Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
a collaboration of the Shodor Education Foundation, Inc., Eastern North Carolina School for the Deaf, Barton College, the National Technical Institute for the Deaf, and Interpreters, Inc.

For Teachers!

Predicting Lunar Eclipses 

My students find 2 patterns in the first set of eclipse dates: 
5/3/01 18:31 
10/27/01 15:01 
4/22/02 18:53 
10/17/02 6:03 
4/12/03 0:13 
10/6/03 15:17 

Some students see that the eclipses are a few days short of 6 months apart. Other students look at every other date and see that the eclipses are a few days short of a year apart. Both patterns are acceptable from the data presented. They can't predict exactly when the next eclipse will happen but they are confident to within a day or so. 

When they check it with the next few eclipses, their predictions don't hold up. We have a discussion about the importance of verifying our model's accuracy. We talk about a scientist's need to be persistent and not give up. Most scientific theories aren't perfect on the first try. When other scientists check out the theory they often find at least a small part to criticize. The scientists then go back and try to either improve the theory or, if the problems are too big, they start over. 

If you give me an eclipse date I can't predict the next eclipse. However, I can predict one that will happen 18 years, 10 and a third days later. The second group of eclipse dates is in a Saros series.  

After the students have their algorithm, give them the spreadsheet of twentieth century eclipses. If they paste these dates onto the left hand column of their spreadsheet they can use them as referents to build their table of eclipses. They can go to: http://sunearth.gsfc.nasa.gov/eclipse/LEcat/LEcatalog.html 
to get information and tables on 5,000 years of lunar eclipses. They can use this information to check their predictions. Their predictions will not be precise to the minute. Ask them to calculate their uncertainty. Ask them to explain why their predictions don't exactly match the times on the NASA web site. 

In the verification activity you can divide the class into 5 or 10 groups if time is an issue. Assign each group a range to check, 1-10, 11-20... Everyone should check the range 40-45. This contains the Saros cycle.  You can download a completed spreadsheet to check their work.

As an extension, they can work through the activity on finding the fastest and slowest orbital speed of the moon. Depending on where the moon is in its orbit, its speed will vary. The earth's speed also varies and affects when the full moon occurs. That can make it a little behind or ahead of schedule. The students may also say that the planets tug on the moon and make it a little late. 

Because the Saros gradually moves up or down the moon some of the eclipses are partial. By knowing where in the cycle we are we can predict whether the eclipse will be partial or complete. Since the moon is closer to the earth at different times in its orbit, it sometimes it appears larger. A good site to explain and view images of the moon at different sizes can be found at: 
http://www.spacescience.com/newhome/headlines/ast19dec99_1.htm 
When it is closer, the earth's shadow is smaller, and therefore may not completely cover the moon. This would be a partial eclipse. 

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This project is supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.