Final answer:
The next new moon after observing a full moon on January 12th is typically seen about 29.53 days later, which would be around February 10th or 11th. This is due to the average length of the lunar cycle, also known as synodic period.
Step-by-step explanation:
If you observe a full moon on January 12th, then you will typically observe the next new moon approximately 29.53 days later, because that is the average length of one full lunar cycle, also known as a synodic period. The synodic period accounts for the Moon's orbit around Earth, as well as the movement of Earth around the Sun. Considering this, you would expect to see the next new moon on approximately February 10th or 11th, depending on the exact time of the full moon and slight variations in the length of the lunar cycle.
During the new moon phase, the Moon is positioned between the Earth and the Sun, making the side that reflects sunlight away from Earth, leaving it largely invisible to us – hence the term new moon, which signifies a fresh lunar cycle. The cycle of the moon has important impacts for various natural phenomena, such as the tides.