[Repost with additional info] Geocentric altitude/az of the sun and moon.

[hidp123]

Sorry to repost this, I have added additional info which I hope will help in answering this query, and thus give a more accurate value.

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Normally, alt & az are topocentric. However, how can I get geocentric alt & az. The altitude at least, if not azimuth.

I ask mainly due to the following (screenshot taken from this paper by Bernard Yallop 1997):

So far looking at other libraries I have found that Swiss Ephemeris has this option, and cosinekitty at astronomy-engine managed to put together something for me in this regard using his library. Here (Swiss Ephemeris) and here is my discussion with cosinekitty in regards to this, hopefully it helps us here as well.
I was hoping it can also be calculated via skyfield due to skyfield's high level of accuracy.

Thanks

[brandon-rhodes]

I can't make any sense of the phrase that defines ARCV, since there's no altitude from the center of the Earth, because there's no horizon there. Have you tried creating a lat/lon whose altitude is negative enough to put it at, or near, the center of the Earth? You could try something like elevation -6378 meters and see if the numbers agree with the paper.

Edit: This weekend I had time to go back and read the crescent-Moon literature a bit more carefully, and I see that I was wrong about how I was trying to interpret the phrase "geocentric altitude". Instead, it really does mean "altitude" in the sense of "altitude-azimuth", computed as though the observer and their local horizon were somehow located down at the center of the Earth.

So I've figured out how Skyfield can compute it! The full details are here, on issue #951, which also asked about that quantity:

#951 (comment)

(Edited to remove wrong version of script; let's instead just link to #951, so the script can be updated there, in one place only, if further bugs are found.)

[hidp123]

You are right, it does feel contradictory, but why I am after this, please see my original post from previously:
#860 (comment)
(or can scroll to the top)

[brandon-rhodes]

The paper you cited merely confused me, since it did not define the term, but it just occurred to me that I could Google the term, and see if a definition existed elsewhere. And results came up! Here is a top result with two diagrams, one in the comment linked, and the other in the comment that follows:

JSBSim-Team/jsbsim#184 (comment)

It looks like "geocentric altitude" is not an angle "altitude" but a distance "altitude", which makes far more sense than how I was initially trying to understand the term! Happily, there is nothing contradictory about trying to measure an altitude above the Earth's surface from the geocenter.

But I'll have to think about whether there's a good way in Skyfield to take the line between the geocenter and an object like the Moon, and compute the point on the Earth ellipsoid's surface that's on that line. I suspect there's a geometry routine in Skyfield we can use, but I'll have to do a search later to learn its name and how it's called.

In any case, you can now return to your work with the other astronomy library, and rework it to use the concept of altitude-as-a-distance, rather than the idea of altitude-as-an-angle-above-the-horizon. It's so unfortunate that English uses the same term "altitude" for both an angle and a distance!

[brandon-rhodes]

My most recent comment, above, was wrong! Scroll up to see that I have edited my answer at the top of this thread, and have provided a sample script that I think computes the value you are after.

[Juned-Patel]

Yes, thank you for investigating the issue. I've just tested the code and confirmed that the result is accurate.

[brandon-rhodes]

Wonderful! I'll mark this as the answer, then.

Note that there was a small bug with the first version of the script that I pasted here, so I've updated the answer to simply include a link to the issue, so that if we make any further improvements, this Discussion won't be left with an out-of-date answer.

I'm glad we got your use case worked out!