RETROGRADE MOTION

Copernicus came up with a reasonable explanation for retrograde motion; it was simply that the Earth catches-up and then leaves behind slower moving outer planets (or that faster moving inner planets, catch-up and then pass the slower moving Earth). This causes the outer (inner) planet to undergo retrograde motion;

The time between retrograde events is the amount of time required for the Earth to lap the outer planet (or for an inner planet to lap the Earth). This time is known as the Synodic Period, E. Symbolically, we have,

1/E = 1/P_Earth - 1/P_planet

for an outer planet or

1/E = 1/P_planet - 1/P_Earth

for an inner planet.

For Mars (an "outer" planet), P_Mars = 1.9 years, P_Earth = 1 year, and the synodic period E ~ 2.1 years.