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Ephemeris Time, D. H. Sadler, Occasional EPHEMERIS TIME D. H. Sadler 1. Introduction. – At the eighth General Assembly of the International Astronomical Union, held in Rome in 1952 September, the following resolution was adopted: “It is recommended that, in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0; that the time reckoned in these units be designated “Ephemeris Time”; that the change of mean solar time to ephemeris time be accomplished by the following correction: ΔT = +24°.349 + 72s.318T + 29s.950T2 +1.82144 · B where T is reckoned in Julian centuries from 1900 January 0 Greenwich Mean Noon and B has the meaning given by Spencer Jones in Monthly Notices R.A.S., Vol. 99, 541, 1939; and that the above formula define also the second. No change is contemplated or recommended in the measure of Universal Time, nor in its definition.” The ultimate purpose of this article is to explain, in simple terms, the effect that the adoption of this resolution will have on spherical and dynamical astronomy and, in particular, on the ephemerides in the Nautical Almanac. It should be noted that, in accordance with another I.A.U. resolution, Ephemeris Time (E.T.) will not be introduced into the national ephemerides until 1960. Universal Time (U.T.), previously termed Greenwich Mean Time (G.M.T.), depends both on the rotation of the Earth on its axis and on the revolution of the Earth in its orbit round the Sun. There is now no doubt as to the variability, both short-term and long-term, of the rate of rotation of the Earth; U.T. does not therefore increase uniformly and can no longer be regarded as a measure of uniform time. But a uniform time is implicitly assumed as the independent argument in dynamical astronomy; this time must accordingly be defined so as to be independent of the Earth's rotation. It is therefore of interest first to say something about the variation in the rate of rotation of the Earth, and to explain the basis of the form of ΔT. 2. Rotation of the Earth. – There are three types of variation in the rate of rotation of the Earth. Firstly, there is the extremely complex secular change due to the interaction of the Sun, Earth and Moon. Until comparatively recently the observed slow secular increase of about 0s.001 in a century in the length of the day was attributed solely to the effect of tidal friction, mainly in shallow seas. An undetected change in the rate of the Earth's rotation, without change in angular momentum, will be interpreted as changes in the mean longitudes of the Sun and Moon proportional to their mean motions; it is, in fact, a change in the time-scale. However, the total energy of the Sun-Earth-Moon system must 104 Royal Astronomical Society Vol. 3 remain constant, so that a decrease in the rate of rotation of the Earth due to tidal friction caused by the Moon is reflected in an acceleration of the Moon in its orbit; similarly in the case of the Sun, for which the effect is so much smaller as to be inappreciable. The ratio of the secular accelerations of the Sun and Moon, calculated on the above basis, is not in accord with that derived from a discussion of the observations. It has now been shown that the phase of the atmospheric tidal oscillation is such that the Sun's gravitational couple may accelerate the fate of the Earth’s rotation; moreover, it is suggested that the energy so required is extracted from the solar heat falling on the Earth's surface through a heat-engine effect. This added factor gives rise to the possibility of bringing the theoretical ratio into accordance with that observed. The determinations of both the theoretical and observational ratios are exceedingly complex, and subject to considerable uncertainty; moreover, it is not possible to make a unique separation between these secular changes and the irregular changes discussed below. Secondly, there are seasonal changes due to a variety of causes which give rise to periodic changes in the rate of rotation of the Earth and thus in the accumulated measure of time. When these changes were first established by comparison with high-precision quartz-crystal clocks, there appeared to be a pronounced annual term, resulting in the Earth rotating more slowly than the average rate in the first half of the year and more quickly in the second half; during the course of the year, the variation in the length of the day was about ±0s.001, leading to a maximum accumulation in the measure of time of about ±0s.05. More recent observations, although confirming the existence of seasonal changes, have suggested that their nature is highly variable from year to year. Many suggestions have been put forward to explain these seasonal changes; perhaps the most reasonable, which gives rise to changes of angular momentum of the right order, is the seasonal movements of air masses in the Earth's atmosphere. Although such periodic changes are of the foremost importance for precise time-keeping, and the associated determination of frequency standards, they are of little interest as regards the determination of ephemeris time, which is essentially a long-term problem. Thirdly, there are irregular changes which follow no pattern and to which no particular cause can be assigned. It is, however, tacitly assumed that the are reflections of changes in the moment of inertia of the Earth (or at least leave the angular momentum unchanged), so that they will cause no direct change in the orbits of the Sun and Moon; thus, they correspond to changes in the mean longitudes of the Sun, Moon and planets which are proportional to their mean motions. These are, in fact, the changes which give rise to the fluctuations (B of the resolution) in the Moon's mean longitude. It is now pretty well established that these fluctuations are due to the accumulated effect of small, random, abrupt accelerations or decelerations producing rather more gradual changes in the rate of rotation of the Earth; certainly the observed values are consistent with this hypothesis. The observed values are difficult to separate from the secular changes. 3. Derivation of the formula for ΔT.–With these types of variation in mind, it is now possible to analyse the resolution and to understand why ephemeris time has been defined in this particular way. First of all, a standard unit should possess two indispensable qualities: it must be invariable, and it must be accessible. To the best of our knowledge No. 17, 1954 Occasional Notes 105 the revolution of the Earth round the Sun provides the most suitable basis for the unit of time; there is there is no evidence of any variation, or any cause of variation for which full allowance cannot adequately be made, and it can be made accessible. There is some choice as regards the precise definition; the more rigid and fundamental it is, the less accessible and subject to error it is. The unit of time is actually defined in the resolution as the sidereal year at 1900.0; that is a unique entity, and is thus clearly invariable. (Actually it would have been slightly more fundamental to have used the tropical year at 1900.0 which could have been deduced from observation without an assumed knowledge of precession.) Accessibility is not, however, straightforward. Celestial mechanics is capable of specifying the motions of bodies in the solar system, on gravitational theory with a uniform time-scale, to ample accuracy for the connection of observations over long periods of time; in particular the motion of the Sun (i.e. the reflected motion of the Earth in its orbit round the Sun) may be regarded as specified by Newcomb's tables. Observations of the Sun's position in its orbit may thus be interpreted as direct measures of ephemeris time. The observations, necessarily made in universal time, will show a progressive discordance from the tables, owing to the influence on the time-scale of the variations in the rate of rotation of the Earth. All such discordances can be identified with corrections to the mean longitude. The difference, ΔT, between U.T. and E.T. is thus simply the time-equivalent of the observed correction, in terms of U.T., to the Sun's mean longitude. Unfortunately the Sun moves only 1° in a day, or 0″.04 in one second of time; direct observation is thus an insensitive method of finding ΔT, and so of measuring ephemeris time. The Moon's motion in its orbit is by far the fastest available (0″.55 in one second) and the Moon is clearly the most sensitive object to use to determine variations in the rate of rotation of the Earth, and thus ΔT. Is it possible to connect observations of the Moon with those of the Sun, so that corrections to the Sun's mean longitude may be deduced from observations of the Moon? The regular and irregular changes in the rate of rotation of the Earth will, as explained in the previous section, correspond to different forms of correction; on the one hand, the regular (secular) changes will not be proportional to the mean motions (the actual ratio being theoretically very complicated), but the irregular changes (or fluctuations, B) will be so proportional. The corrections to the Sun's mean longitude may thus be represented by an expression α + βT + cT2 + 0.074 804 · B in which the last term corresponds to the fluctuation, B, in a similar expression for the correction to the Moon's mean longitude.
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