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Main
Date: 26 Aug 2007 13:34:34
From: SkySea
Subject: Crescent Moon Cusp Orientation
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A friend of mine started a discussion (with a bogus picture of the
Moon over an arctic sea:
http://msgboard.snopes.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=60;t=001201;p=0
) about possible orientations of the crescent Moon.
The upshot is, I'm trying to figure out how to find the extreme ranges
of latitudes and dates when the crescent would be oriented such that
the lower horn tip appears closer in azimuth to the Sun than the upper
horn. That is, when the crescent wouldn't hold any water, as it were.
At the extreme end, I imagine that a crescent near the solstice seen
from the north pole would provide that kind of orientation. But how
far south could you travel, given the most favorable alignments of the
Sun and Moon, and at what time of year, to witness this?
I'm only considering waxing for the moment, even though the polar
example above also works for a waning crescent, but to the right in
azimuth of the Sun of course.
=============
- Dale Gombert (SkySea at aol.com)
122.38W, 47.58N, W. Seattle, WA
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Date: 28 Aug 2007 14:47:59
From:
Subject: Re: Crescent Moon Cusp Orientation
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Bill Owen wrote:
> In order for
> the lower cusp to be closer in azimuth to the sun than the upper cusp,
> the sun must be higher in the sky than the moon.
This doesn't sound right.
Join the Moon and the Sun in a great circle. You can now move the
Sun anywhere along that great circle, while keeping the Moon fixed,
and the cusps will not move. Obviously, there will be plenty of
configurations (assuming the Moon is above the horizon) where the
Sun is lower than the Moon, but where the "top" of the Moon is
illuminated. (Top meaning highest part in altitude.)
P.S. I read your other message and now understand what you were
getting at.
--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
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Date: 28 Aug 2007 13:05:06
From: benk
Subject: Re: Crescent Moon Cusp Orientation
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On Aug 28, 3:54 am, br...@isi.edu (Brian Tung) wrote:
> Bill Owen wrote:
> > The line joining the two cusps of the crescent moon is perpendicular to
> > the line from the moon to the sun. (When I write "line" here, it's
> > really a *plane* defined by the two points in question and the observer.
> > You-know-who will just have to get over it. Anyway....)
>
> Or the great circle on the celestial sphere passing through both the Sun
> and the Moon.
>
> > In order for
> > the lower cusp to be closer in azimuth to the sun than the upper cusp,
> > the sun must be higher in the sky than the moon. For a waxing crescent,
> > this geometry would occur in the *morning*, after moonrise, at all
> > latitudes.
>
> > Note that once the moon becomes gibbous, this conclusion no longer
> > holds. I'll let others explain why. :-)
>
> I must confess I'm not sure what you're getting at. A gibbous Moon at
> moonrise is still lower than the morning Sun. (Unless the Moon rises
> first...but then, that can happen for a crescent as well as the gibbous
> Moon.) I must be missing something.
>
> --
> Brian Tung <br...@isi.edu>
> The Astronomy Corner athttp://astro.isi.edu/
> Unofficial C5+ Home Page athttp://astro.isi.edu/c5plus/
> The PleiadAtlas Home Page athttp://astro.isi.edu/pleiadatlas/
> My Own Personal FAQ (SAA) athttp://astro.isi.edu/reference/faq.html
A gibbous moon doesn't have horns, so the conclusion, while valid, no
longer holds water. At least, that's how I read it...
--Ben
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Date: 28 Aug 2007 21:12:56
From: Paul Schlyter
Subject: Re: Crescent Moon Cusp Orientation
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In article <1188331506.136589.300110@d55g2000hsg.googlegroups.com >,
benk <ben@kolstad.com > wrote:
> On Aug 28, 3:54 am, br...@isi.edu (Brian Tung) wrote:
>> Bill Owen wrote:
>>> The line joining the two cusps of the crescent moon is perpendicular to
>>> the line from the moon to the sun. (When I write "line" here, it's
>>> really a *plane* defined by the two points in question and the observer.
>>> You-know-who will just have to get over it. Anyway....)
>>
>> Or the great circle on the celestial sphere passing through both the Sun
>> and the Moon.
