The reading material only skims the surface about the Saros cycle. Let's see if you can discover some more about eclipses and this amazing algorithm.
Background: Eclipses reoccur in patterns. You know, from the reading, about the 2 week, 6 month (approximately), and the 6,585.3 days (18 years 11 days 8 hours) saros. This pattern was known (by observation) by the ancient Chaldeans who discovered it by observing patterns in lunar eclipses. It was later discovered to work for solar eclipses as well.
1. What is the minimum and maximum number of eclipses (lunar and solar total) possible in any one year?
Answer: The number can vary from 4 - 7 in any given year. The breakdown for the minimum is 4 eclipses (at least 2 of them must be solar) all the way to a maximum of 7 eclipses (very rare .... 3 lunar and 4 solar). In most years, there are 4 eclipses (2 solar and 2 lunar).
2. In any period of 6,585.3 days, approximately how many eclipses are there? How many are solar and how many lunar?
Answer: In any given period of 6585.3 days you will find about 80 eclipses - spilt almost evenly between solar and lunar. After you understand the answer to the last question you will see why this number can change. You actually will need to add up active solar saros cycles and active lunar saros cycles.
Suppose there is an lunar eclipse today. You already know there would be another one in 6,585.3 days. But will it be exactly like the current one? The answer is NO. There will be differences. Your job is to discover these differences by answering the following questions about these two (hypothetical) eclipses separated by 6,585.3 days.
3. In terms of viewing it from your geographical location on the earth, how will this next one (the one in 6,585.3 days) be different from the one today? In your answer explain why some believe the true eclipse cycle should be 3 saros periods ... not one.
Answer: The problem comes in because the saros period is not a whole number but has that nasty ⅓ at the end. This extra 8 hours means the earth will NOT be oriented in space the same way the next time around in the saros cycle. This changes your local horizon and it may not be visible from your location. To see this next eclipse the same way, you would need to be approximately 120 degrees ( ⅓ of 360 degrees) west of your current position. Given that problem, all you have to do is wait 3 complete saros cycles and you will see a lunar eclipse from your same location. This is known as the exeligmos cycle.
4. Will this next eclipse (the one in 6,585.3 days) be the same type of lunar eclipse? Explain. Note: we discuss the types of lunar eclipses in the class material.
Answer: Not necessarily! As you progress in increments of 6,585.3 days, you will notice that the type of lunar eclipse will change ... but the change is very gradual. The progression is best depicted in the following diagram (courtesy Matthew D. Zimmerman). You start out with a penumbral eclipse, progress to a partial eclipse, move to a total eclipse, and then digress back to penumbral. However, this progression typically takes over a thousand years to complete (anywhere from 1226 to 1550 years) so it is most likely you will see the same type of eclipse 6,585.3 days later.
Astronomers have looked at eclipses separated by 6,585.3 days and grouped them together .... forming a cycle. Each cycle has a beginning date and an end date. Each cycle is assigned a unique number. There was a rather uneventful lunar eclipse in 2013. It was a lunar penumbral eclipse on 5/25 that nobody in their right mind would bother to observe. Only 2% of the moon entered the earth's penumbra (and it never got remotely close to the umbra). However, astronomically it was a pretty big deal because it was a start of one of these cycles.
5. What saros number was this new cycle assigned? How many eclipses will be in this cycle? How long will this cycle last?
Answer: May 25, 2013 was the start of lunar saros 150. It will contain 71 eclipses and last for 1262 years (ending on June 30, 3275)