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Comment by gregfjohnson | Hacker News Reader

This brings to mind something I've wondered about for a while. Sunrise on the shortest day of the year is earlier than sunrise for several days after it.

Sunset on these days after the shortest day is of course even later than sunset of the shortest day.

On the beautiful image of the OP, you can see that after dawn of December 21, dawn continues to get later over the next few days.

In my area, sunrise on 12/21/2024 was 6:54am, and it will continue to get later until 1/8/2025, when it is at 6:59am.

Length of day on 12/21/2024 is 9 hours, 54 minutes, and length of day on 1/8/2025 is 10 hours, 2 minutes.

Searching the web, I haven't found an explanation for this that "clicks" for me as both intuitive and rigorous. Any thoughts or pointers on this?

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OK here is my attempt at intuition:

Here is an approximation that captures the main effect (the 23.5 degree tilt of the earth's rotation axis) and overlooks secondary effects.

Consider the equator. Imagine a circle on the X-Y plane centered at the origin. Angle the circle up 23.5 degrees, rotated around the x axis. The projection of this circle back onto the plane is an ellipse on the X-Y plane, with the vertical axis about 92% of the length of the horizontal axis. Now, consider a series of vectors in the X-Y plane starting on the X axis, with angles in steps of 0.986 degrees. (This is approximately the angle the earth progresses around the sun each day.)

Where each vector hits the unit circle, move the point up or down so that it hits the ellipse. The angle will change a bit for most of the rays. In some cases the angle will be a bit smaller, and in some cases a bit larger. These discrepancies are the variations in time of day of sunrise and sunset over the course of a year on the equator.

The apparent movement of the sun is not influenced solely by the Earth's rotation, but also the instantenuous velocity of revolution and also the fact that Earth's axis is slanted w.r.t. the ecliptic.

Study this Wiki article, especially the components part: https://en.wikipedia.org/wiki/Equation_of_time

It’s partly because we have a standardised 24 hour clock and solar noon (when the sun is highest) is sometimes ahead and sometimes behind GMT noon. The sunrise and sunset times relate to solar noon so they vary accordingly.

See ‘equation of time’ and ‘analemma’ for underlying astronomical explanations, as hinted at by sibling posts.

I don’t know if this is sufficient but there was just a StarDate about the topic https://stardate.org/podcast/2024-12-3

Thanks, very much appreciate the thoughts and pointers!

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