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So every four years, we add an extra day. A leap year. This is because a year is actually $365_{1/4}$ days long. But what happens between leap years? After two years, it would get dark at 8:00 AM instead of 8:00 PM. This is obviously not the case. What's going on here?

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As a simplification, think of the length of the year as where the Earth is in its orbit. After 1 year of 365 days, the Earth has not returned to the same spot in its orbit. If we did not have leap years, then the date when seasons occur would change. Leap years keep the seasons in synch with the date. After 365+365+365+366 days (that is, 3 regular years and 1 leap year = 365.25*4), the Earth is at the same spot in its orbit. (This is approximately true because the year is not exactly 365.25 days long).

On the other hand, when it gets dark is related to the length of the day, and that is independent of the length of the year. In order for it to get dark at 8 am, you would need to reset your clocks to 0 after 1 exact orbit (365.25 days).

Now for a little more detail. There is a slight difference between a year measured "when the Earth returns to the same spot in its orbit" as I described above and a year measured "from one vernal equinox to the next". (The first definition is the sidereal year, and the second definition is the tropical year). The "Sidereal vs. Synodic Motions" webpage explains why the sidereal year is about 20 minutes longer than the tropical year. Our calendar is based on the tropical year. So after 1 tropical year (365.242 mean solar days), the Earth still has not returned to the same spot in its orbit! Details, details, details!

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Leap seconds keep the clock in sync with solar time of day. Leap years keep the calendar in sync with the seasons. The two (leap seconds and leap years) have nothing to do with one another. We have leap seconds because a day is now a tiny bit longer than 86400 seconds. We have leap years because a year (tropical year) is about 365.24219 days long.

If we didn't have leap years but did have leap seconds, solar noon and noon by the clock will continue to occur at more or less the same time (ignoring cyclical changes such as the equation of time and daylight saving time). The calendar would become out of sync, becoming almost a month off from the seasons in just a century. Adding an extra day every four years doesn't quite do the trick; this is why 2100, for example, will not be a leap year.

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  • $\begingroup$ You should clarify that leap seconds keep the sun at zenith at noon precisely (ignoring timezone creep), thus making the definition of solar day obvious to the layman. $\endgroup$ – Carl Witthoft Nov 8 '17 at 14:34
  • $\begingroup$ 2000 was a leap year due to a rule that and year that ends with two zeros and is evenly divisible by 400 is a leap year. Otherwise we wouldn't have had an extra day during a presidential election year. The Earth's rotation is never exactly 24 hours. Most obviously, the Moon's tidal drag slows the Earth's rotation constantly, but the day is also affected by volcanic eruptions, large avalanches of land and snow, and tsunamis. $\endgroup$ – Howard Miller Nov 8 '17 at 22:36
  • $\begingroup$ While I get what you mean, It's not exactly true that "The two (leap seconds and leap years) have nothing to do with one another". If you slowed the rotation of the Earth down we would require both more leap seconds, and fewer leap years than the Gregorian calendar sets. (If the rotation was slowed enough to require an average of 86457.3 seconds a day, while it wouldn't effect the actual number of seconds it takes the Earth to complete one orbit of the Sun, it would make leap years unnecessary because the march Equinox would happen every 365 days, because the days themselves would be longer.) $\endgroup$ – Jacob C. says Reinstate Monica Feb 13 '19 at 8:10

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