Synodic Period

The synodic period is the time it takes for two orbiting bodies to return to the same relative position, such as one body lining up again with the Sun and the other body as seen from Earth. It is not the same as the actual orbital period, because the bodies are both moving at once; the formula compares their angular speeds, and the relevant quantity is the difference in those speeds. Taking the absolute value ensures the result is positive whether the inner body moves faster or the outer body moves faster.

Use this when you need the repeat time for conjunctions, oppositions, or similar alignments in astronomy. It is especially useful for planets, moons, and artificial satellites when comparing two periodic motions around the same reference.

• Adding the orbital periods instead of using the difference of their reciprocals
• Forgetting the absolute value and getting a negative period
• Mixing up synodic period with sidereal period, which is the true orbital period relative to distant stars