Final answer:
Mars undergoes retrograde motion when Earth is at a 180-degree angle to Mars with respect to the Sun.
Step-by-step explanation:
According to Copernican Theory, Mars undergoes retrograde motion when it appears to move backward in the night sky relative to the stars. This occurs close to the time when Earth, which moves faster in its orbit, passes Mars in their respective orbits around the Sun. For Mars to appear to be undergoing retrograde motion, Earth must be approximately at a 180-degree angle to Mars, with respect to the Sun, meaning Mars is in opposition. At this point, Mars would seem to move westward rather than the usual eastward across the sky.