Page 67 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 47

Universal time coordinated is equivalent to Greenwich mean time
(GMT), as well as Zulu (Z) time. There are a number of other “univer-
sal time” systems, all interrelated ( Wertz, 1984) and all with the mean
solar day as the fundamental unit. For present purposes, the distinction
between these systems is not critical, and the term universal time (UT),
will be used from now on.
For computations, UT will be required in two forms: as a fraction of
a day and in degrees. Given UT in the normal form of hours, minutes,
and seconds, it is converted to fractional days as

1 minutes seconds (2.18)
ahours b
UT day
24 60 3600
In turn, this may be converted to degrees as

UT° 360° UT day (2.19)

2.9.3 Julian dates*
Calendar times are expressed in UT, and although the time interval
between any two events may be measured as the difference in their calen-
dar times, the calendar time notation is not suited to computations where
the timing of many events has to be computed. What is required is a ref-
erence time to which all events can be related in decimal days. Such a
reference time is provided by the Julian zero time reference, which is 12
noon (12:00 UT) on January 1 in the year 4713 B.C.! Of course, this date
would not have existed as such at the time; it is a hypothetical starting
point, which can be established by counting backward according to a cer-
tain formula. For details of this intriguing time reference, see Wertz (1984,
p. 20). The important point is that ordinary calendar times are easily con-
verted to Julian dates, measured on a continuous time scale of Julian days.
To do this, first determine the day of the year, keeping in mind that day zero,
denoted as Jan 0.0 is midnight between December 30 and 31 of the previ-
ous year. For example, noon on December 31 would be January 0.5, and
noon on January 1 would be January 1.5. It may seem strange that the last
day of December should be denoted as “day zero in January,” but it will be
seen that this makes the day count correspond to the actual calendar day.
A Fortran program for calculating the Julian day for any date and time
is given in Wertz (1984, p. 20), and a general method is given in Duffett-
Smith (1986, p. 9). Once the Julian day is known for a given reference
date and time, the Julian day for any other time can be easily calculated
by adding or subtracting the required day difference. Some “reference
times” are listed in Table 2.2.

∗
It should be noted that the Julian date is not associated with the Julian calendar
introduced by Julius Caesar.