Total Eclipse Geometry

Published 7-31-2017

As we write on July 30, 2017 our daily newspaper weather almanac page proclaims the moon on this date to be in first quarter phase. Careful observers watch the moon cycle through its beautiful phases once in approximately 29 1/2 days each month. On this day the sun, earth and moon form a 90º angle. After sunset, this right angle provides a view of a half illuminated moon surface called first quarter. In the coming week the sun, earth, and moon angle will increase to 180º. The side of the moon facing us will then be fully illuminated, providing a full moon on August 7.

In the week following full moon, the angle of the three bodies slowly decreases. In a week the angle of the three bodies is again 90º with the moon now on the opposite side of the earth. We experience last quarter phase on August 14. The moon is half illuminated again, but this time a different quarter of the moon is visible in sunlight. The geometry of the three bodies changes moment by moment. In one week we arrive at a very significant “straight angle” configuration of the the astronomical bodies. On August 21, 2017 we experience new moon phase. The three bodies are directly in line. In the United States a total solar eclipse is in prospect for millions of residents. We will experience the “new moon of the century” in terms of additional astronomical coincidences.

Not since 1970 and 1979 has a total solar eclipse been visible to so many people in the US. The 1970 total solar eclipse event was visible to many people along the east coast before the shadow passed out to sea near Norfolk, VA. Even though the driving time from my home to Norfolk was approximately six hours, I made an error in judgement in not traveling to Norfolk from northern New Jersey. However, I graphed the temperature drop of 4º F while the partial eclipse progressively covered nearly the entire sun. In northern New Jersey, 3/7/70 occurred on Saturday when school was not in session. I encouraged my students to observe the eclipse with protective eye devices. During the 1979 event only a few states in the Pacific Northwest were able to observe totality.

The effective difference between observing a total eclipse of the sun in the narrow path of totality and observing the partial solar eclipse just outside the path of totality is comparable to the difference between hitting a home run in baseball just inches beyond the outfielder’s glove and having the outfielder make a leaping catch for the out. There are many other analogies we could cite to illustrate the difference between total success and great disappointment. This explains why millions of visitors will travel many miles to observe the August 21, 2017 eclipse in the narrow path of complete totality.

The shadow of a total eclipse of the sun traveling across virtually the entire United States mainland has not occurred in the US since 1918. There have been many partial solar eclipses, annular solar eclipses, and hybrid solar eclipses. Other awe-inspiring eclipses are various types of lunar eclipses. A total solar eclipse visible to so many people is a truly rare and uniquely spectacular event. We will follow the story of this great total solar eclipse both before and after it occurs.

Citizens who position themselves in the path of totality may experience various degrees of success. In one more baseball analogy we claim that totally clear skies on August 21 might be compared to hitting a baseball completely out of Yankee Stadium. But if a turn at bat barely results in a home run there is still cause for rejoicing for the winning team. With the bases empty, the team scores one run. With the bases full, our team scores four runs—a grand slam. If the ball also travels out of the stadium, we would catalog and remember the wonderful additional details forever! The events of the upcoming total solar eclipse will exceed the glory of any conceivable sports event imaginable. We may pray for clear skies, keeping in mind that we are subject to the natural vagaries of weather. Even if it is cloudy, the onset of complete darkness in the middle of the day will be an event to remember.

This eclipse is a completely natural event but it will inspire self-transcendent, overpowering emotions. A memorable Bible verse translated by Eugene Peterson reads, “What a wildly wonderful world, God! You made it all, with Wisdom at your side, made the earth overflow with your wonderful creations” (Psalm 104:24 The Message Translation).

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