The Eclipse September 7, 2017

Copyright © 2017          John F. Oyler

September 7, 2017

The Eclipse

I thoroughly enjoyed the eclipse. However before I get into that I must apologize for an error in my column on the last “Second Tuesday” workshop. The correct date for the next workshop is September 12, not 19 as reported.

I initially made myself a small pinhole projector from a cracker box, but was disappointed in the size of the image. Consequently I fabricated one about forty inches long from a box that originally contained a vacuum cleaner. This was much more successful and I was pleased with the photographs I was able to take of the images.

The children next door had an abundance of special glasses which they shared with me, so I was also able to see the eclipse first hand. It was quite cloudy but the sun kept coming out briefly, just enough for us to keep track of the progress of the eclipse. Coupled with the excellent television coverage of the total eclipse it was a very interesting experience.

I was initially impressed with the fact that some people are smart enough to be able to predict the timing of eclipses precisely until I learned that people have been doing that for several millennia. So then I began to wonder if that is something I could do. After all, civil engineers of my era were automatically surveyors and surveyors of my era were automatically astronomers.

I have concluded that a capable surveyor with an accurate timepiece, a surveyor’s transit (theodolite), a clear view of the east and west horizons, and a lot of time could develop enough information to predict the occurrence of eclipses. The first task is to determine the direction of true north. This we do by observing Polaris (the North Star) sufficiently to average out the variance from its small orbit about the true North Pole. This is something we did at Surveying Camp at Penn State sixty five years ago.

Our next step is to determine the latitude of our observation station. This can be done on either the vernal or autumnal equinox, when the tilt of the earth’s axis relative to its orbit about the sun is negated. It is accomplished by taking a sun shot with the transit, another skill we mastered at Surveying Camp. The angle between the sun’s position and the zenith is the latitude of the observation station.

Now we must observe and record the passage of the sun and the moon through the sky for many days, probably several years. If we didn’t already know the magnitude of the tilt of the earth’s axis (about 23.5 degrees) we would soon discover it, as the sun’s position at Noon varies from our latitude plus or minus 23.5 degrees between the summer and winter solstices. This gives us the ability of predicting the position of the sun at any time in the future.

The moon is more complicated because its orbit about the earth is tilted a little more than five degrees relative to the ecliptic (earth’s orbit). Consequently its path through the sky varies plus or minus five degrees throughout a lunar month (one orbit about the earth), which is about twenty seven and a quarter days. By taking enough observations at night, shortly after sunrise, and shortly before sunset we can learn enough to predict the position of the moon at any time in the future.

For a solar eclipse to occur the moon must pass between the earth and the sun. This requires the moon to be in a vertical plane containing the earth and sun, perpendicular to the ecliptic; and in a horizontal plane containing the earth and sun (the ecliptic). The moon automatically satisfies the first requirement once each lunar month and the second twice a lunar month. The frequency of their occurring simultaneously is miniscule.

The factor that allows eclipses to occur relatively frequently is the fact that the earth is so much bigger than the shadow the moon puts on it during an eclipse. For this summer’s eclipse the umbra had a diameter of seventy miles passing over a disc with a diameter of eight thousand miles. Even if the moon is as much as a degree out of the ecliptic, its shadow can still hit the earth, dramatically increasing the probability that an eclipse will occur, and making it much easier for the amateur to predict its occurrence.

Unfortunately a search on the Internet for “How to Predict an eclipse” sends you to a website with a “fill-in-the-blanks” screen that provides that information for any location on the earth. This highlights my concern that future generations will trade the ability to derive something for the ability to look it up.