Introductory

The phenomenon of precession was discovered by Hipparchus in the second century B.C. By comparing contemporary observations with observations made about a century and a half earlier, he was led to the conclusion that the longitudes of the stars appeared to be increasing at the rate of 36″ per annum (the modern value is about 50″) while, as far as he could detect, their latitudes showed no definite changes. There are two possible explanations; either all the stars examined had real and identical motions in longitude—an improbable hypothesis—or the funda- mental reference point, the vernal equinox T from which longitudes are measured along the ecliptic, could no longer be regarded as a fixed point on the ecliptic. Now T is defined to be one of the two points of intersection of the ecliptic and the equator on the celestial sphere; the observations showed no changes in the latitudes of the stars and therefore it was legiti- mate to conclude that the ecliptic was a fixed plane. According to the second hypothesis (which was adopted by Hipparchus), it was necessary to assume that the equator and, in consequence, the vernal equinox moved in such a way that the longitudes of the stars increased uniformly by an amount in accordance with the observations.

In Fig. 92 let LTM denote the fixed ecliptic, TTR the celestial equator at time t and TT1 R the celestial equator one year later. In one year the vernal equinox has moved from T to T1 and thus the longitude of a star S has increased from TD to T1 D, that is, by about 50″. The uniform backward movement of T along the ecliptic is called the precession of the equinox. Now Hipparchus satisfied himself that the obliquity € of the ecliptic had suffered no appreciable change and it therefore followed that the motion of the equator must be such that the pole P moved from P to P1 around K in a small circle, KP or KP1 being the obliquity ε.

SINCE this book was first published there have been considerable changes in the terminology and the quantities tabulated in the Astronomical Ephemeris and other almanacs. In making this revision I have felt that it is important to recognise these changes and to ensure compatibility of the book with the Astronomical Ephemeris. While I hope that this has been generally achieved, slight differences do remain in the treatment of solar eclipses and in the definition of the Besselian Day Numbers for annual aberration.

Without doubt the most important change in the almanacs has been the introduction of Ephemeris Time. As it is this time that is used as the argument in almost all tabulation in the almanacs, it clearly requires an important place and adequate description in an introductory text such as this. Accordingly I have made substantial revision to the chapter on Time in stressing the distinction between Ephemeris and Universal Time. A difficulty arose, however, in connection with the exposition of this distinction. Professor Smart had used the term, mean sun, to define Universal Time. The mean sun is a wholly fictitious body that was introduced to define solar time long before the distinction, that we are concerned with, was recognised. Newcomb called it the fictitious mean sun and gave it a very precise and formal definition. Newcomb's work naturally related to the subsequent definition of Ephemeris Time and so I have retained, his term, the fictitious mean sun, as a reference point for Ephemeris Time. For continuity, I have also retained Smart's use of the term, mean sun, as a reference point for Universal Time. I hope that this dichotomy, which is not standard usage, will not lead to confusion in practice. It is not intended to imply that only one of the reference points is fictitious; both are.

I have taken the opportunity of adding a number of exercises at the end of several chapters. Some of these are taken, by permission from recent examination papers of Glasgow University. It is hoped that some of these examples will be helpful in illustrating new material that has been added to the text.

The rotation of the earth is a basis for time-measurement and as regards Universal Time (U.T.) this rate of rotation is assumed to be uniform. Recently, first crystal and then atomic clocks-now accurate to 1 part in 1013-have shown that the earth's rotation is at times irregular, the deviations from uniformity being minute—of the order of 1 or 2 milliseconds per day—and unpredictable. In the gravitational theories of the bodies of the solar system, the passage of time is postulated to be uniform', this time is defined as Ephemeris Time (E.T.) and it is in terms of E.T. that astronomical quantities are now tabulated in the almanacs. The epoch from which E.T. is measured is

1900 January 0.5 [E.T.],

more elaborately defined in 1958 as “the instant near the beginning of the calendar year A.D. 1900 when the mean longitude of the sun was 279° 41' 48".04, at which instant the measure of E.T. was 1900 January 0, 12 h. precisely.” The epoch for U.T. is 1900 January 0, 12 h. [U.T.]. Although the two epochs are apparently denoted by the same expression, they do not correspond to the same instant of time, the epoch of E.T. being 4 s. later than that of U.T.

The E.T. for any instant is then defined by the following formula for the geometric mean longitude of the sun:

L = 279° 41' 48".04+129602768".13T+ 1".089T2.

Here T is the ephemeris time measured in Julian centuries of 36525 ephemeris days from the fundamental epoch. The R.A. of the fictitious mean sun is given by the same expression with the effect of aberration added. The R.A. of the fiducial point for U.T., which we are calling simply the mean sun, has the same expression as that of the fictitious mean sun with universal time replacing ephemeris time as the argument.

It may be added that the fundamental unit of time is 1 second (E.T.) derived as 1/31556925.9747 of the length of the tropical year for 1900.0.

Occultations of stars by the moon.

As the moon's sidereal period of orbital revolution around the earth is about 27⅓ days, it moves eastwards with reference to the stars at an average rate of rather more than half a degree per hour. In its passage over the stellar background it is continually interposing its disc between us and the stars, and the sudden disappearance of a star in this way is called the occultation of the star by the moon. After an interval, which depends on a variety of factors, the star reappears. The disappearance and reappearance of the star are generally referred to as immersion and emersion respectively. The disappearance of the star and its reappearance are instantaneous phenomena and, if the time of one or the other is noted accurately, there is obtained at that instant a definite relation between the moon's position in the sky and the position of the observer, it being assumed that the star's position is known accurately. Formerly, occultations were utilised for the determination of longitude, but the introduction of radio time-signals has rendered the occultation method obsolete.

If the moon's position is known accurately, the particulars of the occultation of a star at any place can be predicted and, under these circumstances, it is to be expected that prediction and observation would agree. Now the moon's position is predicted in the almanacs for any instant of Ephemeris Time, while the recorded time of the observation of an occultation will be in Universal Time. The study of suchoccultations, therefore, provides a ready means of determining the relationship between Universal and Ephemeris Time, and, in particular, of deriving the correction ΔT. The occultations of radio sources are also important, as precise radio positions are difficult to measure. The first positive optical identification of a quasar was made by timing the cessation of its radio signals in the course of a lunar occultation.

The geometrical conditions for an occultation.

Consider Fig. 134, in which the earth (regarded as a spheroid) and the moon (regarded as a sphere) are shown with their centres at E and M respectively.