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Why aren't sunrise and sunset 12 hours apart on the equinoxes?

Twice a year the sun is directly over the earth's equator. These moments occur on the vernal (spring) and autumnal (fall) equinoxes.
Many people believe that on those two days, sunrise and sunset occur exactly 12 hours apart, but they do not. For example, in 2013:

the vernal equinox occurs on March 20 when, in Burton, the sun rises at 7:38 AM and sets nearly 12 hours and 10 minutes later at 7:47 PM, and
the autumnal equinox occurs on September 22 when, in Burton, the sun rises at 7:22 AM and sets nearly 12 hours and 10 minutes later at 7:32 PM.
Why is this?
Observed from earth, the sun does not appear as a point of light but as a disk. Sunrise is defined as the moment the rim of the sun is first visible on an unobstructed eastern horizon. Sunset is defined as the moment the rim of the sun is last visible on an unobstructed western horizon. Specifically, the center of the sun's disk is not used as the reference point in determining sunrise and sunset.
Furthermore, the atmosphere refracts (bends) light most along the horizons, so the rising rim of the sun appears to be above the horizon even before it truly is. Likewise, due to light refraction the setting rim of the sun appears to be above the horizon even after it truly is. Put simply, objects (stars, planets, the moon, the sun) that are near the horizon appear to be slightly higher in the sky than they truly are. Thus, we can see the rising sun at the horizon while it is still actually below the horizon, and we can still see the setting sun even after it actually has sunk below the horizon.

Consequently, due to these various factors, the sun's rising rim is visible minutes before the disk's center is truly on the horizon, and its setting rim is visible minutes after the disk's center is truly on the horizon. This is why on both vernal (spring) and autumnal (fall) equinoxes, sunrise and sunset are more than 12 hours apart.

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