## Astronomy For Ha

Greenwich Mean Time, Universal Time. The 0-deg longitude line is referred to as the Greenwich meridian because it is defined by the former site of the Royal Greenwich Observatory. Greenwich Mean Time, GMT, is the mean solar time at 0 deg longitude; that is, GMT is the HA of the mean Sun observed at Greenwich (called the GHA) in hours plus 12¡hours, modulo 24. Greenwich Mean Time is also called Universal Time, UT, and, in spaceflight operations, Zulu, or Z.

Uncorrected UT or UTO (read "UT Zero") is found from observations of stars, as explained in the discussion of sidereal time below. UTO time as determined by different observatories is not the same, however, due to changes in the longitudes of the observatories caused by the wandering of the geographic pole. Therefore. UTO is corrected for this effect to give UT1, which is then a measure of the actual angular rotation of the Earth. The Earth's rotation is subject to periodic seasonal variations, apparently caused by changes in, for example, the amount of ice in the polar regions. When UT1 is corrected by periodic terms representing these seasonal effects, the result is UT2. Even UT2 is not a uniform measure of time. Evidence from ancient eclipse records and other sources shows that the Earth's rate of rotation is slowing; also, unpredictable irregularities in the rotation rate are observed.

Before 1972, the broadcast time signals were kept within 0.1 sec of UT2. Since January 1, 1972, however, time services have broadcast Coordinated Universal

Time, UTC. A second of UTC is equal to a second of International Atomic Time, but UTC is kept within 0.90 sec of UT1 by the introduction of 1-sec steps, usually at the end of June and December.

Ephemeris Time. The irregularities in the Earth's rotation cannot be predicted; however, gravitational theories have been formulated for the orbital motions of the Earth, the Moon, and the planets. In particular, Simon Newcomb's Tables of the Sun, [1898], published at the end of the 19th Century, gives the position of the Sun for regular time intervals. These intervals define a uniform time called Ephemeris Time, ET. In theory, Ephemeris Time is determined from observations of the Sun. In practice, observations of the Moon are used because the Sun moves slowly and its position is difficult to observe. One method is to record the UT of a lunar occultation of a star; the tabulated value of ET for the observed lunar position, corrected for effects such as parallax, is noted and the difference is determined. A table of approximate A T values, both in the past and extrapolated into the future, is provided in The American Ephemeris and Nautical Almanac [U.S. Naval Observatory, 1973]. Ephemeris time at any instant is given by

International Atomic Time. The cesium nuclide, 133 Ce, has a single outer electron with a spin vector that can be either parallel or antiparallel to that of the nucleus. The flip from one orientation to the other, a hyperfine transition, is accompanied by the absorption or emission of microwave radiation of a given frequency. In an atomic clock, the number of these transitions is maximized in a resonator by the introduction of microwave radiation from an oscillator tuned to the same frequency. The cycles of the oscillator are counted to give a unit of time. In 1967, the 13th General Conference on Weights and Measures established the Systeme Internationale (SI) second as the duration of 9 192 631 770 periods of the radiation from the above transition in 133 Ce. This unit is the basis of International Atomic Time, TAI, and was chosen to make the SI second equal to the ephemeris second. The reference epoch for TAI is January 1, 1958, when 0h0m0s TAI equaled 0h0m05 UT2. For most purposes, ephemeris time may be considered to be equal to TAI plus 32.18 sec, the value of A T for January 1, 1958.

Sidereal Time. Sidereal time, ST, is based on the rotation of the Earth relative to the stars and is defined as the HA of the vernal equinox, T. The local sidereal time, LST, is defined as the local HA of T, LHA T, and the sidereal time at Greenwich, GST, is defined as the Greenwich HA of T, GHA T. Sidereal time may also be determined from the HA and right ascension, RA, of any star. The RA of a star is the azimuthal component of the star's position measured eastward from T (see Section 2.2.2). From Fig. J-3 we see that where LHA* and RA* are the HA and RA (both converted to time) of the star. In the example in Fig. J-3, LHA * is 135 deg or 9 hours, RA * is 90 deg or 6 hours, and the LST is 15 hours. Similarly,

ET=bT+UT

where GHA* is the GHA of the star (converted to time). In Fig. J-3, GHA* is 45 deg or 3 hours; thus, GST is 9 hours. Note that the sidereal time at Greenwich is equal to the right ascension of the Greenwich meridian. The difference between LST

ghat ghat

and GST (6 hours in this example) corresponds to the observer's East longitude (90 deg in this example). In general,

where EL is the observer's East longitude in degrees. From the definition of mean solar time, it follows that GMT or UT equals the GHA of the fictitious mean Sun plus 12 hours, or

where R^ is the right ascension of the mean Sun. For a given UT of any calendar date,

=6h38m45s.836 + 86401845.542 T+O» .0929 T2+ UT (J-4)

where T is the number of Julian centuries of 36,525 days which have elapsed since noon (GMT) on January 0, 1900 [Newcomb, 1898]. The corresponding equation for GST expressed in degrees is

GST=> 99° .6910 + 36000° .7689 r+0°.0004 T2+ UT (J-5)

where UT is in degrees and T is in Julian centuries. Julian dates, or JD (Section 1.4), are convenient for determining T in Eqs. (J-4) and (J-5). The JD for Greenwich mean noon on January 0, 1900 (i.e., January 0.5, 1900), is 2 415 020.0. JD's for any date in the last quarter of this century may be obtained by adding the day number of the year to the JD for January 0.0 UT of that year listed in Table J-3. For example, to find the GST for 3h UT, July 4, 1976:

Day number of July 4.125 ( = 3h UTJuly4). 1976 + JD for January 0.0, 1976 = JD for July 4.125, 1976 - JD for January 0.5, 1900 = T in days

■r 36,525 = T in Julian centuries 8640184.542 7+0.0929 T2

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