>>
>>> In order for
>>> the lower cusp to be closer in azimuth to the sun than the upper cusp,
>>> the sun must be higher in the sky than the moon.
Not necessarily.
Consider the situation where the Sun and the Moon are at the same
altitude above the horizon, and they're both very close to your local
zenith - some 10 degrees or so away from it. Also assume that the
azimuth difference is some 90 degrees. In such a situation, the lower
cusp of the Moon will be closer in azimuth to the Sun than the upper
cusp of the moon, merely because the azimuth difference changes more
dramatically when you're close to the zenith (just like the RA changes
more dramatically close to the celestial pole).
>>> For a waxing crescent,
>>> this geometry would occur in the *morning*, after moonrise, at all
>>> latitudes.
>>
>>> Note that once the moon becomes gibbous, this conclusion no longer
>>> holds. I'll let others explain why. :-)
>>
>> I must confess I'm not sure what you're getting at. A gibbous Moon at
>> moonrise is still lower than the morning Sun. (Unless the Moon rises
>> first...but then, that can happen for a crescent as well as the gibbous
>> Moon.) I must be missing something.
>>
>> --
>> Brian Tung <br...@isi.edu>
>> The Astronomy Corner athttp://astro.isi.edu/
>> Unofficial C5+ Home Page athttp://astro.isi.edu/c5plus/
>> The PleiadAtlas Home Page athttp://astro.isi.edu/pleiadatlas/
>> My Own Personal FAQ (SAA) athttp://astro.isi.edu/reference/faq.html
>
> A gibbous moon doesn't have horns, so the conclusion, while valid, no
> longer holds water. At least, that's how I read it...
>
> --Ben
Even if a gibbous moon doesn't have "horns", it still has two points
where the terminator meets the limb. We can count these two points as
"horns", in an extended sense.
--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/
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Date: 28 Aug 2007 17:10:52
From: Bill Owen
Subject: Re: Crescent Moon Cusp Orientation
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Paul Schlyter wrote:
>> On Aug 28, 3:54 am, br...@isi.edu (Brian Tung) wrote:
>>> Bill Owen wrote:
>>> In order for
>>>> the lower cusp to be closer in azimuth to the sun than the upper cusp,
>>>> the sun must be higher in the sky than the moon.
>
> Not necessarily.
Yes, Paul, you are correct. Thanks.
-- Bill
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Date: 28 Aug 2007 14:00:45
From: Bill Owen
Subject: Re: Crescent Moon Cusp Orientation
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benk wrote:
> On Aug 28, 3:54 am, br...@isi.edu (Brian Tung) wrote:
>> Bill Owen wrote:
>>> The line joining the two cusps of the crescent moon is perpendicular to
>>> the line from the moon to the sun. (When I write "line" here, it's
>>> really a *plane* defined by the two points in question and the observer.
>>> You-know-who will just have to get over it. Anyway....)
>> Or the great circle on the celestial sphere passing through both the Sun
>> and the Moon.
>>
>>> In order for
>>> the lower cusp to be closer in azimuth to the sun than the upper cusp,
>>> the sun must be higher in the sky than the moon. For a waxing crescent,
>>> this geometry would occur in the *morning*, after moonrise, at all
>>> latitudes.
>>> Note that once the moon becomes gibbous, this conclusion no longer
>>> holds. I'll let others explain why. :-)
>> I must confess I'm not sure what you're getting at. A gibbous Moon at
>> moonrise is still lower than the morning Sun. (Unless the Moon rises
>> first...but then, that can happen for a crescent as well as the gibbous
>> Moon.) I must be missing something.
>>
>> --
>> Brian Tung <br...@isi.edu>
>> The Astronomy Corner athttp://astro.isi.edu/
>> Unofficial C5+ Home Page athttp://astro.isi.edu/c5plus/
>> The PleiadAtlas Home Page athttp://astro.isi.edu/pleiadatlas/
>> My Own Personal FAQ (SAA) athttp://astro.isi.edu/reference/faq.html
>
> A gibbous moon doesn't have horns, so the conclusion, while valid, no
> longer holds water. At least, that's how I read it...
