Is there an algorithm for solar eclipse duration?

[StephenG1CMZ]

I assume an algorithm for solar eclipse duration exists, but I was surprised it does not appear in Jean Meeus's Astronomical Algorithms (or if it does, its not obvious).

The section on solar eclipses describes types of solar eclipse, but none of the examples give durations.

The only durations appear within the section on lunar eclipses.

I have implemented eclipse calculations here:
https://my.numworks.com/python/steveg1cmz/aeclipse
(It's in Python, so should be easily ported).

Can anyone suggest sources for solar eclipse durations? (Or where on earth they might be seen?)

[StephenG1CMZ]

Ah, I have just seen this, which looks relevant.
https://www.hpmuseum.org/forum/thread-18...ar+eclipse
It seems there is already a PPL implementation for the Prime.

[StephenG1CMZ]

And some of these references could be worth revisiting
https://www.hpmuseum.org/forum/thread-52...ar+eclipse

[Giuseppe Donnini]

You should try to get hold of the following book by Meeus:

MEEUS, Jean, Elements of Solar Eclipses, 1951 – 2200 (Willmann-Bell, ed.; 1989).



It has the same “computational” approach as his well-known Astronomical Algorithms and can (and should) be seen as a must-have companion to the latter. (Do not confuse it with one of the “canons” he co-authored with various other astrophysicists! They do not provide the algorithms you are looking for.)

Unfortunately, Willmann-Bell went out of business in 2020, and although the American Astronomical Society acquired their inventory, Meeus’s Elements have not yet appeared for sale on their online shopping site. The accompanying CD-ROM, though briefly available, is now out of stock:

https://shopatsky.com/products/elements-...-1951-2202

Incidentally, Mr. Eagle, whom you just quoted, did a fine MATHLAB implementation of it:

https://www.mathworks.com/matlabcentral/...r-eclipses

[Johnh]

It could be because while lunar eclipses can last a while, as the moon moves across the large shadow disk of the earth, solar eclipses are far more brief. That's because the angle of view from earth, looking to the sun is almost exactly the same as that of the moon (both just over 0.5 degree). So the full ecllipse is almost instantaneous.

[SlideRule]

Some helpful resources ?

Amateur Astronomy pocket skyguide
  If the umbra passes across Earth, an umbral, or total, solar eclipse occurs. Only people within the umbra see totality; those outside see a penumbral eclipse or no eclipse at all. Both Moon and Earth are moving, so the tip of the umbra moves across the surface of Earth, tracing out the eclipse path. The shadow moves eastward at about 1600 km per hour. The duration of totality is determined by the size of the shadow and the geometry of how it hits the surface of Earth. The maximum length is about 7½ minutes.

Observational Astronomy for amateurs
   Anyone interested in the computation of eclipses should refer to B.3.26.
…
3.26  M.DAVIDSON, the Computation of Total Solar Eclipses (J.B.A.A., 49, No. 8, 299).

Monthly Notices of the Royal Astronomical Society

  v93 i3 1993 Computation of Total Solar Eclipses.pdf (Size: 388.04 KB / Downloads: 19)

BEST!
SlideRule

ps: attachment is MOST helpful

[StephenG1CMZ]

Thanks for the many interesting suggestions.

It seems like the Elements... book will be most useful, though it will take some time to get it.

I have noticed something curious (perhaps a bug?) in my calculation of the eclipse magnitude (the fraction eclipsed, not brightness) for a solar eclipse.

My calculation of this magnitude for the example used by Jean Meeus is OK (edition 2 formula 54.2, example 54.a).
But my calculation for tomorrow's 14 October 2023 solar eclipse is 2.0, whereas online sources are giving a value of 0.9 - and of course one would expect a value less than 1 given the visible ring (although the calculation is not limited to 1).

I am wondering whether this is a problem with the calculation, or a misunderstanding of categorisation.

Jean Meeus states that the formula for the calculation for the solar eclipse applies to a partial eclipse. But the eclipse is categorised as an annular one.

I would have assumed that an annular eclipse is obviously partial, but since the categorisation is "annular" not "partial" perhaps the formula should not be used? (implying a None should be returned rather than a number). [-My code lazily always returns a number even when total.]

Or is the "partial" formula valid for annular eclipses too, in which case my calculation may be in error despite yielding a reasonable result for the example (1993 May 21)
Update: Comparing several magnitudes for 1900-2023 with online values, it seems only partial solar magnitudes are valid using this formula - not annular, hybrid or total (but all lunar eclipse values are OK).

[StephenG1CMZ]

On this website https://hemel.waarnemen.com/Computing/eclipse.html (using different symbols than Meeus*) I see:
"The magnitude of a partial eclipse is equal to the fraction of the solar diameter that is covered by the Moon and given by:

mag = (rs + rm - Δ) / (2 rs)

For an annular eclipse (and I suppose this could also apply to a total solar eclipse), the magnitude is simply:

mag = rm / rs"
implying that an annular eclipse is not categorised as a partial eclipse, and has a different equation.

(*Update: Actually, a different formula)

[KeithB]

1. Get a lawn chair.
2. Put on your solar glasses.
3. When the eclipse starts, start your stop watch
4. When the eclipse ends, stop your start watch.
5. Read the stop watch.

Oh, wait, do you want to calculate it *before* the eclipse happens? 8^)
See the attachment for one of my shots of the eclipse.

[ctrclckws]

Lovely photo!

[KeithB]

Thanks