exupero's blog

# XKCD's "Summer Solstice"

This XKCD comic published on the northern summer solstice highlights a fact I enjoyed discovering a few years ago, that the latest sunset doesn't occur on the longest day of the year. One of the first posts on this blog illustrated the similar phenomenon of the latest sunrise and earliest sunset not occurring on the same date as the winter solstice, and the astronomical wall calendar I created for my kids this year labels not only the solstices but the dates of the earliest and latest sunrises and sunsets.

The comic intimates that the latest sunset doesn't occur on the solstice due to the shape of this Earth's elliptical orbit, and Explain XKCD attributes it to either (or both?) the varying speed of the Earth on an elliptical orbit and the times when we're nearest or furthest from the sun. That explanation isn't accurate. As I explored in another post, the difference between a solstice and the days of earliest and latest sunrise vary by where you are on the Earth's surface, specifically by your latitude. Near the arctic circle, the time between the summer solstice and the latest sunset is only a day:

While a few degrees north of the equator, it's almost a month:

If Earth's orbital speed or the nearest or furthest Earth was from the sun, then the latest sunrise should fall on the same date everywhere on Earth. Since it varies by latitude, that suggests the difference is caused by Earth's tilt, not its orbital characteristics. Our orbit may exacerbate the differences by latitude, but orbit isn't the sole factor. Even with a perfectly circular orbit the longest day wouldn't coincide with the latest sunset due to the rotation of the solar terminus.

Explain XKCD hypothesizes that the difference between solstice and most extreme sunset would disappear if the Earth's orbit was such that solstices occurred when the Earth was closest or furthest from the sun. Yet Wikipedia gives Earth's time of perihelion as January 4, 2023, meaning we're farthest from the sun approximately 182½ days later on July 5. While close to the northern summer solstice, that's not six days later but two weeks later.

The sunset calculations in this post use this algorithm. If you have suggestions on how to alter the parameters of the algorithm to approximate a more circular orbit, feel free to email me.