Why is the time from one full moon to the next longer than the Moon’s orbital period?

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near and far sides of Earth's Moon — Moon (Left) Near side of Earth's Moon, photographed by the Galileo spacecraft on its way to Jupiter. (Right) Far side of the Moon with some of the near side visible (upper right), photographed by the Apollo 16 spacecraft.

The time from one full moon to the next is longer than the Moon’s orbital period because of the Earth-Moon system's simultaneous motion around the Sun.

The Moon’s orbital period, known as the sidereal month, is approximately 27.322 days, representing the time it takes for the Moon to complete one revolution around Earth relative to the background stars. However, because the Earth-Moon system is also orbiting the Sun, the angle of illumination changes by about one degree each day.12

Consequently, the Moon must travel slightly further in its orbit to return to the same position relative to the Sun—the configuration required to repeat the same lunar phase. This interval, known as the synodic month or synodic period, lasts approximately 29.531 days.31