catalogue usually places the stars in the order of their right ascensions, and, in addition to the two co-ordinates, furnishes the necessary data for determining the exact situations of the stars at any particular time.