Synodia

Meet Synodia, a pair of racing planets who keep lapping each other.

A planet's orbital period around the Sun is its sidereal period. The synodic period is something else. It is the time between two lineups of the same kind, such as the moments when Earth passes Mars. Because both planets are moving, the inner, faster one has to gain a full lap.

For two planets with periods P₁ and P₂, where P₁ is the shorter, the synodic period S follows from 1/S = 1/P₁ − 1/P₂. Earth takes 1 year and Mars about 1.88 years, so 1/S ≈ 1 − 0.532 = 0.468 and S ≈ 2.14 years, about 780 days.

That is why Mars comes closest and looks brightest in our sky only about every 26 months.

Space mission planners use synodic periods too, because launch windows to Mars open when the planets line up, which happens on this same roughly two-year rhythm.