The Frequency of Lunar Eclipses

Last night we had a beautiful view of the total lunar eclipse from Orlando. In some ways it was more impressive to see it during the partial phase when only part of the Moon was in the shadow of the Earth. The curved shadow of the Earth across the face of the full Moon provided ample evidence that the Earth was a sphere long before it was finally circumnavigated. Maybe Sherri Shepherd of “The View” got a look.

Lunar eclipses occur when the Moon is on the opposite side of the Earth than the Sun so that the Earth’s shadow falls on the Moon. If the orbit of the Moon were in the same plane as the orbit of the Earth around the Sun, we would have a total lunar eclipse every full Moon. The Moon’s orbit is inclined to the plane of the Earth’s orbit (the ecliptic) by a little over 5 degrees. So the Moon crosses the ecliptic twice each month, but for a lunar eclipse to occur, that crossing point must occur when the Moon is full (meaning that it is on the opposite side of the Earth than the Sun). In rough numbers that occurs twice a year. However, the size of the Earth’s shadow at the distance of the Moon is only a couple of times the size of the Moon, so depending on the exact timing of the Moon crossing the ecliptic, the Moon may not pass through the shadow entirely (resulting in a partial eclipse), or it may only pass through the penumbral shadow (where only part of the disk of the Sun is obstructed by the Earth). Nevertheless, I could not help but wonder how the local Orlando television station got the idea that it would be 40 years before the next total lunar eclipse. In fact the next total lunar eclipse will be in December 2010. The gap between this one and that 2010 total eclipse is actually unusually long. There will be 85 total lunar eclipses in the 21st century, or nearly one every year.

Because the Moon’s orbit is not only inclined to the ecliptic, but is also not circular, there are additional differences in the frequency of eclipses as the orientation of the Moon’s elliptical orbit changes with time and the distance of the Moon from the Earth (and hence the size of the shadow) also changes. Combining the time for the Moon to go around the Earth, the time between two full Moons, and the time for the Moon’s elliptical orbit to return to its same orientation with respect to the Earth and the Sun, we get a cycle for when eclipses will repeat with nearly the same duration and visibility (this holds for solar eclipses as well, which are much more finnicky than lunar eclipses because the shadow cast by the Moon is much smaller than the shadow cast by the Earth). This cycle is called the Saros cycle and is a little over 18 years. So I still don’t know where the local weatherman got his 40 year figure, but the station’s web site has the correct information now.

The more spectacular solar eclipses are far more rare due to the small size of the Moon’s shadow. There is a nice total solar eclipse visible across the United States on August 21, 2017, and another one on April 8, 2024. In the meantime, you’ll have to go quite far to catch one.

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