<p>The angle that the moon appears to be tilted depends on the relative positions of the sun and moon.  The lit part of the moon always points at the sun, but it points at the sun along a &quot;great circle&quot;, and this can create an optical illusion, since a line in the sky that is parallel to the horizon could appear &quot;straight&quot; but it is not a great circle.  Since we tend to judge things relative to the horizon, this can give the impression that the lit part of the moon isn't pointing at the sun.</p>
<p>The angle is fully determined by the relative positions of the moon and sun. So, for example, in winter, the crescent moon will appear more &quot;upright&quot; in the evening, since the slope of the ecliptic tends to be more shallow.  Moreover in the tropics, where the angle is steeper, the crescent moon's horns will be pointing up (giving rise to the Hawaiian notion of a &quot;wet moon&quot;)</p>
<p>In textbooks, the moon is drawn (or the photograph of the moon is rotated) to the vertical, for convenience. It makes the comparison between the phases simpler if they are all drawn at the same angle.</p>

CC BY-SA 4.0
2021-02-28T18:31:49.593Z
OK. What is this great circle? Why not a straight line?
Jen
CC BY-SA 4.0
2021-02-28T19:26:54.143Z
The sky is a sphere.  What is a straight line on a sphere?  A great circle is a line like the equator or the Greenwich meridian. It is the nearest thing that there is to a straight line when you are doing geometry on a curved sphere.  But anyway, search for "great circle" and youll get pictures etc.
James K
CC BY-SA 4.0
2021-03-01T20:14:02.010Z
I don't understand how the sky (space) is a sphere! Do not the Space Station astronauts observe a straight perpendicular line between the Sun and the illuminated part of the Earth? This spherical idea for sky/space is new to me.
Jen
CC BY-SA 4.0
2021-03-01T20:28:55.167Z
Well, of course "space" is 3d, and continues out forever (as far as we can tell)  However we can project the position of stars onto a sphere.  A straight line in 3d space is projected to a great circle, and great circles look "straight". However the horizon creates an optical illusion,  We tend to see lines in the sky that are parallel to the horzion as "straight" even though they are not.
James K
CC BY-SA 4.0
2021-03-03T00:19:17.353Z
This 'celestial' sphere is imaginary and doesn't actually exist except maybe in a planetarium. This I can understand but that doesn't apply in 3D space. So going back to my space station scenario then it must be possible to see/draw a straight perpendicular line between the Sun and the illuminated part of the Earth. The same must apply to viewing the Moon and the Sun from the Earth.
Jen
CC BY-SA 4.0
2021-03-03T06:34:54.543Z
Yes you can draw that line. Yes the side facing the sun is illuminated. Yes the moon's illumination is in direct line with the sun.  But there is an optical illusion that might make it seem as if it is not
James K
CC BY-SA 4.0
2021-03-04T09:39:28.277Z
What is this optical illusion? When I view the moon and sun's relative positions I am in the same 3D space as the space station - its just a matter of scale. I t would be the same If I viewed the space station, the sun, the moon and the earth from say halfway to Mars. I would be able to draw a perpendicular line from the sun to all these objects.
Jen
CC BY-SA 4.0
2021-03-04T16:13:41.780Z
A path in the sky that is parallel to the horizon can look straight.  It isn't.
James K
CC BY-SA 4.0
2021-03-05T18:03:37.733Z
I'm not talking about a path being relative to the horizon or relative to anything. I'm talking about a perpendicular path, in 3D space, between an object that is illuminated by another object. Clearly my observation does not see the moon being illuminated by the sun hence my question. I don't know why this should be so but it is and cannot be argued against. If it can then please show me the explanation. To say that it is an optical illusion is not a scientific answer.
Jen
CC BY-SA 4.0
2021-02-28T12:47:10.487Z
2021-02-28T12:47:10.487Z
James K
<p>When I look at a visible moon in daylight its phase is shown at an angle. However textbook moon phase diagrams only show the phase vertically. What is it that determines the angle?
The reason I ask this questions is the Moon's illumination is not in direct line with the position of the visible sun.</p>

