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The phenomena known as the equation of time describes
the differences in time between the noon passages of
the apparent sun and the mean sun or apparent time
minus mean time. The apparent motion of the sun
as it crosses the sky is mostly affected by the
earth's rotation. The speed that sun travels
across the sky from day to day is not an exact
constant, and varies some. This
variation is affected
by
the following 2 reasons: 1. Differences in the earth's motion around the
sun in its slightly elliptic orbit at its farthest
and closest distance from the sun; and 2. By the
tilt of the earth's equator, 23 degrees and 27 minutes,
to the plane of its orbit.
Since it is impossible to build a clock that accounts for
these variations, of the apparent sun across the sky day
to day, our clocks assume a mean sun. A mean sun
assumes a scenario where the sun comes
across the sky at an equal speed every day, crossing
the local meridian at the highest point in the sky
at exactly noon every day. The apparent sun and mean
sun reach the local meridian at noon 4 times
a year; then at other times of the year they differ.
The difference in the noon passages of the apparent sun
and mean sun is called the equation of time.
In early November, the sun reaches its highest point in
the sky around 1216 pm over South Central Texas, when
the sun is traveling at its fastest motion across the
sky. The sun's daily motion slows down some by late
November and early December; however, the combination
of shorter days and the suns relatively faster motion
across the sky, allow the sun to arrive at the west
horizon earlier than on December 21st. By December 21st,
the sun's apparent motion across the sky has slowed
down, and thus it takes a little longer to reach the
west horizon, even though the shortest day of
the year occurrs December 21st. The later sunrises on December 21st
come because the sun is slower coming up in the east, making
December 21st the shortest day, even though sunsets
are a few minutes later in the afternoon than in
late November and early December. By January, the
sun's apparent motion slows down more, such that the
latest sunrises come in early to mid January.
After Mid January, sunrises get earlier again.
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