Final Answer:
The best time to observe the Moon with a telescope a few hours after sunset is during its first quarter phase.
Step-by-step explanation:
Observing the Moon during its first quarter phase is optimal for several reasons. During this phase, half of the Moon is illuminated and half is in shadow, providing a well-defined boundary between day and night. This boundary, known as the terminator, highlights lunar features like craters and mountains with pronounced shadows, enhancing the viewing experience. Additionally, the first quarter Moon is positioned high in the sky, reducing atmospheric interference and allowing for clearer observations.
The first quarter phase occurs when the Moon has completed one-quarter of its orbit around Earth, approximately 7.4 days after the new moon. At this point, the angle between the Sun, Earth, and the Moon creates a right angle, resulting in a waxing crescent that is 50% illuminated. This geometry produces optimal lighting conditions for telescopic observation, revealing a wealth of lunar details. Moreover, the first quarter Moon rises around noon, reaches its highest point in the sky around sunset, and sets around midnight, offering ample time for observers to study its features. In conclusion, the combination of well-defined lunar features, reduced atmospheric interference, and convenient timing makes the first quarter Moon the best time for telescope observation a few hours after sunset.