CC BY-SA 4.0
2021-02-27T16:09:21.680Z
Do you mean the angle that a line drawn through the poles of the moon would make with the horizon,  so that a crescent moon might have its "horns" pointing up or pointing down, constrasted with the text book that only shows the horns pointing left or right.
James K
CC BY-SA 4.0
2021-02-28T00:04:06.087Z
Sounds like you're asking about the Moon's [parallactic angle](/search?q=parallactic+angle).
Mike G
CC BY-SA 4.0
2021-02-28T05:46:02.067Z
In those textbook diagrams the cameraman has his spine perpendicular to the plane of the Earth-Moon systems orbit around the Sun. The spine of an Earthbound observer usually points at a different direction. Closer to the equator the crescent becomes "a bowl" on occasion.
Jyrki Lahtonen
<moon-phases>
Moon phase angle
Jen
# Moon phase angle

(Asked by: username_0 on 2021-02-27)

When I look at a visible moon in daylight its phase is shown at an angle. However textbook moon phase diagrams only show the phase vertically. What is it that determines the angle?
The reason I ask this questions is the Moon's illumination is not in direct line with the position of the visible sun.

**Tags:** moon-phases
> **Comments:**
> **username_1**: Do you mean the angle that a line drawn through the poles of the moon would make with the horizon,  so that a crescent moon might have its "horns" pointing up or pointing down, constrasted with the text book that only shows the horns pointing left or right.  
> **username_2**: Sounds like you're asking about the Moon's [parallactic angle](/search?q=parallactic+angle).  
> **username_3**: In those textbook diagrams the cameraman has his spine perpendicular to the plane of the Earth-Moon systems orbit around the Sun. The spine of an Earthbound observer usually points at a different direction. Closer to the equator the crescent becomes "a bowl" on occasion.  

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## 1 answers

### Answer by username_1 on 2021-02-28. Score: 5

The angle that the moon appears to be tilted depends on the relative positions of the sun and moon. The lit part of the moon always points at the sun, but it points at the sun along a "great circle", and this can create an optical illusion, since a line in the sky that is parallel to the horizon could appear "straight" but it is not a great circle. Since we tend to judge things relative to the horizon, this can give the impression that the lit part of the moon isn't pointing at the sun.

The angle is fully determined by the relative positions of the moon and sun. So, for example, in winter, the crescent moon will appear more "upright" in the evening, since the slope of the ecliptic tends to be more shallow. Moreover in the tropics, where the angle is steeper, the crescent moon's horns will be pointing up (giving rise to the Hawaiian notion of a "wet moon")

In textbooks, the moon is drawn (or the photograph of the moon is rotated) to the vertical, for convenience. It makes the comparison between the phases simpler if they are all drawn at the same angle.

> **Comments:**
> **username_0**: OK. What is this great circle? Why not a straight line?  
> **username_1**: The sky is a sphere.  What is a straight line on a sphere?  A great circle is a line like the equator or the Greenwich meridian. It is the nearest thing that there is to a straight line when you are doing geometry on a curved sphere.  But anyway, search for "great circle" and youll get pictures etc.  
> **username_0**: I don't understand how the sky (space) is a sphere! Do not the Space Station astronauts observe a straight perpendicular line between the Sun and the illuminated part of the Earth? This spherical idea for sky/space is new to me.  
> **username_1**: Well, of course "space" is 3d, and continues out forever (as far as we can tell)  However we can project the position of stars onto a sphere.  A straight line in 3d space is projected to a great circle, and great circles look "straight". However the horizon creates an optical illusion,  We tend to see lines in the sky that are parallel to the horzion as "straight" even though they are not.  
> **username_0**: This 'celestial' sphere is imaginary and doesn't actually exist except maybe in a planetarium. This I can understand but that doesn't apply in 3D space. So going back to my space station scenario then it must be possible to see/draw a straight perpendicular line between the Sun and the illuminated part of the Earth. The same must apply to viewing the Moon and the Sun from the Earth.  
> **username_1**: Yes you can draw that line. Yes the side facing the sun is illuminated. Yes the moon's illumination is in direct line with the sun.  But there is an optical illusion that might make it seem as if it is not  
> **username_0**: What is this optical illusion? When I view the moon and sun's relative positions I am in the same 3D space as the space station - its just a matter of scale. I t would be the same If I viewed the space station, the sun, the moon and the earth from say halfway to Mars. I would be able to draw a perpendicular line from the sun to all these objects.  
> **username_1**: A path in the sky that is parallel to the horizon can look straight.  It isn't.  
> **username_0**: I'm not talking about a path being relative to the horizon or relative to anything. I'm talking about a perpendicular path, in 3D space, between an object that is illuminated by another object. Clearly my observation does not see the moon being illuminated by the sun hence my question. I don't know why this should be so but it is and cannot be argued against. If it can then please show me the explanation. To say that it is an optical illusion is not a scientific answer.  

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