Year

Fig. J-5. Excess Length of the Day Compared With the Day Near 1900. Note the very irregular fluctuations about the mean slope of 1.5 ms/centuiy (Morrison, 1973].

Using Sidereal Time to Compute the Longitude of the Subsateiiite Point. To determine the direction of geographic points on the Earth as seen from a spacecraft, it is necessary to know both the spacecraft ephemeris and the longitude of the subsateiiite point. For any UT, Eq. (J-4) can be used to determine the Greenwich sidereal time, GST, which in turn can be used to determine the East longitude, ELspe, of the subsateiiite point for any. satellite for which the right ascension of its position in geocentric coordinates is known. From Eq. (J-3), we have

where RA is the right ascension in degrees of the spacecraft at time GST. Because UTC is accurate to about 1 sec, the accuracy of the resulting longitude will be about 0.005 deg if the spacecraft ephemeris is known precisely.

References

1. Allen, C. W., Astrophysical Quantities, Third Edition. London: The Athlone Press, 1973.

2. H. M. Nautical Almanac Office, Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. London: Her Majesty's Stationery Office, 1961.

3. Morrison, L. V., "Rotation of the Earth from AD 1663-1972 and the Constancy of G," Nature, Vol. 241, p. 519-520, 1973.

4. M uller, Edith A. and Amdst Jappel, Editors, International Astronomical Union, Proceedings of the Sixteenth General Assembly, Grenoble, 1976. Dordrecht, Holland: D. Reidel Publishing Co., 1977.

5. Newcomb, Simon, Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, Bureau of Equipment, U.S. Department of the Navy, Washington, DC, 1898.

6. U.S. Naval Observatory, The American Ephemeris and Nautical Almanac. Washington, DC: U.S. G. P. O., 1973.

7. Woolard, Edgar W„ and Gerald M. Clemence, Spherical Astronomy. New York: Academic Press, 1966.

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