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Equation of Time and its affects on Sunrise in January

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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