September 10th will mark the last quarter moon. It will appear half lit by sunshine and half immersed in its own shadow. The last quarter moon rises in the middle of the night, sets at noon, and transits the meridian at Sunrise. Here is more information about it
The best time to watch the last quarter moon is shortly after moonrise that is shortly after midnight. The shadow dividing their night on the moon it’s called the lunar Terminator and shows where it is sunset on the moon. The last quarter moon can also help and identifying the Earth's direction of motion in orbiting around the sun. Using the last quarter moon as a guidepost to find Earth's direction around the sun is easy as it can be done from anywhere in the world.
The last quarter moon appears to be immersed in its own shadow. It so happens that the last quarter moon is only half lit up by sunlight and the other half does not receive sunlight to reflect then for it appears to be immersed in its own shadow. Last quarter moon and half-moon look similar as both look like a semi-circle. The last quarter moon shows how ½ of the moon disk is illuminated, the side that reflects the sunlight and the other half is either not visible at all or is immersed in complete darkness.
It is dependent on which side of the moon is lit up while facing the orbiting around the earth. When the side facing the sun is lit up, it is called Half Moon phase. When the side away from the sun while orbiting the Earth is lit up, it is called the Last quarter or 3rd quarter phase of the moon.