SPHERICAL ASTRONOMY The Celestial Sphere.—In surveying the universe from a fixed point we can define the position of any object by specifying (I) its direction and (2) its distance. Owing to the property of prop agation of light in straight lines we can immediately observe the direction of any visible object, but we cannot tell how far away it is. Our knowledge of astronomical distances is derived by more in direct methods, and it never attains the precision of our knowl edge of directions. Hence our study of position begins with a study of direction only ; or, we may put it, we study the location of heavenly bodies, not in space, but on the celestial sphere. The celestial sphere, then, is a sphere with the observer as cen tre, of radius which is arbitrary though it is perhaps convenient to choose it very great ; and an observation of direction fixes the object (or projects it) on some point of this sphere. For the pres ent we can regard the fixed stars as fixed points of this sphere (ignoring their very slow proper motions). They play the part of the figures on a clock face, and we observe the sun, moon and planets moving across them like the hands of the clock. Primar ily the actual observer himself is the centre of this sphere ; but for combining with observations at other times and places we often apply corrections so as to give the positions which would have been observed from the centre of the earth or of the sun— geocentric or heliocentric positions. The correction necessary to reduce the original position to geocentric or heliocentric position is called parallax. The closer the object the greater is the par allax; for example, the moon has so large a parallax that if we point a moderately powerful telescope to its geocentric position (the position given in the Nautical Almanac) it will probably be out of the field of view; we, so to speak, look over the top of it.
The first thing we notice is that the celestial sphere carrying the stars is rotating; the stars rise in the east and set in the west.
(Of course we know that it is really our earth that is rotating, but this is not the appropriate moment to air our superior knowl edge.) We can determine the axis of rotation because the end of the axis will remain still. One well known star remains nearly still; we always find it in practically the same direction and alti tude in the sky. This must accordingly be very near the end of the axis, and the star is called Polaris or the Pole Star. By careful observation we fix the unchanging point or Pole more accurately among the stars, and find that Polaris is about away from it. There is an opposite pole in the other hemisphere not marked by any bright star but equally locatable ; and midway between them runs a great circle called the Equator of the celes tial sphere.
The observer can also mark on the celestial sphere the zenith or point which (momentarily) is vertically overhead. This is given by the direction of gravity (including centrifugal force) ; it is perpendicular to any undisturbed liquid surface, and in prac tice is generally determined by a method employing reflection from a trough of mercury. Opposite to the zenith is the nadir, and the great circle midway between them is the horizon. This ce lestial horizon does not quite agree with the observed terrestrial horizon ; because if we are on a hill we see rather more than half the celestial sphere. At fixed observatories we usually measure angles from the zenith; but at sea the sailor measures altitudes above the sea-horizon, and he has to subtract a correction called the "dip of the horizon" to give the altitude above the celestial horizon (corrected altitude=9o°— zenith distance).
It may be asked, How does the spher oidal figure of the earth affect the accur acy of this statement? The statement is still exact, because the latitude shown on maps is defined by this astronomical definition; but the spheroidal shape has the effect of making a degree of latitude greater (in miles) near the pole than near the equator.
The earth rotates once in 23h.56m'4-901S. of ordinary time (mean solar time). But although the astronomer supplies mean solar time for the convenience of the general public, he has for his own use another reckoning of time called sidereal time and the fore going period is equal to 24 sidereal hours. Thus in 24 hours by the sidereal clock the celestial sphere makes one revolution and comes into the same position again. The convenience of such a clock will be evident when we realize that if we have once seen a star in a certain direction at 5 o'clock (sid.), we always find it there at 5 o'clock (sid.). The hour angle (or indeed any angle) can be expressed in the usual way in degrees, minutes, seconds, but it can also be expressed in time units by converting at the rate of 36o° to of time.
When converted into time units in this way the hour angle tells us how long by the sidereal clock the celestial sphere will take to turn through the angle QPZ and so bring Q on to the meridian. If it is now 5 o'clock (sid.) and the easterly hour angle of Q is 8 hours, Q will cross the meridian at 13 o'clock (sid.) .
