How does the length of the day vary from one day to the next throughout the year?

Day_to_day change in length of daylight during 2011_Nick Lomb

The change from one day to the next in the length of daylight durind 2011. Graph and calculation Nick Lomb

The length of the day is the interval between sunrise and sunset. We have discussed in a previous post how that varies during the year. Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.

Let us now ask what is the change in the day length from day-to-day? You may have noticed that the time of sunset since 2 January has not changed so far and will not change for a few more days until Friday 14 January 2011. The time of sunrise has been becoming later by about a minute each day so that the length of the day has been shortening accordingly.

The diagram above makes things clearer. The change from one day to the next at the time of the summer solstice in late December is around zero. Similarly, there is little change from day-to-day at the time of the winter solstice in June. This is not surprising as solstice means ‘the day the Sun stood still’, so at those two times of the year we expect little change from day-to-day.

There is more change at the time of the equinoxes – autumn and spring – in March and September respectively. At those times the changes day-to-day can be up to three minutes.

The curve above is surprisingly messy and not the smooth curve that would be expected. The probable explanation is that it is due to the rounding to the nearest minute in the calculation of sunrise and set times. If they were calculated to the nearest second then the curves calculated from them would be smoother. However, there is no point in giving sunrise and set times to any higher precision than a minute as atmospheric conditions each day can make the actual times vary slightly from the calculated times.


5 responses to “How does the length of the day vary from one day to the next throughout the year?

  • I have a basic grasp of the content above.

    I don’t understand why the percentage of rate (day light) increases or decreases through out the year. Why isn’t it some sort of constant?
    Speed of the planet in an elliptical orbit combined with the tile of the earth?

    I live near the 47 parallel and the change is quite apparent over time. In watching the astronomic date on my weather channel I note that the daylight comes and goes at this different percentage at different times.

    I’d appreciate some direction as to where to look next. I ask that you keep the vocabulary simple in that I have no degrees in this, simply a curiosity,

    • > You have to remember that the length of day light varies due to the 23.5 degree tilt that the Earth rotates on. Day length would always be equal if the Earth wasn’t tilted, but because it is, as the Earth travels around the sun, different parts of the planet will be tilted further towards (Summer time, which results in more daylight hours) or further away (Winter time, which results in more night time hours).
      Speed of the planet is irrelevant here.
      The picture on this may help:
      However, it is contextualised towards America, so wherever you see a season, swap it in your mind for the opposite season.

      • We could look at this mathematically: this post displays the change-in-length-of-day which is the gradient or slope of the length-of-day plot shown in the previous post mentioned. The length-of-day plot is ‘cosinusoidal’ therefore its gradient plot is sinusoidal.

      • Doge

        Thanks for helping me understand what was right in front of me all the time.

        In being an elliptical orbit around the sun, the velocity is not at a constant rate. Therefore what I’m viewing in the rate of change is an effect driven by this difference.

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