Santa's Science

Assume there are 2.5 children per house. That means Santa has to make 842 million stops on Christmas Eve. Now let's say these homes are spread equally across the land masses of the planet. The Earth's surface area is, given a radius of 6,400km(3,986 miles), 510,000,000 sq km (196,600,000 sq miles), calculated as radius squared, multiplied by 4 pi. Only 29 per cent of the surface of the planet is land, so this narrows the populated area to 150,000,000 sq km (57,9000,000 sq miles). Each household therefore occupies an area of 0.178 sq km (0.069 sq miles). Let's assume that each home occupies the same sized plot, so the distance between each household is the square root of the area, which is 0.42 km (0.26 miles).

Nick D Kim - more cartoons here The Giving of Gifts

Every Christmas Eve, Santa has to travel a distance equivalent to the number of chimneys - 842 million - multiplied by this average spacing between households, which works out to be 365 million km (221 million miles). This sounds daunting, particularly given that he must cover this distance in a single night. Fortunately, Santa has more than twenty-four hours in which to deliver the presents. Consider the first point on the planet to go through the International Date Line at midnight on 24 December. From this moment on, Santa can pop down chimneys. If he stays right there, he will have twenty-four hours to deliver presents to everyone along the date line. But he can do better than this, by travelling backwards, against the direction of rotation of the Earth. That way he can deliver presents for almost twenty-four hours to everywhere else on Earth, making forty-eight hours in all, which is 2,880 minutes or 172,800 seconds.

From this, one can calculate that Santa has little over two ten-thousandths of a second to get between each of the 842 million households. To cover the total distance of 356 million km (221 million miles) in this time means that his sleigh is moving at an average of 2,060 km (1,279 miles) per second. Ignoring quibbles about air temperature and humidity, the speed of sound is something like 1,200 km (750 miles) per hour, or 0.3 km (0.2 miles) per second, so Santa is achieving speeds of around 6,395 times the speed of sound, or Mach 6395.