The Total and Annular Solar Eclipse: A Celestial Feast
The annular eclipse of October 14, 2023 has led to magnificent, awe inspiring photographs by members of the Amateur Astronomers Association. Thankfully, the skies were generally clear. The technical knowledge and skill of our members have been superb. Our colleagues travelled to the path of the eclipse which included the Western United States, Mexico, Central America, and South America. Those of us who stayed home are benefiting from their efforts and expertise with many incredible images displayed in this and subsequent issues of Eyepiece. The photographs have captured the movement of the moon, a massive, roughly spherical object 3.5 million meters in diameter, travelling at over 1 kilometer per second, and interposing itself between the Sun and the Earth creating “a ring of fire”. This annular solar eclipse will soon be followed by a total solar eclipse on April 8, 2024 … an event which will create another celestial feast for our members.
The alteration between an annular and total solar eclipse stems from the moon’s somewhat elongated orbit, an ellipse. We can thank two scientists for creating this concept: In the late 16th century Tycho Brahe and Johannes Kepler worked with the sextant and quadrant to acquire data on the movements of the planets with an accuracy within 2 arc minutes … all without a telescope. Then in the early 17th century Kepler synthesized the data into three laws of planetary motion. The model of Nicolaus Copernicus published in 1543 proposed that the planets orbited the Sun in perfect circles. However, Kepler found that circular orbits fit Tycho’s data very poorly and realized that fit could be achieved by elliptical orbits.
This revolutionary astronomy, known as Kepler’s first law, overturned about 2,000 years of theories in which celestial bodies orbit in circles. The definition of an ellipse is that, for any orbital system, the distance from one focus of the ellipse (the Sun) to the planet plus the distance from the planet to the alternate focus is the same regardless of the planet’s position in its orbit. See Figure 1a.
The ellipse is an elongated circle, and eccentricity measures that elongation (Figure 1b). The further apart the two foci of the ellipse, the greater the elongation, and the higher the eccentricity. With the exception of Mercury, whose eccentricity is 0.206, the eccentricities of the planets orbiting the Sun range from 0.007 for Venus to 0.093 for Mars. The eccentricity of the moon’s orbit around the Earth lies between these: 0.055. The eccentricity of the Earth’s orbit is 0.017 which is close to a circle. Perhaps this explains why no one identified elliptical orbits prior to Kepler. Also, because Mars has a relatively high eccentricity and because it is relatively close to Earth, Kepler may have leaned heavily on Mars for developing his laws.
For a solar eclipse to occur, two conditions are required: (1) there must be a new moon, and (2) the Sun, moon and Earth must be aligned. If this is so, then at perigee (when the moon is closest to the Earth), the moon’s shadow covers the Sun entirely, but the lowest level of the Sun’s atmosphere, the chromosphere, is often visible (Figure 2a). As the moon progresses in its orbit, it comes to apogee (when the moon is furthest from the Earth). If once again the moon is new, and the Sun, moon and Earth are aligned, the result is an annular eclipse (Figure 2b). (“Annular” comes from the Latin, Annulus, meaning a ring.)
Solar eclipses display three remarkable phenomena: First, we see a total eclipse alternating with an annular eclipse; the moon’s eccentric orbit is essential for this pattern. Second, the number of total eclipses is nearly the same as the number of annular eclipses, 71 and 73, respectively, in the 100 years of the 20th century, a difference of less than 3%. Third, in a total eclipse the chromosphere, the lowest segment of the Sun’s atmosphere, extends beyond the Sun’s surface by about 0.6% of the Sun’s radius (Figure 3a), and the ring of the annular eclipse extends beyond the moon’s shadow by about 5% of the Sun’s radius (Figure 3b). These small percentages are most likely coincidental.
If the only requirements for a solar eclipse are that the moon comes between the Earth and the Sun and that the moon is new, why don’t we get a solar eclipse whenever there is a new moon? That should give us an average of more than 12 eclipses per year instead of 1.44. The answer is that the plane of the moon’s orbit is tilted about 5 degrees relative to the plane of Earth’s orbit (See Figure 4).
These eclipses are indeed special events. The photography of AAA members demonstrates just how remarkable these events can be.
I am grateful to David Kiefer, Joel Gonzalez, and Stan Honda for their careful review and improvements to this article.
