How do we predict solar eclipses?

Predicting Solar Eclipses

Suppose that you observe a solar eclipse in your hometown and want to figure out or predict when you and your neighbors might see another eclipses. What would you begin? First, we remember that a solar eclipse can occur only if the line of nodes points toward the Sun at the same time that there is a new moon. Second, you must know that it takes 29.53 days (one synodic month) to go from one new moon to the next. Because solar eclipses occur only during new moon, you must wait several whole lunar months for the proper alignment to occur again.

However, there is a complication: The line of nodes gradually shifts its position with respect to the background stars. It takes 346.6 days to move from one alignment of the line of nodes pointing toward the Sun to the next identical alignment. This period is called the eclipse year.

Therefore, to predict when you will see another solar eclipse, you need to know how many whole lunar months equal some whole number of eclipse years. This information will tell you how long you will have to wait for the next virtually identical alignment of the Sun, the Moon, and the line of nodes. By trial and error, you find that 223 lunar months is the same length of time as 19 solar eclipses years, because

223 x 29.53 days = 19 x 346.6 days = 6585 days

This calculation is accurate to within a few hours. A more accurate calculation gives an interval, called the saros, that is about one-third day longer, or 6585.3 days (18 years, 11.3 days). Eclipses separated by the saros interval are said to form an eclipse series.

You might think that you and your neighbors would simply have to wait one full saros interval to go from one solar eclipse to the next predict. However, because of the extra one-third day, Earth will have rotated by an extra 120° (one-third of a complete rotation) when the next solar eclipse of a particular series occurs. The solar eclipse path will thus be one-third of the way around the world from you. 

Therefore, you must wait three full saros intervals (54 years, 34 days) before predict the solar eclipse path comes back around to your part of Earth. The illustration shows a series of six solar eclipse paths, each separated from the next predict by one saros interval.

There is evidence that ancient Babylonian astronomers do knew about the predict saros interval. However, the discovery of the saros is more likely to have come from lunar eclipses than solar eclipses. If you are far from the eclipse path, there is a good chance that you could fail to notice a solar eclipse. Even if half the Sun is covered by the Moon, the remaining solar surface provides enough sunlight for the outdoor illumination not to be greatly diminished. By contrast, anyone on the nighttime side of Earth can see an eclipse of the Moon unless clouds block the view.