A period is defined as the amount of time that it takes any repeating action, such as an orbit or rotation, to complete a full cycle.
Sidereal is defined as the amount of time necessary for a period to repeat, based on fixed stars. A way to recall this is the fact that the word sidereal derives from the Latin word sidus, meaning "star."
Synodic is the amount of time necessary for a period to repeat itself based on a solar body. A way to recall this is by the fact that the word synodic derives from the Greek word synodos, meaning a "coming together" or a "meeting," such as one would attend at a Jewish synagogue.
According to Professor Richard Pogge of Ohio State University, astronomers refer to these periods as "simple motions." The Sidereal Day describes one day's earth rotation based on the stars. A Sidereal Month is one moon orbit around earth relative to the stars, while a Sidereal Year is defined as one earth orbit around the sun based on the position of stars.
Synodic periods require the combination of two sidereal periods. Astronomers refer to this as a two-part compound motion, measuring how long it takes for two things to "come together."
A Synodic Day, also referred to as a solar day, describes one day's earth rotation relative to the sun, meaning the period of time necessary for the sun and the local meridian to reunite in the sky.
A Synodic Month is based on one moon orbit around the earth relative to the sun, or how long it takes for the sun and moon to reunite as viewed from earth.
A Synodic Period of the Planet describes the time between successive oppositions of a superior planet, or how long it takes for a specific planet and the sun to reunite as viewed from earth.
There are two different ways of measuring the length of a day. The Sidereal Day of 23 hours, 56 minutes, and four seconds is used primarily by astronomers and times the rotation of the Earth relative to the stars, while the Solar, or Synodic, day of 24 hours is measured by the rotation of the earth relative to the sun.
The Sidereal Month, measuring the orbit of the moon around the earth, based on the position of stars, takes only 27.3 days. Then, 2.3 days later, the combined motion of the earth and moon relative to the sun completes the lunar month and brings on a new moon.
"The length of a lunation is greater than the time it takes the moon to complete an orbit of the earth because the moon must complete more than one orbit to bring it back in line with the sun," writes John Naylor in his book "Out of the Blue: A 24-Hour Skywatcher's Guide."