Is there such a thing? I don’t mean a perfect observing experience (which we all hope for but don’t always get), but an aspect of an eclipse that, if attainable, would be abstractly beautiful in its own way: where the sun, the moon, its node, and its perigee are all exactly lined up. That’s what I’m calling a ‘perfect’ eclipse; a kind of heavenly harmony, appreciated only if you know it’s there. The much-anticipated solar eclipse of April 8, 2024 will sweep up from Mexico then northeast through the heartland of this country into eastern Canada. Will it be ‘the one’? If not, will there be another within its own Saros family?
To answer these questions, we’ll need to dissect the springtime eclipse and its near Saros relatives. April’s eclipse will assuredly be beautiful and dazzling, but how will it stack up astronomically? We’ll mathematically x-ray it and its kin to find out. The Babylonians puzzled-out the Saros and exeligmos patterns of the eclipses and scratched their results onto clay tablets thousands of years ago. Now we have rather more advanced techniques to investigate (and record) the subtle changes within those cycles. These may help us in our quest.
The April solar eclipse is part of Saros 139, a thirteen-century-long collection of 79 eclipses which began in May 1501 CE – around the time young Copernicus was studying law in Italy while his heart was in Ptolemy’s astronomy – and won’t end until July 2763. So we’re not yet in the middle of this series.
Shifts and Tilts
Refresher: The places where the moon’s tilted orbital plane intersects the plane of the ecliptic are called the nodes; there are two of them, one where the counterclockwise moon transits above the ecliptic plane, and the other where it travels down below it. With that in mind, consider these two classes of solar eclipses:
Ascending node solar eclipses have odd Saros numbers [1]. They occur when, during the eclipse, the moon passes through its “ascending node” to spend time above the plane of the ecliptic. The April 2024 eclipse track tilts up from Mexico up to eastern Canada, like a plane taking off. But not all eclipses even in the same series follow that type of arc, since the projection of a moving lunar shadow onto the top or bottom hemisphere of a seasonally-tilted, rotating spheroid is a complex business, especially near the poles. We can say that with each eclipse in the Saros series (that is, every 18 years, 11 and 1/3 days), the curved path shifts southward, usually by several hundreds of kilometers and gamma decreases. (Gamma, as you’ll recall from our last article, is the measure of how aimed-at-the-center of earth the shadow is, with north of it being positive and south of it being negative, and dead-center being zero.) In odd-numbered solar eclipses, then, gamma diminishes (goes increasingly negative) as the paths continue to shift southerly with each eighteen-year cycle, till after its final pass grazing the south polar region centuries later, the Saros series ends.
Descending node solar eclipses (i.e., where the moon drops below the plane of the ecliptic during the eclipse) have even Saros numbers. The upcoming annular eclipse of October 14, 2023, for example, is in even-numbered Saros 134. With each eclipse in the even Saros series the path shifts northward, usually by several hundreds of kilometers. Gamma thus increases as the paths shift northward on each cycle until the series ends.
Now that that’s all clear in your mind, let me add that with lunar eclipses, the above rules are switched! Saros numbers of ascending node lunar eclipses are even, and those of descending node lunar eclipses are odd. This can be confusing! So, when in doubt try looking at this chart:
April eclipse line-up
Given the advent of another North American eclipse, and to begin our inquiry, we are drawn to looking at its ‘chart’ of vital signs – and to interrogate it in the context of its family history. We’ll check first the three eclipses before and after it, covering a century, and describe our findings. Some of the subtler eclipse trends are only discernible when you stack them over time.
We’ve picked seven eclipses in Saros 139 bracketing the April eclipse. Even with that small sample of the overall series, we can see in a compact way the march of Saros, gamma, nodes, and perigee; we don’t need thirteen centuries of eclipse data to make our point.
Saros interval: First notice the Saros interval itself between each event, of 18 years, 11 days, and about 8 hours. Each eclipse in Saros is, as noted in our last article, geographically similar to the one before: similar in shape but shifted West by 120⁰. Compare for example the earlier-posted path of the March 29, 2006 solar eclipse over Africa with the upcoming one of April 8, 2024 over North America.
Exeligmos eclipses: You can spot the two exeligmos eclipses that bookend our sample: the first is on March 7, 1970, and the last is on May 11, 2078. Note how close the times of their maximum eclipse are to the time of April’s eclipse maximum. Exeligmos eclipses are also geographically similar but shifted in latitude. Compare the earlier-posted map of the March 7, 1970 eclipse with that of the April 8, 2024 eclipse.
Distance of the moon from its node: There would not be an eclipse unless the moon is at or near the node, the place where its orbit intersects the earth-sun ecliptic plane. The moon moves round its orbit counterclockwise, but (as we discussed in our last article) the nodes move the other way. The third to last column of the chart shows the moon’s distance in degrees from the nodal point at each Saros event. All of these in the list are actually quite close (not surprising since they belong to the same Saros series) – especially given the fact that some form of partial eclipse can typically occur even when the moon is 17 or 18 degrees away from the node. But for the eclipse of April 8, 2024, the moon will be less than 4 degrees away.
