How Often Do Eclipses Happen? New Data for an Old Question

Revisiting a Classic Astronomy Question

If you stood at a random spot on the Earth, how long would you have to wait for a solar eclipse to happen?

At the beginning of the 1980s, a mathematician and astronomer named Jean Meeus used one of the first-ever personal computers to crunch some data and come up with an answer. Four decades later, the same question was revisited by mungfali.galihkartiwa07.workers.dev using the power of modern computer servers.

Our main findings were as follows:

• We obtained a figure for the frequency of a partial solar eclipse at a given place: once every 2 years and 7 months on average.
• We provided further insights into the “latitude effect”: Solar eclipses occur most frequently around the Arctic and Antarctic Circles.
• We found evidence for a roughly 21,000-year cycle in the frequency of eclipses in the Northern and Southern Hemispheres.

We’ve reported our results in a paper posted on the preprint database arXiv and accepted for publication by the Journal of the British Astronomical Association —the same journal Meeus published his paper in all those years ago.

How Often Solar Eclipses Occur

In 1982, Meeus used a small HP-85 personal computer to calculate the average frequencies of total and annular eclipses at a given place on the Earth’s surface.

In our study, we ran two Supermicro servers continuously for 102 days. This difference in computing power enabled us to reduce the uncertainty in Meeus’s estimates, and produce a new finding for partial eclipses (which Meeus did not calculate).

A comparison between Meeus’s results and our results is shown in the table below.

Meeus’s figure of once every 375 years for the frequency of a total solar eclipse at a given place has become an oft-repeated statistic. We were able to reduce the uncertainty in his estimate and suggest a small shift in the headline figure to once every 373 years on average.

Our figure for the frequency of a partial eclipse at a given place—once every 2.59 years on average—is a new finding. 2.59 years is approximately 2 years and 7 months.

Another way of expressing this is to say that, every time a solar eclipse occurs somewhere in the world, there is a roughly one-in-six chance that any given town or city will be included.

Testing a Classic Eclipse Calculation

“We approached this with some trepidation, knowing that any disagreement with Meeus would have been hard to explain,” says Dr. Frank Tveter, a senior backend developer at mungfali.galihkartiwa07.workers.dev who holds a PhD in celestial mechanics and is a co-author of the study.

“Seeing that our results closely matched Meeus’s for total and annular eclipses was reassuring—and a testament the durability of his work. That reassurance gave us the confidence to push further, extending the analysis into new areas, such as partial eclipses.”

Where Do Eclipses Happen Most Often?

Meeus showed in his 1982 paper that there is a “latitude effect.” In other words, the average frequencies of eclipses at a given place depend on how far that place is north or south of the equator.

We were able to provide further insights into the latitude effect, and show that eclipses are most frequent around the Arctic and Antarctic Circles.

The following chart shows the return period of partial eclipses at different latitudes. At the equator (0 degrees) the return period is around 2.8 years, while at the Arctic and Antarctic Circles (+66.6 degrees and -66.6 degrees) the return period is around 2.2 years.

To put it another way, on average, you have a shorter wait for an eclipse to happen in the polar regions than in the tropics.

A Tale of Two Hemispheres

Meeus also showed that total eclipses are more frequent in the Northern Hemisphere than the Southern Hemisphere, while the opposite is true for annular eclipses.

At the present time, the Northern Hemisphere summer coincides with aphelion, the point in Earth’s orbit where it is farthest from the Sun. The farther we are from the Sun, the smaller it appears in the sky, and the greater the chance of the Moon being able to cover all of it.

Likewise, the Southern Hemisphere summer coincides with perihelion, when Earth is at its closest to the Sun. The bigger the Sun appears in the sky, the greater the chance of it forming a “ring of fire” around the Moon.

Overall, the Sun spends more time above the horizon during the summer months than the winter months, creating more opportunity for an eclipse to be visible from a given location. Meeus’s data showed that this gives the Northern Hemisphere an advantage for seeing a total eclipse, while the Southern Hemisphere has the advantage for an annular eclipse.

A Long-Term Eclipse Cycle

With a much larger dataset, we were able to go one step further than Meeus and study how the frequency of eclipses in each hemisphere changes over time. Meeus worked with 600 years of data; we looked at 14,999 years.

The dates of aphelion and perihelion are not fixed: They drift slowly through the calendar in a cycle lasting roughly 21,000 years. Our results show how this leads to a shift in the balance of eclipses between the Northern and Southern Hemispheres.

Around 9500 years from now, aphelion will coincide with the December solstice, while perihelion will coincide with the June solstice—a reversal of the current situation. Our results indicate that total eclipses will therefore be more frequent in the Southern Hemisphere, while annular eclipses will be more frequent in the Northern Hemisphere.

It is well known that, at a global level, solar eclipses follow predictable patterns such as Saros cycles, where similar eclipses repeat every 6585 days over periods of 12 or more centuries. The 21,000-year cycle that emerges from our data shows how eclipse patterns extend not just over many centuries, but over many millennia.

The Beauty Behind the Numbers

“Solar eclipses are magic and science mixed together,” says Dr. Renate Mauland-Hus, an astrophysicist and data analyst at mungfali.galihkartiwa07.workers.dev who worked on the study and holds a PhD in cosmology.

“Eclipses have made longstanding contributions to scientific discovery, from testing general relativity to studying the Sun’s corona,” she adds. “They are beautiful both in themselves and in the way they reveal the underlying physics and mathematics of the universe.”