What is the name of the phase of the moon, if, in the process of moving around the Earth

What is the name of the phase of the moon, if, in the process of moving around the Earth, we see the right half of the lunar disk illuminated?

If we see the illuminated right side of the moon, then this is the phase of the first quarter or the growing moon. As soon as the Sun sets over the horizon, the Moon immediately appears in the sky with the illuminated right side in this phase. For comparison, if the left side of the moon was illuminated, then this is the phase of the waning moon or the third quarter. The waning moon rises closer to the night. On the celestial horizon, the Sun illuminates it from the east.



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