A first quarter moon is a primary phase of the lunar cycle that appears in the middle way between a new moon and a full moon.

Third phase of the lunar cycle
A first quarter moon is the third phase of the lunar cycle, as it comes after a new moon and a waxing crescent moon.
The meaning of a first quarter moon

The moon is called “first quarter” because it is the time when the moon passes a quarter of the way in its orbit around Earth.
A first quarter moon appears as a half-moon or 50% illuminated in the sky.
Rise and set time of a first quarter moon
A first quarter moon rises around noon, reaches its highest point in the sky (overhead point) around sunset and sets around midnight.
A first quarter moon rises around noon because it is 90° away from the sun on our sky’s dome.
A first quarter moon is visible in the daytime
A first quarter moon is visible in the afternoon because the sunlight reflected from a first quarter moon is bright enough to be seen against the daytime blue sky.
Age of a first quarter moon
A first quarter moon is about 7 days old because it appears in the sky about a week after the new moon.
The duration of a first quarter moon
A first quarter moon has no duration as it occurs at a specific moment in time. It is the moment when the moon passes a quarter of the way in its orbit around Earth.
Looks opposite in opposite hemispheres
A first quarter moon appears as a half-illuminated moon in the sky from anywhere in the world. However, it looks opposite in opposite hemispheres.
In the northern hemisphere, the right half of the moon is visible, and in the southern hemisphere, the left half of the moon is visible.
People living in the southern hemisphere (south of the equator) observe the same first quarter moon from opposite angles than the people living in the northern hemisphere (north of the equator). As a result, a first quarter moon looks upside down.
Occurs once every 29.531 days
A first quarter moon occurs once every 29.531 days because the moon takes 29.531 days to complete one orbit around Earth with respect to the sun. This is called a synodic month.
Only 8% bright of a full moon
A first quarter moon appears 50% illuminated but it is only 8% bright of a full moon.
The relation between the apparent magnitude and brightness of an object is not linear, but it’s exponential. It follows the below equation:
2.512^(M – m) = change in brightness
So a difference of one magnitude corresponds to a 2.512 times change in brightness.
Now, the apparent magnitude of a full moon is -12.7, and that of a first quarter moon is -10. Remember, the brighter the object, the lower its magnitude value.
Here, change in magnitude = -12.7 – (-10) = -2.7
So change in brightness = 2.512^(-2.7) = 0.08
So a first quarter moon is only 8% bright of a full moon. In other words, a full moon is (100/8) = 12.5 times brighter than a first quarter moon.
The terminator line

The terminator line – the line between light and dark – divides the moon into two equal halves during a first quarter moon.
As you see the longest terminator line during a first quarter moon, it is an ideal time to see lunar craters and mountains along the terminator. Look for them in the early evening when a first quarter moon is high in the sky.
The terminator line of a first quarter moon shows sunrise on the moon as the illuminated area of the moon grows day by day after a first quarter moon.
Read about all eight phases of the moon:
New moon
Waxing crescent moon
First quarter moon
Waxing gibbous moon
Full moon
Waning gibbous moon
Third quarter moon
Waning crescent moon
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