Unlike the Northern Hemisphere, the Southern Hemisphere has no bright pole star to mark its south celestial pole – the point in the sky that’s at zenith over the Earth’s South Pole. Here, in the Northern Hemisphere, we are indeed lucky to have the moderately-bright star Polaris pinpoint our north celestial pole.
The Southern Hemisphere must wait another 7,000 years or so before a star matching Polaris’ brilliance will reign as a comparably good South Pole Star. Because of precession, the star Delta Velorum in the constellation Vela the Sail will come to within 0.2o of the south celestial pole in the year 9250. (As a basis of comparison, Polaris comes to within 0.5o of the north celestial pole in the year 2100.)
For reference, the moon’s diameter spans 0.5o of sky.
The stars are not truly fixed. Because stars actually change positions relative to one another over the long course of time, Sirius will even take its turn as the South Pole Star. In the year 66270, Sirius will come to within 1.6o of the south celestial pole, and again, in the year 93830, Sirius will miss aligning with the south celestial pole by only 2.3o.
As darkness falls, use Orion’s Belt to star-hop to Sirius, the future South Pole Star.
Source: Mathematical Astronomy Morsels V by Jean Meeus, pages 353 to 363