Moon and planets

The Moon is the most noticeable object in the night sky, and it is then no wonder that it has fascinated mankind since antiquity. If you observe it for several days, you will no doubt notice that its appearance changes: most of the time only part of it is illuminated, and this part seems to grow until it covers the whole moon (full moon) and then decrease until nothing is illuminated (new moon), and then grow again, in a cycle that repeats about every month.

One possible explanation that comes to mind is that the dark part we see on the Moon is the shadow that the Earth casts on it. But there are problems with this explanation. For one, if this were true, the Moon should be in its new phase when it at its farther from the Sun. We know when this happens, because then the Moon rises at the same time as the Sun sets; and we can observe that at this point the Moon is full, not new! Besides, if the Moon passes through the Earth's shadow every month, then when it is at the opposite side of its orbit it should get directly in between the Sun and the Earth, producing a solar eclipse much more often than it actually happens. No, this explanation cannot be the right one.