To answer this question, let’s return to the concept of one day. The day is when it’s clear, and when it’s clear it’s because the sun’s rays are shining on us. On the other side of the earth at the same time there is no sunbeam (they cannot cross the earth) and therefore it is night. At any given time, half of the planet is illuminated and the other half remains in shadow.
The moon revolves around the earth, so sometimes it is opposite the sun (and therefore clearly visible to earthlings immersed in the night), sometimes on the same side as the sun (and therefore visible to earthlings in broad daylight ).
However, one important thing needs to be added: its shape. In fact, we observe the illuminated part of the moon. If the moon is in the opposite direction to the sun, then the entire part facing the earthlings is well lit: we see a beautiful disc, it’s full moon.
It’s a bit like reading a book: with a lamp over your shoulder, the pages are well lit and reading is easy. On the other hand, when the moon is almost in the same direction as the sun, not only does the sun blind us, but we only have access to the unlit part of the moon: impossible to see anything (it’s the new moon then)!
For the intermediate directions between these two extremes, we see only a fraction of a disk, between a thin crescent (just before or after the new moon) and an almost complete disk (just before or after the full moon), passing through the crescents – moons (first and last quarter, stack between new moon and full moon).
So you can see the moon during the day (when the sky is clear) but not any shape at all times. For example, the last quarter will be visible in the morning, the first quarter in the afternoon…
To know the exact moonrise and moonset times, you can consult the IMCCE website.
To better understand the phases, you can do a little experiment that you can find on page 18 of this book (published by Réjouisciences).
This analysis was written by Yaël Nazé, astronomer at the Institute of Astrophysics and Geophysics at the University of Liège (Belgium).
The original article was published on the website of The conversation.