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20190509, 04:22 PM (ISO 8601)
 Join Date
 Jun 2013
 Location
 Bristol, UK
What is the curve on the inside of a cresent moon?
It's not an arc of the same radius as the outer, is it circular at all?
The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20190509, 04:28 PM (ISO 8601)
 Join Date
 Jul 2015
Re: What is the curve on the inside of a cresent moon?
Not an astronomer, but it seems like it should be the arc of the earth's circular shadow where it intercepts the moon. However, a quick spot of research suggests otherwise. From Wikipedia's entry on "Cresent":
The shape of the lit side of a spherical body (most notably the Moon) that appears to be less than half illuminated by the Sun as seen by the viewer appears in a different shape from what is generally termed a crescent in planar geometry: Assuming the terminator lies on a great circle, the crescent Moon will actually appear as the figure bounded by a halfellipse and a halfcircle, with the major axis of the ellipse coinciding with a diameter of the semicircle.

20190509, 04:36 PM (ISO 8601)
 Join Date
 Jun 2013
 Location
 Bristol, UK
Re: What is the curve on the inside of a cresent moon?
No, that's not even close to right, half an ellipse would mean that the arcs near the poles were narrowing much more rapidly.
I thought about this for a while, and it's nothing simple. First off, the sun is fuzzy, it is not a point source of light. I suppose we could pretend that the sun was a point source, it still wouldn't be trivial.The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20190509, 05:43 PM (ISO 8601)
 Join Date
 Feb 2015
Re: What is the curve on the inside of a cresent moon?
I don't know what you mean here. The interior curve on a crescent moon is the terminator  the division between the lit and unlit portions of the moon. Assuming the moon is a sphere, the terminator is a great circle. Except during new moon or full moon, this circle is viewed obliquely. A circle viewed obliquely is seen as an ellipse.
Maybe that last part requires explanation. You are familiar with cones? The usual cone you see is a right circular cone, where the base is a circle, and the line from the base to the vertex is perpendicular to the base. If, instead, the line from the base to the vertex is at some other angle, you get a oblique circular cone. The family of curves you get by slicing an oblique circular cone by a plane is the same family of curves you get by slicing a right circular cone by a plane.
Now we can draw the lines from your eye to the terminator of the moon to get an oblique circular cone. The curve you see is the intersection of this cone with the plane perpendicular to the line (the image plane), and so is an ellipse. Or would be, if you could see the entire terminator, instead of just the portion on the face of the moon you can see. Instead you see just half of the ellipse.
The sun being at a finite distance, and being larger than a single point modifies this very slightly. The terminator will still be a circle, just not quite a great circle, so you will see a part of an ellipse tangent to the outer limb of the moon, but it won't quite be half an ellipse. But I expect this to be a very minor effect.

20190509, 11:23 PM (ISO 8601)
 Join Date
 May 2009
Re: What is the curve on the inside of a cresent moon?
I agree that there is an ellipse involved, but I don't believe what you see can fairly be described as "half an ellipse". It's less than half, because you can't actually see a full half of the moon.
That's why you don't see a clear meniscus at the edge, because that part of the ellipse is out of view.
Given that you can't see the most distinctive part of the ellipse shape, I think what you can see is as near as makes no real difference to being a small arc of a much larger circle."None of us likes to be hated, none of us likes to be shunned. A natural result of these conditions is, that we consciously or unconsciously pay more attention to tuning our opinions to our neighbor’s pitch and preserving his approval than we do to examining the opinions searchingly and seeing to it that they are right and sound."  Mark Twain

20190510, 06:10 AM (ISO 8601)
 Join Date
 Feb 2015
Re: What is the curve on the inside of a cresent moon?
But how could this ellipse not be tangent to the outer limb of the moon? That seems to be the question, about the "meniscus". By imagining the extreme case where the moon is very close, I can see that the visible section of the ellipse needn't be exactly half.
Last edited by DavidSh; 20190510 at 06:32 AM.

20190510, 06:52 AM (ISO 8601)
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 Dec 2010
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 The Great White North
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Re: What is the curve on the inside of a cresent moon?
You see half of the ellipse (if the Moon was a perfect sphere). Spheres are radial symmetric, so it does not matter the angle you see the terminator at. It will always be half an ellipse, from one semimajor axis to the other.
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20190510, 07:10 AM (ISO 8601)
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 Feb 2015
Re: What is the curve on the inside of a cresent moon?

