The Moon takes about 27.3 days to complete one full orbit around the Earth relative to the fixed stars; this period is called the sidereal month. However, because the Earth-Moon system is also orbiting the Sun, it takes approximately 29.5 days for the Moon to return to the same phase (e.g., from new moon to new moon). This longer period is known as the synodic month or lunar month

. In summary:

• Sidereal month (orbit relative to stars): ~27.3 days
• Synodic month (orbit relative to Sun and lunar phases): ~29.5 days

The difference arises because as the Moon orbits Earth, Earth itself moves along its orbit around the Sun, so the Moon must travel a bit further to reach the same phase alignment with the Sun and Earth