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The moon is currently in the phase of waxing crescent, having just gone through the New Moon phase. The First Quarter phase is coming up in two days, Tuesday, at 7:48 pm in Los Angeles, just 11 minutes after the sun sets.
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This will be an ideal opportunity to measure the angle between the sun and moon at the First Quarter.
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When the sky is clear in the evening (like right now in L.A.) you can get a very good look at the moon, and you can readily see which direction the sun is shining from, since that portion of the moon illuminated by the sun is angled downward at about 40 degrees from the horizontal (the crescent's angle of repose), in the direction of where the sun just set.
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You measure this angle of repose by holding a straight edge up to the moon with the two points of the moon's crescent touching the straight edge, and then measure the angle from the horizontal. It measures 40 degrees by sight, without any optical instruments, with a margin of error of about 5 degrees plus or minus. If you use a simple optical instrument you can get that error down to less than one degree.
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It is most instructive to watch the moon right now because you can easily see (if you want to see, that is -- but most flat-earthers just don't want to see!) that the sun is moving DOWNWARD over the horizon, not horizontally as flat-earthers are wont to proclaim.
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The moon continues its aspect of pointing downward toward the distant sun while the moon is still visible in the sky, and after the sun has set. If the sun were to take a ridiculous right turn upon setting (as the flat-earthers imply with their silly nonsense videos taken out of context) the illuminated side of the moon would reveal that change of direction in the sun, and the crescent would lie at an increased angle as it arcs toward moon-set, approaching 90 degrees from the horizontal. BUT IT DOES NOT DO THAT. The moon, in fact does the precise OPPOSITE of what flat-earthers want it to do: its waxing crescent reclines increasingly every day more toward the horizontal instead of toward the vertical.
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The moon's crescent shows its angle of 40 degrees (approximately) at this time in the evening, and the angle decreases slightly as it moves over a 60-degree arc in the sky today. Tomorrow, it will move over a 75 degree arc, and Tuesday it will move over a 90 degree arc, increasing every day by about 15 degrees. (A few days ago at the New Moon, this angle was zero, since the sun and moon were in the same place in the sky.)
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When the moon sets today, I expect to see an angle of repose of about 35 degrees. Tomorrow, it will increase to 60 degrees in the evening, decreasing to 30 degrees at moon-set, and so on, each day until the First Quarter arrives on Tuesday evening. Tuesday evening, the moon will be high in the sky, at astronomical high noon when the sun sets. The quarter moon illuminated will show a straight line dividing the moon in half from top to bottom, with the line of division only very slightly angled downward, about 2 degrees. This goes to show the immense distance from the sun to the moon relative to the distance from the earth to the moon. It is not a proportion that is explained by anything less than many tens of thousands of times different.
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As the moon arcs down to its setting position, the angle of repose will approach about 15 degrees, which will account for the declination of the sun's path around the earth, which this time of year is angled about 15 degrees from the vertical. When the summer solstice arrives, this angle of declination will be 11.5 degrees, for at high noon the sun will be directly overhead, as in Los Angeles we are at latitude 34 degrees, and the sun reaches 23.5 degrees north of the equator.
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Then the moon will remain a quarter moon as it arcs through those 90 degrees toward the eastern horizon. All the while, the illuminated side of the moon will angle downward more steeply from sunset to moon-set, further substantiating that the direction to the sun follows its course around and under the earth from our perspective on the earth's surface. That means the sun is shining on the moon from under our feet at a great distance from the earth, a distance measurable at many tens of thousands of times the distance from the earth to the moon.
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