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In the geocentric solar ecliptic (GSE) system of coordinates, the position of the Moon is described by its longitude and latitude. The former is, with great accuracy, the angular distance between the sun and the Moon, and thus can be determined by the Moon phase. If it is totally new moon, the longitude is 0°, and if it is a full moon, the longitude is 180°, and, with some geometry, the longitude can be determined for any phase and, therefore, with simple equipment, such as a camera.

My question is: Is there also a simple way to determine the Moon's latitude, that is, it's angular distance to the ecliptic?

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  • $\begingroup$ Wouldn't that just be the GSE latitude, by its very definition? $\endgroup$ Commented Sep 3, 2022 at 23:09
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    $\begingroup$ That is precisely what I am asking how to determine $\endgroup$
    – WordP
    Commented Sep 3, 2022 at 23:18
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    $\begingroup$ @GregMiller OP gets (a good approximation to) the GSE longitude by equating it with lunar phase, and (I think) is looking for a similarly simple way to get GSE latitude. It's going to have to be something that takes into account (in a simple, sine-wavy way) the precession of the lunar nodes cf. Lunar standstill so it's going to have an 18.6 year cycle to it. $\endgroup$
    – uhoh
    Commented Sep 4, 2022 at 0:04
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    $\begingroup$ In the case of longitude, an error of 5 degrees is not very significant, but 5 degrees in the latitude is almost 100% of error, since the inclination of the moon's orbit is about 5.1 degrees $\endgroup$
    – WordP
    Commented Sep 4, 2022 at 18:39
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    $\begingroup$ Yes. I was able to have an error of about 1 degree when determining the longitude from a high quality picture of the Moon, by taking the ratio of the bright pixels to the total area of the Moon in pixels - so it would be great to have another method for measuring the latitude with simple equipment. As you said, there are many factors that go into account to precisely measure the latitude and longitude, but since I am considering an amateur context, it doesn't need to be extremely precise. $\endgroup$
    – WordP
    Commented Sep 4, 2022 at 20:28

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