Tag: obliquity to the ecliptic

Earliest Sunset, Latest Sunrise

Why does the Earliest Sunset come before the Winter Solstice and the Latest Sunrise after?


Why does the Earliest Sunrise come before the Summer Solstice and the Latest Sunset after?

Ever wonder? I have. And aside from some hand-wavy explanations, I’ve never been able to explain this very well. Here’s the best explanation I have seen yet, provided in the December 2007 issue of Sky & Telescope, p. 55:

You’d think the earliest sunset would come on the shortest day (or longest night) of the year, at the winter solstice. But in fact, the day-night cycle shifts back and forth a little with the seasons, due to the tilt of Earth’s axis and the ellipticity of Earth’s orbit. At the beginning of December, sunrise, midday, and sunset all happen a little earlier than they “should”, and in January they run a little late. So the earliest sunset ends up being two or three weeks before the solstice, and the latest sunrise is two or three weeks afterward. The exact dates depend on your latitude.

Continuing along that same line of thought…

At the beginning of June, sunrise, midday, and sunset all happen a little later than they “should” and in July they run a little earlier. So the earliest sunrise ends up being about a week before the solstice, and the latest sunset is about a week afterwards. The exact dates depend on your latitude.

I know, I know. You still have a question. “Why are the dates of earliest sunrise and latest sunset closer to the summer solstice than the dates of earliest sunset and latest sunrise to the winter solstice?” Good question. I think it has everything to do with the fact that the Earth is near aphelion at the time of the summer solstice, and thus moving most slowly in its orbit around the Sun (the Earth’s orbit is slightly elliptical and not circular). That means that the Sun is moving slowest against the background stars and thus the accumulated difference between the sidereal day and solar day is the smallest at that time of year. That means the spread of days between earliest sunrise and latest sunset is less. Conversely, at the winter solstice, Earth is near perihelion, and therefore it is moving most quickly in its orbit around the Sun. That means that the Sun is moving fastest against the background stars and thus the accumulated difference between the sidereal day and solar day is largest at that time of year. That means the spread of days between earliest sunset and latest sunrise is more.

Here in Dodgeville, Wisconsin, where the latitude is just shy of 43˚ N and the longitude is just a tad over 90˚ W, the earliest sunset this year is today, Tuesday, December 8, 2020, at 4:25:49 p.m.

Latest sunrise in 2021 will be on both Saturday, January 2 and Sunday, January 3 at 7:31:51 a.m.

Pause to consider that if we were on year-round daylight saving time, latest sunrise wouldn’t be until 8:31:51 a.m.

My preference would be to stay on standard time year-round, as Arizona does.

Milutin Milanković

Serbian engineer, mathematician, and scientist Milutin Milanković was born 140 years ago on this date in 1879, in the village of Dalj on the border between Croatia and Serbia—then part of the empire of Austria-Hungary. He died in 1958 in Beograd (Belgrade), then in Yugoslavia and today in Serbia, at the age of 79.

Milanković is perhaps most famous for developing a mathematical theory of climate based on changes in the Earth’s orbit and axial orientation. There are three basic parameters that change with time—now known as the Milankovitch cycles—that affect the amount of solar energy the Earth receives and how it is distributed upon the Earth.

I. Orbital eccentricity of the Earth changes with time

The eccentricity (e) tells you how elliptical an orbit is. An eccentricity of 0.000 means the orbit is perfectly circular. A typical comet’s orbit, on the other hand, is very elongated, with an eccentricity of 0.999 not at all uncommon. Right now, the Earth’s orbital eccentricity is 0.017, which means that it is 1.7% closer to the Sun at perihelion than its semimajor axis distance (a), and 1.7% further from the Sun at aphelion than its semimajor axis distance.

The greater the eccentricity the greater the variation in the amount of solar radiation the Earth receives throughout the year. Over a period of roughly 100,000 years, the Earth’s orbital eccentricity changes from close to circular (e = 0.000055) to about e = 0.0679 and back to circular again. At present, the Earth’s orbital eccentricity is 0.017 and decreasing. We now know the Earth’s orbital eccentricity changes with periods of 413,000, 95,000, and 125,000 years, making for a slightly more complicated variation than a simple sinusoid, as shown below.

II. Tilt of the Earth’s axis changes with time

The tilt of the Earth’s polar axis with respect to the plane of the Earth’s orbit around the Sun—called the obliquity to the ecliptic—changes with time. The Earth’s current axial tilt is 23.4°, but it ranges between about 22.1° and 24.5° over a period of about 41,000 years. Greater axial tilt means winter and summer become more extreme. Presently, the axial tilt is decreasing, and will reach a minimum around 11,800 A.D.

III. Orientation of the Earth’s axis changes with time

The Earth’s axis precesses or “wobbles” with a period of around 26,000 years about the north and south ecliptic poles. This changes what latitude of the Earth is most directly facing the Sun when the Earth is closest to the Sun each year. Currently, the southern hemisphere has summer when the Earth is at perihelion.

Milanković used these three cycles to predict climate change. His ideas were largely ignored until 1976, when a paper by James Hays, John Imbrie, and Nicholas Shackleton in the journal Science showed that Milanković’s mathematical model of climate change was able to predict major changes in climate that have occurred during the past 450,000 years.

These Milankovitch cycles are important to our understanding of climate change over much longer periods than the climate change currently being induced by human activity. Note the extremely rapid increase of greenhouse gas concentrations (CO2, CH4, and N2O) in our atmosphere over the past few decades in the graphs below.

https://www.noaa.gov/news-release/greenhouse-gases-continued-to-increase-rapidly-in-2022

The world population has increased by 93% since 1975. In 1975, it was about 4 billion and by 2020 it is expected to be 7.8 billion.