The 23:59:38.7 value is the true solar day for September 16th, as compared to the mean solar day which is defined to be 24 hours exactly when averaged over the

The 23:59:38.7 value is the true solar day for September 16th, as compared to the mean solar day which is defined to be 24 hours exactly when averaged over the course of a year. The article for Equation of Time describes it in more detail, with rather wordy explanations, I'll try to simplify. http://en.wikipedia.org/wiki/Equation_of_time http://en.wikipedia.org/wiki/Equation_of_time It's a sine wave with two components. The larger comes from the Earth's elliptical orbit around the Sun. When the Earth is near perihelion in January, it moves faster and farther each day along its orbit, so needs an extra few seconds for more rotation to bring your spot on the surface back under the noon Sun. And the converse in July, where the slower orbital speed at aphelion means each solar noon occurs a few seconds earlier. The smaller component comes from the axial tilt and runs at twice the frequency (two cycles per year). Near the solstices, the Sun's declination (angle above the horizon at noon) remains nearly constant day to day, so all of its daily motion is in the east-west direction. Near the equinoxes, the Sun's apparent path is more oblique, so some of its apparent velocity occurs in the north-south direction leaving its apparent east-west motion slower. That shortens the solar day since the Earth has to rotate less far to the next solar noon. The slope of the equation reaches its negative maximum on Sept 16th, so that is the shortest solar day. On this day, the Earth is roughly halfway from aphelion to perihelion, so experiences its greatest orbital acceleration. And it is near the autumnal equinox, where the Sun's apparent east-west motion slows, additively with the same sign as the orbital component, thus creating the global maximum. It's worth noting all of this refers to "day" as noon to noon or midnight to midnight, affecting daytime and nighttime equally. The phenomenon doesn't affect the daylight/nighttime ratio or insolation or temperatures like the seasonal cycle does.