Page 65 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 45

is measured, thus enabling the satellite position and the earth station
location to be coordinated.
■ The satellite-to-earth station position vector is transformed to the
topocentric-horizon system, which enables the look angles and range
to be calculated.

2.9.1 Calendars
A calendar is a time-keeping device in which the year is divided into
months, weeks, and days. Calendar days are units of time based on the
earth’s motion relative to the sun. Of course, it is more convenient to
think of the sun moving relative to the earth. This motion is not uniform,
and so a fictitious sun, termed the mean sun, is introduced.
The mean sun does move at a uniform speed but otherwise requires
the same time as the real sun to complete one orbit of the earth, this time
being the tropical year. A day measured relative to this mean sun is
termed a mean solar day. Calendar days are mean solar days, and gen-
erally they are just referred to as days.
A tropical year contains 365.2422 days. In order to make the cal-
endar year, also referred to as the civil year, more easily usable, it is
normally divided into 365 days. The extra 0.2422 of a day is signifi-
cant, and for example, after 100 years, there would be a discrepancy
of 24 days between the calendar year and the tropical year. Julius
Caesar made the first attempt to correct the discrepancy by intro-
ducing the leap year, in which an extra day is added to February
whenever the year number is divisible by 4. This gave the Julian cal-
endar, in which the civil year was 365.25 days on average, a reason-
able approximation to the tropical year.
By the year 1582, an appreciable discrepancy once again existed
between the civil and tropical years. Pope Gregory XIII took matters in
hand by abolishing the days October 5 through October 14, 1582, to
bring the civil and tropical years into line and by placing an additional
constraint on the leap year in that years ending in two zeros must be
divisible by 400 without remainder to be reckoned as leap years. This
dodge was used to miss out 3 days every 400 years. To see this, let the
year be written as X00 where X stands for the hundreds. For example,
for 1900, X 19. For X00 to be divisible by 400, X must be divisible by 4.
Now a succession of 400 years can be written as X (n 1), X n, X
(n 1), and X (n 2), where n is any integer from 0 to 9. If X n is
evenly divisible by 4, then the adjoining three numbers are not, since
some fraction from 1/4 to 2/4 remains, so these three years would have
to be omitted. The resulting calendar is the Gregorian calendar, which
is the one in use today.