Why are sunsets getting later if the days are getting shorter?

It is December 11th here in Seattle. The days will keep getting shorter until we reach the winter solstice in 10 more days. None of this is surprising to a Seattle native. The strange thing is that sunsets are beginning to get later. Today the sun will set at 4:17 pm. The earliest of the year. By the solstice the sun will set at 4:20 pm. So how can the days get shorter? The sun rose today at 7:47 am and on the solstice it will rise at 7:54 am. Why don’t the days get shorter in a symmetric way? Why are both the sunrise and sunset getting later over the same interval? The answer is not particular to Seattle. In fact, the same asymmetry occurs everywhere on the planet.

To resolve this conundrum you have to recognize that Earth is a bit closer to the sun in December than it is in June. You also need to understand the difference between a sidereal day and a solar day. A sidereal day is defined as the amount of time it takes Earth to revolve once of it’s axis. A solar day is time between the moments in the day when the Sun is highest in the sky. A solar day is 24 hrs. long. A sidereal day is about 4 minutes shorter. There is a difference because Earth is revolving around the Sun while it is rotating. Imagine you see the sun at highest point it will reach in the sky. Exactly one sidereal day later Earth will have rotated once on its axis but you won’t see the sun at the highest point in the sky quite yet. Earth has moved just about 1 degree in it’s path around the Sun so it has to rotate about 1 degree further before you will be facing toward the Sun again. This extra degree takes about 4 minutes. So a sidereal day is about 4 minutes shorter than a solar day. But… the difference between a sidereal day and a solar day is not constant through the year. Sidereal days are gradually getting longer as Earth’s rotation slows but they stay fairly constant throughout the year. In contrast, solar days change in length according to an annual cycle. See https://en.wikipedia.org/wiki/Solar_time for more details.

In December, Earth is closest to the Sun. According to both conservation of angular momentum and conservation of energy, Earth must be traveling fastest around the Sun in December. As a consequence of the shorter distance and greater speed, Earth moves through a greater angle in it’s path around the Sun during a sidereal day in December compared to June. This means that Earth must rotate through a greater angle to reach solar noon again in December. Thus solar days are actually a bit longer (about 30 seconds) in December than June. As a result, solar noon, gradually gets later in the day during December. This effect is significant enough to make the sunsets later each day even though the days (times between sunrise and sunset) are still getting shorter.