In fact: We sometimes see the moon during the day for the same reason we see it at night, it is reflecting light from the sun and its closeness to Earth makes it brighter than the daytime or nighttime sky.
Live Science
“In order to be visible during the daytime, the moon has to overcome the scattered light from the sun, Edward Guinan, a professor of astronomy and astrophysics at Villanova University in Pennsylvania, told Live Science. For two or three days around the new moon, it is invisible to observers on Earth, as its position in the sky means that the sun’s scattered light outshines the moon. But, as is usually the case, the moon’s relative closeness to Earth (238,900 miles on average, or 384,400 kilometers) means that the light it reflects appears brighter to us than objects emitting or reflecting light which are farther away, such as stars or other planets.”
Space
“The moon is visible in daylight nearly every day, the exceptions being close to new moon, when the moon is too close to the sun to be visible, and close to full moon when it is only visible at night. The best times in the month to see the moon in daylight are close to first and last quarter, when the moon is 90 degrees away from the sun in the sky.”
The Washington Post
“The best time to see the moon during the day is when it’s in the first and last quarter phases (90 degrees away from the sun) because that’s when we can see half of the moon’s lit side while the sun is still up.”
Ever wondered why you can see the moon sometimes during the day →
Science ABC
“There are two reasons why we sometimes see the moon during the day. First of all, the moon is bright and close enough to be seen against the blue hue of the sky. Secondly, the duration for which it is above the horizon of Earth coincides with the sun, making it possible to be seen during the daytime.”