We have explained how to regulate the rate of the sidereal clock but we have not yet explained how to set it. At sidereal time a certain fixed mark of the equator (fixed relative to the stars) must be crossing the meridian NZS. We call this mark "the first point of Aries" and denote it by P. Evidently at any mo ment the sidereal time will be equal to the hour angle of measured towards the west. Every other star has its fixed time of passing the meridian by the sidereal clock and this time is called the right ascension of the star. This gives the third, and most usual, way of specifying positions on the celestial sphere, viz., Right Ascension, the time by the sidereal clock at which the point passes the meridian, or the angle TPQ measured towards the east; Declination, the complement of the north polar distance, or In this system it is no longer necessary to refer to the time of observation, since if the point is in a constant position with re spect to the stars the right ascension and declination remain con stant (subject to corrections mentioned later).
The sun goes round the ecliptic towards the east increasing in declination after passing and therefore giving us (in the north ern hemisphere) the long summer days. After reaching a maximum declination of 23 2 ° it descends, passes through the point opposite `lr' about Sept. 2I, and continues to a minimum declination of 23°. It has to make a complete circuit in 3651 days and there fore has to do an average of nearly I ° a day. Thus when the ce lestial sphere has made one complete turn it has still I ° more to go before the sun is brought back to the meridian; that takes 4 minutes more, or, to give the accurate figures, the average sidereal time between two successive passages of the sun over the meridian is 2,0.3m'56.555s.• Since our daily affairs are more or less regu lated by the sun we set this equal to 24h• of ordinary (mean solar) time. Clocks regulated by this time keep pace with the sun on the average throughout the year, but not exactly from day to day (see EQUATION OF TIME). The sidereal clock gives one extra "day" in the year compared with the mean clock; hence there is only one instant in the year when the two clocks agree. About March 2 I the sun coincides with P , so that it is on the meridian (noon) when ri' is on the meridian, i.e., at oh- sidereal time ; midnight which is the beginning of the civil day (o''.) accordingly coincides with 12h. sidereal time about March 21. Thus the time when the two clocks agree is at the autumnal equinox about Sept. 2I. These statements, however, need a slight correction because of the equa tion of time, true midnight on Sept. 2I being at about I I.S3 p.m. local mean time.
The orbit of the moon is inclined at a small angle 5°g' so that the moon's position in the sky is always within this distance of the ecliptic. The principal planets also have small inclinations, so that it is possible to define a zone not much more than Io° wide within which the sun, moon and planets are always to be found.
This zone is called the zodiac, and its course amongst the stars is marked by the I2 well known constellations of the zodiac. An gular distance from the ecliptic is called latitude, and distance round the ecliptic measured from P is called longitude. Posi tions of objects are often given in longitude and latitude instead of in right ascension and declination. It should be noted, how ever, that the names are rather misleading, because right ascen sions and declinations are the proper analogues on the celestial sphere to longitudes and latitudes on the earth.
(2) Aberration of light (q.v.) . This may be anything up to 20•5", but the correction can be calculated without any uncer tainty. It arises because, owing to the fact that the earth's veloc ity in its orbit is not insignificant compared with the velocity of light, the apparent direction of the light-ray is not the true direc tion of the object.
(3) Parallax. For bodies belonging to the solar system a sensi ble correction is required to reduce observations made from the observer's particular station on the earth's surface to a common standard, viz., an imaginary station at the centre of the earth. For a few stars an analogous correction is required to reduce observa tions from a particular point on the earth's orbit to a standard station coinciding with the sun ; but for the most part stellar parallax is a matter of specific observation rather than a serious correction required for other investigations.
(4) Precession. We have hitherto treated the equator and 'Y' as fixed marks in the sphere of the stars but actually they are con tinually moving—a fact which causes the practical astronomer no end of trouble. When positions observed at different times have to be compared or combined together, corrections must be applied for the difference between the equators and equinoxes with re spect to which they have been measured. The steady part of this change is called Precession (See PRECESSION OF THE EQUINOXES).
(5) Nutation. This is part of the same phenomenon as preces sion; it comprises the periodic or oscillating part of the motion.
A modern branch of spherical astronomy is concerned with the projection of the celestial sphere on a plane photographic plate. The problem is equivalent to a central projection of the sphere on a plane which is tangent to it ; and formulae have been de veloped for converting position measured on the plate (in plane rectangular co-ordinates) into right ascension and declination on the celestial sphere. Photographic determinations of position are necessarily differential, that is to say, the photograph must include a number of "reference stars" whose right ascensions and declina tions are already known ; from these the "plate-constants" for the particular plate under discussion are determined; and the plate constants are in turn used for deducing right ascensions and declinations of other objects in the photograph.
(A. S. E.)