Page 66 - Satellite Communications, Fourth Edition

46 Chapter Two

Example 2.7 Calculate the average length of the civil year in the Gregorian
calendar.
Solution The nominal number of days in a 400-year period is 400 365 146,000.
The nominal number of leap years is 400/4 100, but as shown earlier, this must
be reduced by 3, and therefore, the number of days in 400 years of the Gregorian
calendar is 146,000 100 3 146,097. This gives a yearly average of
146,097/400 365.2425.

In calculations requiring satellite predictions, it is necessary to deter-
mine whether a year is a leap year or not, and the simple rule is: If the
year number ends in two zeros and is divisible by 400 without remain-
der, it is a leap year. Otherwise, if the year number is divisible by 4 with-
out remainder, it is a leap year.

Example 2.8 Determine which of the following years are leap years: (a) 1987,
(b) 1988, (c) 2000, (d) 2100.
Solution
(a) 1987/4 496.75 (therefore, 1987 is not a leap year)

(b) 1988/4 497 (therefore, 1988 is a leap year)
(c) 2000/400 5 (therefore, 2000 is a leap year)
(d) 2100/400 5.25 (therefore, 2100 is not a leap year, even though 2100 is divisible
by 4 without remainder)

2.9.2 Universal time
Universal time coordinated (UTC) is the time used for all civil
time–keeping purposes, and it is the time reference which is broad-
cast by the National Bureau of Standards as a standard for setting
clocks. It is based on an atomic time-frequency standard. The funda-
mental unit for UTC is the mean solar day (see App. J in Wertz, 1984).
In terms of “clock time,” the mean solar day is divided into 24 h, an
hour into 60 min, and a minute into 60 s. Thus there are 86,400 “clock
seconds” in a mean solar day. Satellite-orbit epoch time is given in
terms of UTC.

Example 2.9 Calculate the time in days, hours, minutes, and seconds for the
epoch day 324.95616765.
Solution This represents the 324th day of the year plus 0.95616765 mean solar
day. The decimal fraction in hours is 24 0.95616765 22.9480236; the decimal
fraction of this expressed in minutes is 0.9480236 60 56.881416; the decimal
fraction of this expressed in seconds is 0.881416 60 52.88496. Thus, the epoch
is day 324, at 22 h, 58 m, 52.88 s.