Celestia Forums

My very, very sick father mistakes my enthusiasm for sophistication and so he asked me this a few years back when he was whole. It struck me as an excellent question and I've tried time and again to find the answer - without any success. I should very much appreciate finally to respond. Dad would be so pleased that I remember his having asked it... pleased that I, too, find it intriguing, and pleased that I have carried it with me for all this time.

(Sorry for the melodrama!)

The Question:
When the moon is near the horizon and very nearly new, there is a phase when its cusps are sharply defined. Sometimes -infrequently, I believe- the cusps are both equally up-turned toward the zenith. At these times a line connecting the tips would seem to parallel the horizon.

Can you ascribe any periodicity to this striking appearance so that its occurences might be predicted ?
Has the phenomenon (such as it is) a name at all?

Thanks very much!

Just at a guess, but doesn't the orientation of the moon in the sky depend on the latitude of the observer on the Earth? I'd have thought the terminator would be parallel to the horizon only on or near the equator wouldn't it? (or at least, along the line directly underneath the moon's orbit on the earth's surface)

Remember that the Moon is being illuminated by the Sun. The visible center of the sunlit portion of the Moon is directly on the line that you can draw on the sky between its center and the center of the Sun. The two "horns" are equidistant from that centerline.

It's "only" a matter of 3D spherical trigonometry to figure out how to predict the angle of the centerline with respect to the horizon.

Sorry, actually determining that formula would take me quite a while. I suspect there are one or two other people on the forum for whom it'd be trivial.

some thoughts:

Near sunrise and sunset, the Moon's cusps (horns) will be horizontal when the azimuth angle of the moon is the same as the azimuth angle of the sun. That is, when the moon is vertically above or below the sun.

Predicting the azimuthal angles of the Sun and Moon is "an already solved problem," and there are several Web pages that include Java Applets to do this. See, for example, http://www.jgiesen.de/sunmoonpolar/. That Web page includes a discussion of how their azimuthal angles change with time and the location of the observer.

This site, Dr Giesen's, is a treasure trove of charming applets.
Your advice and linkage are very helpful and I thank you.

When near the equator, that's how the crescent moon rises and sets every day, with the line connecting the cusps being horizontal.

Since the moon must be directly above the Sun as defined by the Earth's horizon for this to happen, it's pretty rare from non-equatorial latitudes. If the moon were at the high point in its orbit (~ 5 degrees above the ecliptic, and it just passed new moon phase, it could pass directly above the the Sun, but it would be so close to a new moon that I doubt you'd see it.

"it's pretty rare from non-equatorial latitudes. If the moon were at the high point in its orbit (~ 5 degrees above the ecliptic, and it just passed new moon phase, it could pass directly above the the Sun, but it would be so close to a new moon that I doubt you'd see it." -Tony


Yes Tony that makes sense -common, even- that I can grasp. My latitude is 43N and I suspect that it'd limit the possibility of my seeing the cusps as even as I'd like... perhaps to no more than 43 - 5 = 38° .
If the ideal levelness is 180° I could only observe (180 - 38) = 142° and as a precious slender crescent.

If I understand you correctly the delicate crescent would wax just as the angle would progressively depart from the horizontal on a daily basis.?

I think you should be able to see a perfectly even crescent from 43 N.

Tony's right ... when the Moon sails past 5 degrees north or south of the Sun, it's too close to see a crescent. Shame, that, because then you'd see a crescent tilted at right angles to the Moon's orbit, and your "even horns" situation would be visible from the Earth's poles.
But theory and observation show that the thinnest crescent becomes visible at around 7.5 degrees from the Sun. (And it's very flat, since the visible illumination doesn't extend all the way to the Moon's poles.) So the new Moon needs to sneak a little ahead of the Sun before it becomes visible, even when it is passing at its maximum angular distance from it. Take the extreme situation: if the Moon shows its first, thinnest crescent at the moment it reaches its maximum height above the ecliptic (and if my spherical trig is okay), the crescent should be tilted ~41 degrees to the line of the Moon's orbit (which is at that moment parallel to the ecliptic, since the Moon is just reaching its highest point and is about to turn down again).
Right. Now, at spring equinox the ecliptic is tilted ~23.5 degrees north of the equator at sunset. So if the first crescent of the new Moon occurs just after sunset on the spring equinox, when the Moon is also 90 degrees from its ascending node, you should be able to see "even horns" at 23.5+41 = 64.5 degrees north latitude. Similarly, the ecliptic is tilted 23.5 degrees north of the equator at sunrise on the autumn equinox: so if the very last, slimmest crescent of the old Moon occurs just before sunrise on the autumn equinox when the Moon is 90 degrees from its ascending node, you'll have a similar view. (The situation in the southern hemisphere is left as an exercise for the interested student ... )
In practice I think these situations would be both extremely rare (requiring a concatenation of orbital circumstances), and very difficult to observe.
But at lower latitudes you begin to be able to mix and match the illumination angle of the Moon and the angle its orbit makes with the horizon ... you can get beefier crescents in darker skies, and the circumstances under which the "even horns" occur become more varied.
"Even horn seasons" will occur regularly when the Moon is 90 degrees from a node at the time of the equinoxes, and the farther north or south you are the closer you'll have to be to a perfect match before you've a chance of seeing "even horns". But I'm pretty sure a detailed computer search for new Moon circumstances at your site coordinates would be required in order to make a tight prediction.

Grant

"...But I'm pretty sure a detailed computer search for new Moon circumstances at your site coordinates would be required in order to make a tight prediction. "
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Grant,
I thank you for this patient and thoughtful post. You *have* teased me a bit, you know. To imagine that a stranger - in this case, a simple country doctor who enjoys the sky yet knows no spherical trig that isn't in HA Rey- is likely capable of taking this concluding advice of yours and putting it toward the resolution of the question.. well, let's say you're optimistic!

Though I still don't know what to tell Dad (regarding when we might be able see this sight) I thank you for your contribution, your very generous contribution.

Maggot wrote:You *have* teased me a bit, you know. To imagine that a stranger - in this case, a simple country doctor who enjoys the sky yet knows no spherical trig that isn't in HA Rey- is likely capable of taking this concluding advice of yours and putting it toward the resolution of the question.. well, let's say you're optimistic!

Sorry, it wasn't meant as a tease ... it was more an admission of defeat. I was intending to convey that, while I can wave my hands with the best of them, I couldn't give you a perfect answer.
Have you tried writing to Sky & Telescope? Your topic is something that might motivate them to produce an article.

Grant