Another curious thing about the First Quarter Moon: since the Moon's orbit closely mimics the Ecliptic (the fictitious orbit the Sun takes around the Earth over the course of one year), the First Quarter Moon, when viewed due south, has an altitude off the equatorial horizon similar to what the Sun will have at local noon one season (or three months) later. For example, near the Vernal Equinox Day, the Sun is more or less over the Equator at sunset, so the First Quarter Moon will have a surprising high altitude, similar to what the Sun exhibits, at local noon, on the Summer Solstice. For Chicago, the solar altitude on the Summer Solstice Day is around 72 degrees. Therefore, the First Quarter Moon's altitude around the Vernal Equinox will be about 72 degrees as well. See the 3/11 picture, which shows the First Quarter Moon's altitude, when due south, to be about 75 degrees.
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For the Vernal and Autumnal Equinox days, the First Quarter Moon's terminator will be more or less vertical. See the 3/11 and 9/14 pictures.
Using the same reasoning, on or near the Summer Solstice Day, a First Quarter Moon's terminator will be slanted upwards, or smiling. See the 6/17 picture.
Suppose for example that you are viewing the First Quarter Moon sometime around the Winter Solstice Day. On days near the Winter Solstice, the Sun is more or less shining directly over the Tropic of Capricorn, or -23.5 degrees. As a result, the First Quarter Moon's terminator will be slanted downwards (frowning). See the 12/12 picture.
Since where the Sun shines most directly over Earth is correlated to the seasons, the First Quarter Moon's terminator (or shadow line) can be read to tell you what season it is.
A curious result of this mutual profile business is that the terminator of the First Quarter Moon, the edge of the Moon's shadow, shows by its slant where the Sun is shining most directly over Earth that day.
One thing about the First Quarter Moon: when you, an observer in the Northern Hemisphere, look at the Moon when it is due south (at 6 PM local standard time), you see what both the Earth and the Moon look like in profile, as if you were viewing them from outer space.