What is a “semester series” for eclipse prediction? - Solar saros series 147 and 152

Yet again, I just stumbled across another baffling eclipse question (actually, two now). I was interested in two eclipses (Saros series 147 and 152) that will both be occurring in 2021. Each of these eclipses will occur relatively near the opposite poles of the earth. The Wikipedia link for saros 147 provided the following additional information:

"Solar eclipses of 1964-1967

This eclipse is a member of a semester series. An eclipse in a semester series of solar eclipses repeats approximately every 177 days and 4 hours (a semester) at alternating nodes of the Moon's orbit.[1] "

These are both fairly young saros series. Saros 152 is comprised of 70 eclipses, while saros 147 contains a total of 80 eclipses. Observations: They are 10 eclipses difference in length - They each began 180 years apart. So, following on from that, I checked out their ending dates and found, much to my amazement, that both series end during the exact same year - exactly 177 day apart - in the year 3049 !!!

So, since this additional information, my new questions concerning these eclipses have become:

1) What exactly is a "semester series" for eclipses (any detail)? The day spacing definition is obvious but doesn't explain much else.

2) Does this mean that some or all eclipses in series 147 and 152 are in the same semester series?

Any eclipse is a coincidence of a new or full moon (repeating every 29.53 day lunation or synodic month) and a lunar node (moon crossing the ecliptic, repeating every 27.21 day draconic month). A semester is 6 synodic months, close enough to 6.5 draconic months that eclipses can occur at that interval in a series 3 or 4 years long.

The interval between any two solar or lunar eclipses can be expressed as $$aI + bS$$, where $$S$$ is the saros interval of 223 lunations, $$I$$ is the inex interval of 358 lunations between adjacent saros series, and $$a$$ and $$b$$ are integers. The semester interval of 6 lunations is $$5I - 8S$$; for each eclipse in saros $$n$$, there may be an eclipse in saros $$n-5$$ one semester earlier, an eclipse in saros $$n+5$$ one semester later, or both. As the eclipses in a given saros series are about 18 years apart, each is in a different semester series.

For example, one semester series runs from 2015 to 2018 and includes one solar eclipse in each of saros series 120, 125, 130, 135, 140, 145, 150, and 155. Another runs from 2018 to 2021 and includes one solar eclipse in each of saros series 117, 122, 127, 132, 137, 142, 147, and 152.

• Hi Mike. I think you answered me in the past and I do appreciated it. Sorry, I'm not so good with visualizing the math. So, are you saying that a "semester series" is technically only three or four saros cycles in length and involve saros series numbers that are n+1 or n-1 difference in numbering? If that is true, do semester series occur multiple times during the life of any given saros series? If that is true, then how many years intervene between each "semester series grouping"? – user22542 Oct 19 '18 at 18:15
• I am also very intrigued about why these two saros series end in exactly the same year - year 3049 (I assume at opposite poles). Can you shed any light on that coming happenstance? – user22542 Oct 19 '18 at 18:20
• @user22542 Added examples. – Mike G Oct 19 '18 at 19:15
• Thanks, Mike. I actually meant n+5 and n-5 above. Given your examples then, the next semester series should run from 2021 to 2024 and include the saros series 119, 124, 129, 134, 139, 144, and 149. Is this correct? Forgive any pattern presumption on my part. if this is so, I can try to figure the rest. That being said, any idea why 147 and 152 would end together in 3049? – user22542 Oct 19 '18 at 20:25
• I know it is a simplified summary, but every active saros series is therefore represented like this during every 18 year saros period. In reality, I see that there is some (minimal) overlaps between semester series numbers and there are also occasional exceptions when a new saros series begins or an old saros series ends. – user22542 Oct 20 '18 at 13:37