In astronomy there’s no such thing as a half-moon. Only quarters, be it first or last quarter of a lunar month.
What appears as a half moon is actually one of the Moon’s quarter phases. Tonight (August 25, 2020) marks a first quarter moon. Viewed from anywhere on Earth, it appears at sunset, sets after midnight. Gazing skyward we see half a moon pie, What you’re seeing is half the moon’s day-side, but only a quarter of the whole moon. Measured from one new moon to the next, it’s one quarter around its orbit of Earth. Reason why there are no half moons in astronomy.
First quarter moons are characterized by “Lunar X and V”, specific locations illuminated by sunlight. A spectacle known as pareidolia.
“Lunar X and Lunar V appear when the moon is near its 1st quarter phase. They aren’t really Xs and Vs on the moon. They’re just high areas, catching sunlight, creating an example of pareidolia on the moon. Aqilla Othman in Port Dickson, Negeri Sembilan, Malaysia, caught them both in May 2017. Notice that he caught Lunar X and Lunar V.”
“Tom Wildoner wrote: “One of my favorite areas to photograph on the moon near the 1st quarter! I captured this view of the sun lighting up the mountain range called Montes Apenninus. The moon was casting a nice shadow on the back side of the mountains. This mountain range is about 370 miles (600 km) long with some of the peaks rising as high as 3.1 miles (5 km).””
Click here to see animation. As seen from the north side of the moon’s orbital plane, the Earth rotates counterclockwise on its rotational axis, and the moon revolves counterclockwise around Earth. The terminators of the Earth and moon align at first and last quarter moons, and only the near half of the moon’s day side is visible from Earth.