of a solar day then the length of a second
would also vary throughout the year, which is clearly undesirable. In
order to avoid this problem, astronomers have invented a fictitious
body called the mean sun. The mean sun travels around the
celestial equator (from west to east) at a constant
rate which is such that it completes one orbit every tropical year. Moreover,
the mean sun and the true sun coincide at the spring equinox. Local mean noon at a particular observation
site is defined as the instance in time when the mean sun culminates at
the meridian. Since the orbit of the mean sun is not inclined to the
celestial equator, and the mean sun travels around the celestial equator at a uniform rate, the time
interval between successive mean noons, which is known as a
mean solar day, takes the constant value of 24 hours, or
86,400 seconds, throughout the year. Universal time (UT)
is defined such that 12:00 UT coincides with mean noon every day at
an observation site of terrestrial longitude 
. If we define local time
(LT)
as
hrs., where 
is the terrestrial longitude
of the observation site, then 12:00 LT coincides with mean noon
every day at a general observation site on the earth's surface.
According to the above definition, the right ascension, 
, of the mean
sun satisfies
 |
(108) |
is the sun's mean ecliptic longitude. Moreover,
it follows from Eqs. (16) and (98) that the right ascension
of the true sun is given by
 |
(109) |
is the inclination of the ecliptic to the celestial
equator, 
the sun's equation of center, and 
its mean anomaly. Now, neglecting the small time variation of the longitude of the
sun's perigee [i.e., setting 
in Eq. (95)], we
can write [see Eqs. (100), (101), and (103), as
well as Table 30]
 |
(110) |
, we have
 |
(111) |
 |
(112) |
 |
(113) |
an
hour), and is known as the equation of time. If 
is
positive then local noon occurs before mean local noon, and vice
versa.
The equation of time specifies the difference between time calculated using a sundial or sextant--which is known as solar time--and time obtained from an accurate clock--which is known as mean solar time. Table 34 shows the equation of time as a function of the sun's ecliptic longitude. It can be seen that the difference between solar time and mean solar time can be as much as 16 minutes, and attains its maximum value between the autumnal equinox and the winter solstice, and its minimum value between the winter solstice and vernal equinox.
|
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JD). The elements are optimized for use in the
time period 1800 CE to 2050 CE. Source: Jet Propulsion Laboratory (NASA), http://ssd.jpl.nasa.gov/. The motion rates have been converted into tropical motion rates assuming a uniform precession of the equinoxes
of
.
,
, and
.
At epoch (
, and
.
and 
denote minutes and seconds.
28