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The geometry and physics behind the Great American Eclipse

7 August 2017

Orbital inclinations and tidal forces complicate an otherwise simple alignment of Sun, Moon, and Earth.

Solar eclipse, 11 August 1999
The total solar eclipse of 11 August 1999 belongs to the same Saros cycle as the one that will occur on 21 August 2017. Credit: Rowan McLaughlin, CC BY 2.0

On 21 August, Sun, Moon, and Earth will line up in beautiful syzygy and produce a stunning solar eclipse visible across the continental US. The Moon’s umbral shadow will sweep a path that starts in the North Pacific Ocean, makes landfall in northern Oregon, and slides off the coast of South Carolina into the Atlantic. Sky watchers will see up to 2 minutes and 40 seconds of totality in which the Moon will completely mask the solar disk. Everyone in the continental US will witness at least a partial eclipse.

What ingredients have to combine to create this magical moment? Although eclipses are predictable and have been for thousands of years, the orbital dynamics are pretty complicated, says Fred Espenak, a retired astrophysicist who spent decades calculating eclipses for NASA. Both Earth’s orbit about the Sun and the Moon’s about Earth are elliptical, and the two are on different planes. To really throw a wrench in the works, both Earth and the Sun are constantly exerting tidal forces on the welterweight Moon.

The inclination of the Moon’s orbit with respect to the ecliptic is about 5º, perhaps a consequence of the impact that spawned our natural satellite. Just as Earth’s axial tilt leads to the seasons, the misaligned orbital planes of Earth and the Moon impact the Sun’s illumination angle. For about five months of the year, the Moon is too far above Earth to cast its shadow on the planet when in its new moon phase. The opposite occurs for another five months, with the new moon too far south to cast shadows on Earth.


For most of the year, the Moon is either “too high” (top) or “too low” to cast a shadow on Earth. Only during eclipse seasons is the alignment just right (bottom). Credit: NASA’s Scientific Visualization Studio

Only about twice a year, for limited stretches of time, do the orbital planes of the Moon and Earth match up closely enough to create eclipses. Because the Moon is really close and the Sun is really big, the alignment doesn’t have to be perfect. Eclipse seasons last between 31 and 37 days; during that time, a solar eclipse occurs somewhere on Earth during every new moon and a lunar eclipse takes place during every full moon. We’re currently in the midst of an eclipse season, and today, 7 August, we happen to have a full moon. As a result, sky watchers in Asia, Australia, and parts of Africa are witnessing a partial lunar eclipse. It’s the lunar appetizer to the solar entrée that will be served half a world away when the Moon becomes new.

The angular separation of the Sun and Moon determines the impressiveness of each eclipse. A central eclipse, in which the entire Moon covers the Sun, occurs when the two celestial objects are within 10º of each other. Whether it’s a total eclipse, in which the Sun’s surface is completely obscured, or just an annular eclipse, in which the Sun’s surface forms a ring around the Moon, depends on the relative distances of the two objects to Earth. To maximize totality, you want the Sun as far away from Earth as possible, making it appear smaller, and the Moon very close to boost its obstruction ability.

Eclipse seasons do not occur at the same time every year. Due to tidal forces from the Sun and Earth, the points where the Moon’s orbit crosses the ecliptic, known as nodes, are constantly shifting. “The Moon’s orbit is like a rubber band being yanked and pulled,” Espenak says. Over the course of a year the nodes migrate westward 19.4º. That roughly one-eighteenth of a rotation means that the following year’s eclipse season starts about an eighteenth of a year, or 19 days, earlier.

Understanding migrating nodes and eclipse seasons offers some power for predicting eclipses in the near term. But looking way ahead, the trick is to think about Saros cycles, sequences of eclipses that share similar geometries. The cycles are the result of taking the lowest common denominator of several distinct periods: the 346.6-day eclipse year (19 days short of a full year); the 29.5-day synodic period of lunar phases; and the 27.6-day anomalistic month, the time it takes the Moon to go from perigee (its closest approach to Earth) to perigee. Start counting from zero each time an eclipse occurs, and the next time those periods will sync up is just over 6585 days later—more specifically, 18 years, 11 days, and 8 hours. Each eclipse in a particular Saros cycle covers a path that is similar, but not identical, to the one before it.

The Great American Eclipse belongs to Saros 145, which made its last appearance on 11 August 1999. On that day Europe, the Middle East, and India enjoyed a total solar eclipse with a maximum of 2 minutes 23 seconds of totality. Because of the eight hours between consecutive eclipses of a particular Saros, each event occurs one-third of a turn westward from the preceding one. And, because the synodic period and eclipse year don’t sync up perfectly, the Moon makes a little more progress each time than the Sun does. That’s why the 21 August eclipse will feature 17 seconds more of peak totality.

Saros cycles provide an incredible amount of eclipse-predicting power, but individual cycles don’t last forever. Saros 145 debuted on 4 January 1639. At the very start of an eclipse season, the Moon’s umbral shadow passed a few thousand kilometers above Earth’s northern polar region. Viewers in a small slice of Siberia experienced a partial solar eclipse. Another partial eclipse occurred near the North Pole on 14 January 1657. This time the event migrated slightly southward, since the Sun is at a higher angle in the sky on 14 January than on 4 January, and the Moon covered a tad more of the Sun. Since then the pattern has continued: Each solar eclipse, in general, has occurred closer to the equator and been more impressive than the previous one.

Saros 145 will climax on 25 June 2522 with an epic eclipse for those who make the trip to see it. Parts of southern Africa will experience 7 minutes and 12 seconds of totality—a mere 20 seconds shy of the theoretical maximum. Then, starting with the next eclipse, the Moon will increasingly overshoot the Sun. The last Saros 145 event, a marginal partial eclipse near the South Pole, will occur at the very end of an eclipse season in April 3009, nearly a millennium after the Great American Eclipse.

Editor’s note, 14 August: A previous version of the article incorrectly said that the Moon can cast shadows on Earth during the full moon phase.

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