Final answer:
The phase following the third quarter moon is the waning crescent, where less than half of the Moon's visible side is illuminated as it moves towards the new moon phase. This period sees the Moon rising and setting later each day, with changing shadows on the surface that enhance its features for observation.
Step-by-step explanation:
The moon phase after the third quarter when the sunlit portion is decreasing and less than half is illuminated is known as the waning crescent. This phase occurs as the Moon moves from the third quarter phase, denoted as position G in the lunar cycle diagrams, towards the new moon phase, or position A.
Following a third quarter moon, which appears when exactly half of the Moon's visible hemisphere is lit, the illuminated part that we can see from Earth continues to shrink each night. The Moon has already completed three-quarters of its orbit around Earth at the third quarter phase, and it continues its journey to eventually arrive at the new moon phase.
During this time, the Moon rises later each day and sets later as well. The visibility of the moon's surface varies with its phases. For instance, during the waning crescent phase, the angle of sunlight illuminating the Moon creates shadows that can accentuate topographical features, making it a rewarding time for observation through binoculars or a telescope.
This understanding of the Lunar cycle, particularly the phases after the full moon leading back to the new moon, gives us insight into how the interplay of light and shadows on the Moon's surface creates the diverse appearances we observe from Earth. These phases are a beautiful manifestation of the celestial dance between the Earth, Moon, and Sun.