Gamma drift: The moon’s distance from the node shifts by almost half a degree with each Saros cycle. This is an empirical manifestation of the mean .48 degree per Saros ‘gamma drift’ we talked about in our last article. It’s the reason that every Saros series ultimately comes to an end, when the node is simply too far away from the moon at syzygy to allow any further eclipses of the series. In this Saros 139, we can see in the data that gamma gets closer to zero with each eclipse, signaling the steady southward shift of the moon’s shadow track on the surface of the earth. It is plus .3431 for the April 2024 eclipse. It will be closest to zero (γ = .0525) for the eclipse of June 3, 2114, where the center of the moon’s shadow will pass smack over Saudi Arabia, and gamma then turns negative for subsequent eclipses. In the last eclipse of Saros 139, on July 3, 2763 (γ = –1.5132), the moon’s tiny shadow just nicks the lit edge of Antarctica, then mostly in its wintertime darkness.
Distance of the moon to the lunar perigee: The Babylonians seemed interested in how eclipses lined up with the apsides of the lunar orbit – perigee (when it is closest to the earth) and apogee (when it is farthest from the earth), as evidenced to them by the respective speeding up or slowing down of the apparent motion of the moon in the course of its orbit around the earth. (We know this occurs because the moon’s orbit is slightly elliptical.) We have a special interest in it too, inspired by our question.
A solar eclipse can occur when the moon is neither at apogee nor perigee. The line of apsides (an imaginary line connecting apogee and perigee) revolves once every 8.848 years, precessing eastward in the same direction as the moon. Sometimes (here’s the interesting part) it lines up with the nodal line. You can see the perigee changes in the next to last column of the above table, and that, for the April 2024 eclipse, the moon is reasonably close to perigee, about 17 degrees away, having sailed past it the previous evening. Because the moon is close to the earth at this eclipse, it signals a longer-duration event. Luckily for totality-lovers, the moon is then only a day past its perigee, at only 359,781 km away, its 33.3 arcminute size fully covering the solar disk.
As an interesting consequence of the April 2024 lineup, the solar eclipse of October 14, 2023, occurring half a year earlier at the opposite (descending) node (and belonging to a different, even-numbered Saros 134), occurs somewhat close to the moon’s apogee, having passed it only four days earlier on the 10th. Hence: an annular eclipse results, where the moon is insufficiently close to the earth to fully cover the solar disk.
Is it a 'perfect' eclipse?
You may have looked at figures for the April 2024 eclipse on the above chart and thought, okay, the moon is fairly close to the node but it doesn’t seem all that close to the perigee. Wouldn’t a more exceptional eclipse be when the moon and perigee are both very close? The chart gives a hint of when this might be. You can see the declining distance of the moon both from the node and perigee with each eclipse in this sample of Saros cycle 139. Perhaps we can turn the clock ahead mathematically to see if and when perigee might approach zero.
As a matter of mathematical and astronomical curiosity and inspired by a technique used by antiquities scholar Alexander Jones in a recent paper to ascertain the likely epoch of the Antikythera mechanism [2], I decided to chart the closeness of the perigee with the closeness of the nodes on this Saros cycle, reaching ahead to the eclipse of July 27, 2204. Here is the graph of that exercise. Each little diamond in our sample represents consecutive solar eclipses in Saros 139:
The graph continues where our chart of data left off, at the eclipse of May 11, 2078. Included here are the further consecutive Saros 139 events of May 22, 2096, June 3, 2114, June 13, 2132, June 25, 2150, July 5, 2168, July 16, 2186, and July 27, 2204 [3].
As we suspected, there is indeed a future solar eclipse in this part of Saros 139 where perigee distance from the new moon is very near zero: on July 16, 2186. At that solar eclipse, over northern South America, the moon and perigee are joined at the hip: perigee occurs within an hour of totality. If for our perfect eclipse we seek to maximize the length of totality, we would definitely want to pick the eclipse of July 16, 2186: imagine a maximum 7 minute and 29 second period of darkness! In fact, it’s the longest duration of totality in the entire 1,262-year Saros 139. Our April eclipse will have a respectable but not exceptional maximum totality of 4 minutes and 28 seconds.
But suppose our idea of perfection entails a balance of nodal distance and perigee distance. You’ll notice that while we’ve closed the perigee distance gap with the July 16, 2186 eclipse, the distance from the node to the moon is excellent but not spectacular (at least in our theoretical eclipse sweepstakes, where under this metric we need a clear winner in both categories to get the prize). There may have to be a little tradeoff (at least in this range of dates) to locate an optimum that satisfies both criteria. To find the sweet spot where both node and perigee are each exceptionally – if not perfectly – close, we must search for the eclipse closest to zero on both axes. That happens to be the eclipse occurring on June 13, 2132. There, the nodal distance is spot-on and perigee is the same day, only eight hours before the new moon. It will be maximum over Cuba, for an almost 7-minute totality. That, in my book, would get the prize for the (almost) perfect eclipse!
NOTES
[1] Lunar and solar saros are independently numbered series. They can have the same numbers. For example, the lunar Saros 139 didn’t begin until 1658.
[2]Jones, Alexander. “The Epoch Dates of the Antikythera Mechanism (With an Appendix on its Authenticity).” Institute for the Study of the Ancient World Papers 17, (2020). http://dlib.nyu.edu/awdl/isaw/isaw-papers/17/.
[3] Saros eclipses in Saros 139 and times were taken from https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros139.html. Determinations of lunar parameters for eclipse dates and times came from Aldo Vitagliano’s Solex program.
Comentarios