20190510, 09:15 AM (ISO 8601)
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 Dec 2010
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 The Great White North
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20190510, 01:36 PM (ISO 8601)
 Join Date
 Jun 2013
 Location
 Bristol, UK
Re: What is the curve on the inside of a cresent moon?
I suspect that this is almost it.
The limits are the outer edge of the moon, when the sun is eclipsed or the moon is as new as it can be, and a straight line when the moon is halffull, and back to the edge of the moon when the moon is totally full. The edge of the moon is a circle because the moon is a sphere, and the straight line is an arc of a circle of infinite diameter, the question is what happens in between, are those lines all arcs from increasingly larger circles or something else?
A circle is an ellipse of course, but I don't think that the line is a full half of a noncircular ellipse, because that would imply that the taper from the tips was more exaggerated than what we see, particularly near the half moon there would be very curved horns to the inner edge of the moon, and I don't think I've seen that.The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20190510, 03:23 PM (ISO 8601)
 Join Date
 Sep 2016
Re: What is the curve on the inside of a cresent moon?
Spoiler: Um Phases not eclipses (left lack of thinking for record)
The thing [earth] creating the shadow is roughly spherical.
The light source is roughly spherical
.
If we:
ignore the moon as a distraction and have a giant static sheet of paper in space
ignore oblate spheroidness
The light source, line to planet, planet, line to shadow, and hence the shadow will be rotationally symmetric around the axis.
Hence the shadow would be a pure circle, the only possible deviations from a platonic circle being that the edge is 'grey', and in fact I think the primary sun size effect is rather that the 'shadow' shrinks at first.
If we have a 2D circular moon, we're now cutting out near the circle (radius moon sized) another circle (with a slightly different centre and radius depending on earth. Still circular.
If we're projecting onto a spherical moon, then the circle will be distorted a little. The shadow at the equator will be just a smidgin bigger (it's nearer the sun and nearer us than the poles, so the effect is doubled). IMO the deviation is negligible.
[ETA except then what about when the moon in >1/2.]
Actually I think I can rescue this. The shadow of the moon on the moon, by similar reasoning must also be circular. WLOG have the sun at (0,0,Lots), the moon radius 1 at (0,0,0). The moons shadow is thus a circle (sin t, cos t, 0).
(Tangent) If the suns radius is sufficiently big then it is actually a (cross sectional) circle at the point which (viewed from above) has a tangent that reaches the suns edges. Still a circle, but a bit further back (or if the sun was small and near, front).
We're now viewing from an angle, this effectively compresses the x coordinates, while leaving the y coordinate unchanged. So the inside edge should be a curve of the form (x sin t, cos t), I.E an ellipse. This is literally a conic section (circular 'shadow' projected onto a perspectivey cone ... so makes sense.)Last edited by jayem; 20190510 at 03:50 PM.

20190510, 03:53 PM (ISO 8601)
 Join Date
 Feb 2015
Re: What is the curve on the inside of a cresent moon?
Some day I want to take a series of pictures of a lunar eclipse, and stack the pictures to show the full extent of the Earth's shadow. But the last few lunar eclipses for me have either had the Moon behind clouds, or below the horizon.

20190512, 07:21 PM (ISO 8601)
 Join Date
 Jun 2013
 Location
 Bristol, UK
Re: What is the curve on the inside of a cresent moon?
Wow, that was some lack of thinking.
I think I've come to the conclusion that in the case of my underthinking it has to be all of a half of an ellipse. I certainly haven't noticed the horns on almost half moons, I suppose maybe I usually see them when they're just over half not just under, or maybe I took it for clouds being in the way or something.Last edited by halfeye; 20190512 at 07:21 PM.
The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.

20190513, 02:14 AM (ISO 8601)
 Join Date
 Sep 2016
Re: What is the curve on the inside of a cresent moon?
That was my thinking too. Or if you like a full ellipse (for parallel rays going through the poles) that we only see the near half of (except at new/full moon where both are exactly on the edge).
For non parallel light (big sun or near sun) I think you still see half an ellipse (but especially giving my mix up earlier I'm going to be cautious)
I don't get how people do, "phase/shadows etc... make it trivially obvious it's a sphere". With paper and enough time and thinking you can just about do it. Alternatively with bright lights and reflective surfaces. But even knowing the answers, it's easy to get confused.

20190513, 05:52 AM (ISO 8601)
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 May 2007
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 The Land of Cleves
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Re: What is the curve on the inside of a cresent moon?
Yes, the horns of an almosthalf moon are very narrow, for a short length. The reason you've never noticed them before is that they're very narrow, for a short length. Since the Sun is not a point source, there's some fuzziness to the terminator, and that fuzziness is increased as viewed from Earth by atmospheric effects, so the short, narrow horns get blurred out.
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20190513, 07:14 AM (ISO 8601)
 Join Date
 Jul 2010