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.
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2$\begingroup$ 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. $\endgroup$– James KFeb 27, 2021 at 16:09
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1$\begingroup$ Sounds like you're asking about the Moon's parallactic angle. $\endgroup$– Mike GFeb 28, 2021 at 0:04
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$\begingroup$ 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. $\endgroup$– Jyrki LahtonenFeb 28, 2021 at 5:46
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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.
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$\begingroup$ OK. What is this great circle? Why not a straight line? $\endgroup$– JenFeb 28, 2021 at 18:31
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$\begingroup$ 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. $\endgroup$– James KFeb 28, 2021 at 19:26
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$\begingroup$ 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. $\endgroup$– JenMar 1, 2021 at 20:14
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$\begingroup$ 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. $\endgroup$– James KMar 1, 2021 at 20:28
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$\begingroup$ 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. $\endgroup$– JenMar 3, 2021 at 0:19