# 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?

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.