Final answer:
The Sun is below the horizon at the South Pole from around March 21 to September 21, marking the period of continuous darkness there, which is option A).
Step-by-step explanation:
For someone at the South Pole, the Sun is continuously below the horizon during the period that corresponds to winter in the Southern Hemisphere. According to the celestial events, the Sun rises at the South Pole at the September equinox and sets at the March equinox.
Therefore, the period of continuous darkness at the South Pole runs approximately from the March equinox to the September equinox. Considering the given options, the correct answer is from March 21 to September 21, which represents the start of autumn and the end of winter in the Southern Hemisphere, corresponding to option A).