Solar Eclipse percentage

[bjarkeandersen]

In the method SearchLocalSolarEclipse you get the kind and start, end and peak time for a solar eclipse at a given coordinate. For partial eclipses it would be great to also get the peak percentage. Is that something you plan to add to the library in the nearest future?

[cosinekitty]

That is a great idea. For partial and annular eclipses, there is some fraction of the Sun not blocked by the Moon for a given observer.

However, it's not obvious how to calculate the visible fraction of the Sun, because this is a problem of two overlapping discs. The obvious solution would not be very efficient: essentially pixel counting. Maybe someone else knows how to calculate the area of a disc when another disc of different size overlaps with it? At any rate, I will think about this, because it would be a handy addition, so long as it doesn't slow down the whole calculation significantly for applications that don't need it.

[hidp123]

That's great.

Will the result be geocentric (i.e. same result regardless of observer location) or topocentric? If geocentric, then a topocentric result addition will be good too, as location makes a big difference on eclipses.

[cosinekitty]

There are 3 eclipse finders: SearchGlobalSolarEclipse, SearchLocalSolarEclipse, and SearchLunarEclipse.

• For global solar eclipses, I would report the percentage as seen at the point on the Earth where the peak eclipse occurs. The global solar eclipse finder already includes the latitude and longitude of the peak eclipse, so it shouldn't be too hard to use that location as the basis for the percentage calculation.
• For local solar eclipses, I would report the percentage seen by the observer at the requested geographic location.
• For lunar eclipses, I would report the percentage of umbra coverage on the Moon as seen by a geocentric observer, because (a) there is no geographic location specified for this call, and (b) any parallax error would be tiny compared to the blurriness of the actual shadow. (Note that because I also report penumbral lunar eclipses, it is possible for the umbra coverage to be 0%.)

[bjarkeandersen]

As a follow-up, I realize we would need to be clear about what percentage we are talking about. Is it the percentage of the Sun that is still visible, or the percentage of the Sun that is hidden by the Moon?

I guess it doesn't matter as long as it is obvious from the name of the property. The most logic in my head is the percentage of the sun that is covered - i.e. a full eclipse would be 100%

[cosinekitty]

a full eclipse would be 100%

Yes, that's the definition I was thinking of also. Good!

[bjarkeandersen]

These are internal fields inside the eclipse calculator code. In the case of a local solar eclipse:

shadow.r = The distance in kilometers between the observer and the shadow axis (the center of the Moon's shadow). shadow.p = The penumbra radius in kilometers at the plane passing through the observer's location, perpendicular to the shadow axis.

I don't believe the formula above for peakPercentage can be correct. For example, even in a total eclipse, it will not say the coverage is 100%, because both r and p will be positive numbers.

I will need to sit down and think this through, to see if there is an efficient way to calculate coverage. There might be, but it's not obvious.

You are right about that - at a full eclipse I got values like 99.74% and 99.86% (very close to 100% but obviously not totally correct). It will be interesting to find out the difference between this number at the right number, when you've added the correctly calculated property. I'll take it as an exercise of long forgotten math to find out why they are different.

[cosinekitty]

Before adding any new feature to Astronomy Engine, I always make sure I can find some reliable test data. I found this explanation of eclipse magnitude on timeanddate.com. It turns out that what we have been talking about, the fraction of apparent area that is blocked (solar eclipse) or darkened by shadow (lunar eclipse) is called obscuration.

There is another term eclipse magnitude that indicates the fraction of the Sun/Moon's diameter that is blocked/shaded. Eclipse magnitude can sometimes be confused with magnitude, that describes how bright an object is, but is a completely different idea.

I'm open to calculating either/both obscuration (area blockage) and eclipse magnitude (diameter blockage). However, before I do that, I need to find test data. The timeanddate.com site provides eclipse magnitude numbers, so we are covered there.

I thought about trying to convert one to the other, but it won't work. For example, if two different partial solar eclipses block half the diameter the Sun (eclipse magnitude = 0.5), the obscurations can be different, because the Moon can be at a different distance from the Earth, thus having a larger or smaller apparent angular diameter. The same amount of the Sun's diameter can be blocked, but by a different Moon silhouette shape, resulting in a different amount of blocked area. This variability can be surprisingly large because the Moon's orbit is highly eccentric.

Does anyone know of a good source of test data for obscuration numbers?

[hidp123]

http://astro.ukho.gov.uk/eclbin/query_usno.cgi

This reputable site gives obscuration values in %, but not very user friendly.

[hidp123]

Another reputable site:
https://aa.usno.navy.mil/data/

Direct link with obscuration %:
https://aa.usno.navy.mil/data/SolarEclipses
https://aa.usno.navy.mil/data/Eclipse2024

Example: https://aa.usno.navy.mil/calculated/eclipse/solar?eclipse=22023&lat=37.76&lon=-122.44&label=San+Francisco%2C+CA&height=0&submit=Get+Data

[hidp123]

https://cocalc.com/share/public_paths/4e2e251d8e397d4436d158301ff5f0de9767e81d

Some python code to calculate obscuration.

[hidp123]

Stellarium also has some code to calculate obscuration, I'm not sure if/how the value is displayed in the software though:

https://github.com/Stellarium/stellarium/blob/master/src/core/modules/Planet.cpp
(CTRL F, search for "obscuration" on the page)

[cosinekitty]

Thank you again, @hidp123!

[cosinekitty]

I just released Astronomy Engine v2.1.7, which supports calculation of obscuration for lunar eclipses and solar eclipses. The affected functions are SearchLunarEclipse, SearchGlobalSolarEclipse, and SearchLocalSolarEclipse (along with their respective "Next..." functions). There is a new field obscuration in the three data types returned by those functions.