<p>Any eclipse is a coincidence of a new or full moon (repeating every 29.53 day lunation or <a href="https://moonblink.info/Eclipse/why/months#Synodic" rel="nofollow noreferrer">synodic month</a>)
and a lunar node (moon crossing the ecliptic, repeating every 27.21 day <a href="https://moonblink.info/Eclipse/why/months#Draconic" rel="nofollow noreferrer">draconic month</a>).
A <a href="http://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles_cycles.htm#semester" rel="nofollow noreferrer">semester</a>
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.</p>

<p>The interval between any two solar or lunar eclipses <a href="http://users.skynet.be/felixverbelen/cycles.htm" rel="nofollow noreferrer">can be expressed</a> as <span class="math-container">$aI + bS$</span>,
where <span class="math-container">$S$</span> is the saros interval of 223 lunations,
<span class="math-container">$I$</span> is the <a href="https://en.wikipedia.org/wiki/Inex" rel="nofollow noreferrer">inex</a> interval of 358 lunations between adjacent saros series,
and <span class="math-container">$a$</span> and <span class="math-container">$b$</span> are integers.
The semester interval of 6 lunations is <span class="math-container">$5I - 8S$</span>; for each eclipse in saros <span class="math-container">$n$</span>, there may be an eclipse in saros <span class="math-container">$n-5$</span> one semester earlier, an eclipse in saros <span class="math-container">$n+5$</span> 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.</p>

<p>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.</p>

CC BY-SA 4.0
2018-10-19T18:15:07.800Z
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
CC BY-SA 4.0
2018-10-19T18:20:04.397Z
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
CC BY-SA 4.0
2018-10-19T19:15:31.237Z
@user22542 Added examples.
Mike G
CC BY-SA 4.0
2018-10-19T20:25:42.050Z
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
CC BY-SA 4.0
2018-10-19T20:31:29.007Z
There is such a series from 2022 to 2025, ending with an [eclipse in saros 154](https://en.wikipedia.org/wiki/Solar_eclipse_of_September_21,_2025). I think the ends of saros series should be a separate question.
Mike G
CC BY-SA 4.0
2018-10-20T13:19:54.763Z
OK thanks.  I figure that there are roughly five semester series contained within each saros period of 18 years. Each semester series has 7-8 eclipses spaced 177 days between them. Each active semester series rotates with the other four semester series and lasts apprx 3.6 years or so. The "saros numbering" within each semester series member is spaced by five. Simplified example: A) 117, 122, 127, 132, 137, 142, 147, 152 B) 118, 123, 128, 133, 138, 143, 148, 153 C) 119, 124, 129, 134, 139, 144, 149, 154 D) 120, 125, 130, 135, 140, 145, 150, 155 E) 121, 126, 131, 136, 141, 146, 151, 156 ... etc.
user22542
CC BY-SA 4.0
2018-10-20T13:37:17.417Z
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
CC BY-SA 4.0
2018-10-20T13:43:20.860Z
Mike G. Let me know if I have any gross errors or omissions in any of this. I will try to ask about why solar saros 147 and 152 end together in a separate question.
user22542
CC BY-SA 4.0
2018-10-19T17:45:36.707Z
2018-10-19T21:38:30.783Z
2018-10-19T21:38:30.783Z
Mike G
<p>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. <strong>The Wikipedia link for saros 147 provided the following additional information:</strong></p>

<blockquote>
  <p>"Solar eclipses of 1964-1967[edit]</p>
  
  <p><strong>This eclipse is a member of a semester series</strong>. <em>An eclipse in a
  semester series of solar eclipses repeats approximately every 177 days
  and 4 hours (a semester)</em> at alternating nodes of the Moon's orbit.[1]
  "</p>
</blockquote>

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

<p>So, since this additional information, my new questions concerning these eclipses have become: </p>

<blockquote>
  <p>1) <strong>What exactly is a "semester series" for eclipses (any detail)?</strong> <em>The day spacing definition is obvious but doesn't explain much else.</em> </p>
  
  <p>2) <strong>Does this mean that <em>some or all</em></strong> eclipses in series 147 and 152 are in
  the same semester series?</p>
</blockquote>

<the-sun><solar-system><observational-astronomy><solar-eclipse><lunar-eclipse>
What is a "semester series" for eclipse prediction? - Solar saros series 147 and 152
user22542
# What is a "semester series" for eclipse prediction? - Solar saros series 147 and 152

(Asked by: username_0 on 2018-10-19)

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[edit]
>
> **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?

**Tags:** the-sun, solar-system, observational-astronomy, solar-eclipse, lunar-eclipse

---

## 1 answers

### Answer by username_1 on 2018-10-19. Score: 2 | Accepted answer

Any eclipse is a coincidence of a new or full moon (repeating every 29.53 day lunation or [synodic month](https://moonblink.info/Eclipse/why/months#Synodic))
and a lunar node (moon crossing the ecliptic, repeating every 27.21 day [draconic month](https://moonblink.info/Eclipse/why/months#Draconic)).
A [semester](http://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles_cycles.htm#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](http://users.skynet.be/felixverbelen/cycles.htm) as $aI + bS$,
where $S$ is the saros interval of 223 lunations,
$I$ is the [inex](https://en.wikipedia.org/wiki/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.

> **Comments:**
> **username_0**: 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"?  
> **username_0**: 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?  
> **username_1**: @user22542 Added examples.  
> **username_0**: 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?  
> **username_1**: There is such a series from 2022 to 2025, ending with an [eclipse in saros 154](https://en.wikipedia.org/wiki/Solar_eclipse_of_September_21,_2025). I think the ends of saros series should be a separate question.  
> **username_0**: OK thanks.  I figure that there are roughly five semester series contained within each saros period of 18 years. Each semester series has 7-8 eclipses spaced 177 days between them. Each active semester series rotates with the other four semester series and lasts apprx 3.6 years or so. The "saros numbering" within each semester series member is spaced by five. Simplified example: A) 117, 122, 127, 132, 137, 142, 147, 152 B) 118, 123, 128, 133, 138, 143, 148, 153 C) 119, 124, 129, 134, 139, 144, 149, 154 D) 120, 125, 130, 135, 140, 145, 150, 155 E) 121, 126, 131, 136, 141, 146, 151, 156 ... etc.  
> **username_0**: 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.  
> **username_0**: Mike G. Let me know if I have any gross errors or omissions in any of this. I will try to ask about why solar saros 147 and 152 end together in a separate question.  

---

