Final answer:
The first quarter and third quarter are the most similar lunar phases as both show half of the Moon's illuminated side. The first quarter is visible in the afternoon and the third quarter is visible in the morning. These phases occur approximately one week after the new moon and one week after the full moon respectively.
Step-by-step explanation:
When considering the phases of the Moon, the two that are the most similar are the first quarter and third quarter phases. During these phases, we can see exactly half of the Moon's face that is illuminated by the Sun, hence they are also referred to as the 'half moon' phases. However, they occur at different stages in the lunar cycle, with the first quarter marking approximately one week after the new moon and the third quarter occurring roughly one week after the full moon. In terms of visibility, during the first quarter phase, the Moon is visible in the afternoon and early evening, setting around midnight. On the other hand, the third quarter moon rises around midnight and is visible in the morning sky, setting around noon.
The lunar phases are a result of the Moon's orbit around Earth and the position of the Sun illuminating half of the Moon throughout this monthly cycle. Considering that the Moon completes a full cycle in about 29.5 days, it makes sense that the first quarter and third quarter phases showcase half of the Moon's illuminated side from Earth's perspective at different times of the month.