Final answer:
About 59% of the Moon's surface can be photographed over a month due to libration. The first or third quarter phases are optimal for photographing the Moon's surface details because of the shadow-enhancing oblique sunlight.
Step-by-step explanation:
Over the course of a month, approximately 59% of the Moon's surface can be photographed. This is because of a phenomenon called libration, which allows observers from Earth to see slightly different sides of the Moon at different times. Normally, only half of the Moon is visible from Earth, but because the Moon oscillates slightly in its orbit, more of its surface becomes visible over time. As the Moon goes through its phases, the angle at which sunlight hits its surface changes, revealing different topographic details. The best time to photograph the Moon for clear details is during the first or third quarter phases, where oblique sunlight casts sharp shadows and enhances the visibility of craters and other surface features.