As the Earth moves around the Sun, the length of the day (defined as the time between sunrise and sunset) changes. The extent to which it changes depends on latitude, as shown in the graph below:

As you can see, the length of a day changes far more during the year at higher latitudes than at lower latitudes. (Latitudes beyond 66°33′ are not shown because the Sun does not always rise or set at these latitudes.) The graph runs from one winter solstice to the next, with the two equinoxes clearly visible in March and September.

It’s quite interesting to look at by how much the length of a day changes every day. This graph would have the same shape as the previous one, but not if we look at *percentage* change. In a way, this gives an impression of how quickly it appears that “the nights are drawing in”.

At higher latitudes the length of day changes quite noticeably in early January and mid-November. In some situations two adjacent days are different in length by nearly five minutes, and at some points the day loses nearly fourty minutes over the course of a single week.

OMG! I just got excited after seeing this post here. That sounds great to know statistically that what is the rate of change of day length with latitude. I’m thankful to you for making this informative post.

Thanks, always wanted to know this. But can you explain WHY the rate of change is faster either side of the winter solstice also the curious shape of the curve mid spring and mid autumn? Answer must be topological

I’m not sure I understand what you mean by “answer must be topological”?

Hi, I was finding your comment “It’s quite interesting to look at by how much the length of a day changes every day. This graph would have the same shape as the previous one” most confusing – because clearly when daylength is max/min, rate of change of daylength is close to zero – and at the equinoxes, rate of change is clearly max. In other words, the graph you allude to ought to be a graph of the first derivative, not an identical graph.

However, that equates to a sine/cosine situation ie: d/dx sin x = cos x – so it’s not the same graph but the same shape of curve moved along 1/4 year.

I think this could do with clearing up.

I’ve come up with two explanations for the asymmetry, one mathematical and one geometrical.

First, it’s a percentage change so it depends on the value and not just the rate of change (as would the first derivative) so an equal change in the length of day would be a greater percentage change near the winter solstice when the day length is smallest. This happens when the absolute change is small, which means the two effects are somewhat at odds, leading to the seemingly strange shape of the graph.

There’s also the fact that the sun is large enough for its light to not arrive at Earth perfectly parallel, so slightly more than half the planet is in daylight at any given time. So since (as an offset from 12 hours) summer days are longer than winter days are short (a careful inspection of the first graph reveals this) the percentagewise change will be even more perturbed.

The first effect is very dominant at higher latitudes. As an extreme example, above 70° in the Arctic the day-to-day percentage change in sunlight hours would be infinite (division by zero) with the first sunrise after a long winter with no daylight.

If there are other significant factors I’d be glad to hear them.

Can I edit that? Geometry is math. What I meant was arithmetic or algebraic reasons vs geometric.

This is interesting. The asymmetry of the 2nd graph is not intuitive. I think Toby provides an explanation. It would be helpful to have a graph of time delta, not as a percent, as well.

Um i can count to letter 5

Thank you. The exact graph I was looking for to show that at about the first week of February the sun speeds north and days lengthen at a quick and steady rate. Much more so than the previous weeks after winter solstice.

Is it a suitcase or a grocery bag?

Is it a grocery bag or a suitcase? I’ve been questioning my existence ever since I’ve thought of this question.