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Synodic period is a particular type of orbital period of a solar system object such as a planet, i.e., a measure of the time for it to complete an orbit. Specifically, it is the period after which the object has same position in relation to the Sun as seen from Earth. The alternate concept of an orbit's period is its sidereal period, the time it takes the body to return to the same position in relation to the stars, which better matches the concept of "once around the orbit".
For a planet much closer to the Sun such as Mercury, its synodic period is a bit longer than its sidereal period: the Earth has moved a bit while Mercury orbits and Mercury must come around a bit more to reach the same position relative to a line between the Earth and the Sun. For a planet much further from the Sun than Earth such as Neptune, its synodic period is just a bit longer than Earth's sidereal period: Neptune has moved a bit while Earth orbits and Earth must orbit a bit further to reach the same position relative to a line between Neptune and the Sun.
The relative position to which a planet returns after the synodic period is not necessarily exact, given the differences in orbital planes. The time period also varies due to orbital eccentricity, so a cited single value is likely the mean of the possible periods. The period between occasions the Moon has the same phase (e.g., between times when the Moon is exactly full) is its synodic period. For a planet beyond Earth's orbit (superior planet), the period between occasions when the planet is opposite the Sun from Earth would be its synodic period.
The term synodic period can also be used for the rotation period of such a solar system object, which may be synodic (the synodic rotation period or solar day) or sidereal (sidereal rotation period).