>
> --Ben
>
What I was *trying* to say ... well, let me try again.
Certainly the great circle (or plane if you prefer) joining the cusps is
perpendicular to the great circle joining the sun and the moon.
In the borderline case where the cusps are vertical, the great circle
joining them passes through the zenith. The sun is then on a great
circle which passes through the moon and intersects the horizon at +/-
90 degrees in azimuth away from the moon. This great circle reaches its
maximum altitude where the moon is = > the sun will always be lower in
the sky than the moon when the cusps are vertical. Always above the
horizon for a crescent, *on* the horizon (neglecting refraction) at the
instant of first or last quarter, and always below the horizon if the
moon is gibbous.
Now tip the cusps so that the top one is farther in azimuth from the sun
than the bottom one and the crescent "can't hold water" to use the OP's
phrase. The great circle containing the sun now rotates as well. But
in no case is the sun below the horizon and also less than 90 deg from
the moon. The sun *can* be below the horizon and *more* than 90 deg
from the moon, and it's therefore possible for the cusps of a gibbous
moon to be in the "can't hold water" orientation. But not for a crescent.
The only way to see a "tipped-over" crescent is for the sun to be above
the horizon too. Not necessarily higher in altitude than the moon, but
simply above the borderline great circle I described above (passing
through the moon and through the horizon 90 deg away).
I hope this clarifies things....
-- Bill Owen
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Date: 27 Aug 2007 08:32:14
From: Bill Owen
Subject: Re: Crescent Moon Cusp Orientation
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SkySea wrote:
> A friend of mine started a discussion (with a bogus picture of the
> Moon over an arctic sea:
>
> http://msgboard.snopes.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=60;t=001201;p=0
> ) about possible orientations of the crescent Moon.
>
> The upshot is, I'm trying to figure out how to find the extreme ranges
> of latitudes and dates when the crescent would be oriented such that
> the lower horn tip appears closer in azimuth to the Sun than the upper
> horn. That is, when the crescent wouldn't hold any water, as it were.
>
> At the extreme end, I imagine that a crescent near the solstice seen
> from the north pole would provide that kind of orientation. But how
> far south could you travel, given the most favorable alignments of the
> Sun and Moon, and at what time of year, to witness this?
>
> I'm only considering waxing for the moment, even though the polar
> example above also works for a waning crescent, but to the right in
> azimuth of the Sun of course.
Good question to get one thinking on a Monday morning....
The line joining the two cusps of the crescent moon is perpendicular to
the line from the moon to the sun. (When I write "line" here, it's
really a *plane* defined by the two points in question and the observer.
You-know-who will just have to get over it. Anyway....) In order for
the lower cusp to be closer in azimuth to the sun than the upper cusp,
the sun must be higher in the sky than the moon. For a waxing crescent,
this geometry would occur in the *morning*, after moonrise, at all
latitudes.
Note that once the moon becomes gibbous, this conclusion no longer
holds. I'll let others explain why. :-)
-- Bill Owen
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Date: 28 Aug 2007 00:54:39
From: Brian Tung
Subject: Re: Crescent Moon Cusp Orientation
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Bill Owen wrote:
> The line joining the two cusps of the crescent moon is perpendicular to
> the line from the moon to the sun. (When I write "line" here, it's
> really a *plane* defined by the two points in question and the observer.
> You-know-who will just have to get over it. Anyway....)
Or the great circle on the celestial sphere passing through both the Sun
and the Moon.
> In order for
> the lower cusp to be closer in azimuth to the sun than the upper cusp,
> the sun must be higher in the sky than the moon. For a waxing crescent,
> this geometry would occur in the *morning*, after moonrise, at all
> latitudes.
>
> Note that once the moon becomes gibbous, this conclusion no longer
> holds. I'll let others explain why. :-)
I must confess I'm not sure what you're getting at. A gibbous Moon at
moonrise is still lower than the morning Sun. (Unless the Moon rises
first...but then, that can happen for a crescent as well as the gibbous
Moon.) I must be missing something.
--
Brian Tung <brian@isi.edu >
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.html
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