Clara's grandfather is a captain of a cargo ship. He prefers to navigate his ship through the moderate neap tides. At these times, the line between Earth and the sun is at a right angle to the line between Earth and the moon. Which phase or phases of the moon describe this alignment?

The phases are the first and third quarters.

Explanation:

During the first quarter of the moon phases, the line between Earth and the Sun is at a right angle to the line between Earth and the moon. At this time the moon has completed the first quarter of its orbit around the earth. At this point, half of the moon is fully reflecting light from the sun.

Also during the third quarter which is the last quarter, the line between the earth and the sun is at a right angle to the line between the earth and the moon. This is the time when the second half of the moon which was not illuminated during the first quarter becomes completely illuminated.