This question comes from N. Murdoch, who was thinking about how the three wise men in the Christmas story followed a star to Bethlehem where they found the baby Jesus.
The question is: what if you did walk towards a known star at a fixed speed? What path would you trace on the Earth? Sirius is the brightest star in the sky other than the sun.
If the wise men left Jerusalem on December 25, 1 AD, and walked toward Sirius day and night, even when it's below the horizon, this spiral is the path they would follow over the surface.
The size of the spiral is determined by how far a person can walk in half a day.
If we allow a little theological confusion and assume the wise men can walk on water, they'll eventually wind up going in an endless circle, 30 kilometers in diameter, around the South Pole.
But let's be a little more realistic; the wise men are hardly going to walk toward the star while it's behind the Earth.
Let's assume that they only walk toward the star when it's in the sky and the Sun has set, but they can still walk on water. In that case, their path actually takes them through Bethlehem.
If they don't stop there, after a few years, they wind up circling Botswana: These paths are calculated using, among other things, PyEphem, which provides tools for determining the historical positions of astronomical objects.
It's tricky to figure out exactly what the wise men would have been following.
There aren't very many good astronomical candidates for the Star of Bethlehem (Chinese records don't show a supernova at the right time, and none of the other obvious candidates check out) And, furthermore, there's a lot of historical and theological debate over Jesus's date – and even year – of birth.
