## O

Greenwich Mean Time is used because 0 deg longitude is defined as going through the site of the former Royal Greenwich Observatory in metropolitan London. Eastern Standard Time in the United States is obtained by subtracting S hours from the Universal Time.

Because calendar time is inconvenient for computations, we would like an absolute time that is a continuous count of time units from some arbitrary reference. The time interval between any two events may then be found by simply subtracting the absolute time of the first event from that of the second event. The universally adopted solution for astronomical problems is the Julian day, a continuous count of the number of days since noon (12:00 UT) on January I, 4713 BC. This strange starting point was suggested by an Italian scholar of Greek and Hebrew, Joseph Scaliger, in 1582, as the beginning of the current Julian period of 7980 years. TTiis period is the product of three numbers: the solar cycle, or the interval at which all dates recur on the same days of the week (28 years); the lunar cycle containing an integral number of lunar months (19 years); and the indiction, or the tax period introduced by the emperor Constantine in 313 AD (15 years). The last time that these started together was 4713 BC and the next time will be 3267 AD. Scaliger was interested in reducing the astronomical dating problems associated with calendar reforms of his time and his proposal had the convenient selling point that it predated the ecclesiastically approved date of creation, October 4, 4004 BC. The Julian day was named after Scaliger's father, Julius Caeser Scaliger, and was not associated with the Julian calendar that had been in use for some centuries.

Tabulations of the current Julian date may be found in nearly any astronomical ephemeris or almanac. A particularly clever procedure for finding the Julian date, or JD, associated with any current year (/), month (J), and the day of the month (K), is given by Fliegel and Van Flandern [1968] as a FORTRAN arithmetic statement using FORTRAN integer arithmetic:

.//) = /£—32075+1461 «(/ + 4800 + (./—14)/12)/4 + 367*(y-2-(y— 14)/12*12)/12 -3*((/+4900+(y- 14)/12)/100)/4

For example, December 25, 1981 (7= 1981, 7= 12, K=2S) is JD 2,444,964.*

The Julian date presents minor problems for space applications. It begins at noon Universal Time, rather than 0 hours Universal Time and the extra digits required for the early starting date limit the precision of times in computer storage. However, no generally accepted substitute exists, and the Julian day remains the only unambiguous continuous time measurement for general use.

For internal computer calculations, the problem of ambiguity does not arise and several systems are used. The Julian Day for Space, or JDS, is defined as JD-2,436,099.5. This system starts at 0 hours UT (rather than noon), September 17, 1957, which is the first Julian day divisible by 100 prior to the launch of the first

'Note that in FORTRAN integer arithmetic, multiplication and division are performed left to right, the magnitude of the result is truncated to the lower integer value after each operation, and -2/12 is truncated to 0.

manmade satellite by the Soviet Union on October 4, 1957. This system is used internally in NASA orbit programs, with time measured in seconds rather than days. (Measuring all times and time intervals in seconds is convenient for computer use because the large numbers involved do not pose a problem.) The European Space Operations Center uses the Modified Julian Day, which starts at 0 hours UT, January I, 1950. Attitude determination programs at NASA's Goddard Space Flight Center measure time intervals in seconds from 0 hours UT, September I, 1957. Unfortunately, the origin of this particular system appears to have been lost in antiquity.

### References

1. Bassett, D. A., "Ground Controlled Conversion of Communications Technology Satellite (CTS) from Spinning to Three-Axis Stabilized Mode," AIAA paper no. 76-1928 presented at AIAA Guidance and Control Conference, San Diego, CA., Aug. 1976.

2. Clarke, Arthur C., The Promise of Space. New York: Harper & Row, 1968.

3. Fliegel, Henry F. and Thomas C. Van Flandern, "A Machine Algorithm for Processing Calendar Dates," Communications of the ACM, Vol. 11, p. 657, 1968.

4. Future Space Programs J 975 (3 volumes), Report prepared for the Subcommittee on Space Science and Applications of the Committee on Science .and Technology, U.S. House of Representatives, 94th Congress (Stock numbers 052-070-02889-1, 052-070-02890-4, 052-070-02891-2), July-Sept. 1975.

5. Glasstone, Samuel, Sourcebook on the Space Sciences. Princeton, N.J.: D. Van Nostrand Company Inc., 1965.

6. NASA, Outlook for Space. NASA SP-386, 1976a.

7. NASA, A Forecast of Space Technology. NASA SP-387, 1976b.

8. Soviet Space Programs, 1966-70, Staff Report for the Committee on Aeronautical and Space Sciences United States Senate, 92nd Congress, Document No. 92-51, Dec. 9, 1971.

9. von Braun, Wernher, and Frederick I. Ordway, History of Rocketry and Space Travel, New York: Crowell, 1975.

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