Where do you have to be on Earth to see the south celestial pole at your zenith? What is the maximum possible elevation (angle) of the Sun above the horizon at that location? On what date is this maximum elevation achieved?
To determine the location where the south celestial pole is at your zenith, you need to find the Earth's latitude at which the south celestial pole is directly overhead.
The south celestial pole is the point in the southern hemisphere around which all the stars appear to rotate. Its counterpart in the northern hemisphere is the north celestial pole. The south celestial pole is typically not visible from most populated areas due to its position in the far southern sky.
To see the south celestial pole at your zenith, you would need to be at the geographic South Pole, which is located at approximately 90 degrees south latitude.
Regarding the maximum possible elevation (angle) of the Sun above the horizon at this location, it depends on the time of year. The South Pole experiences a phenomenon known as the "midnight sun" during the austral summer, which lasts from around late September to late March. During this time, the Sun remains continuously above the horizon, reaching its highest point around the December solstice (around the 21st or 22nd of December). At its peak, the Sun appears to be at an elevation angle of approximately 23.5 degrees above the horizon.
Therefore, the maximum possible elevation of the Sun above the horizon at the South Pole is approximately 23.5 degrees.
Please note that the specific date when this maximum elevation is achieved can vary slightly due to the Earth's axial tilt and irregularities in its orbit.