Now that Thanksgiving has passed and we are well into December, we're all looking to Christmas as the next big time of the year. Of course, with Christmas, comes Santa. Let's consider if this jolly, cookie guzzling entity is even possibly real.

Santa brings presents to children, which would be about 30% of the 7 billion world inhabitants, or 2.1 billion people. Santa is also classically a Christian phenom, which would whittle that number to 400 million, considering Christians comprise 15% of the world. At an average of 3.5 children per household, Santa would have 114 million visits to make. Assuming that a child has an equal chance of being naughty or nice, it is feasible that each home has at least one nice child.

Let's now discuss time. Santa could travel east to west, or west to east. The former takes advantage of time zones and Earth's rotation, giving him (or her, feasibly) 31 hours to deliver. This would yield a rate of delivery of 0.0098 sec/household. Wow. Now assume that all households are evenly distributed across the Earth (the 148 million square km of land), and we have a distance of .88 km between each household (assuming each household is in the middle of a square of area .77 km^2). This gives a total distance of 100.32 million kilometers, and a necessary velocity of 898.92 km/s. This is about 22 times faster than the fastest man made object, the Juno space shuttle, clocking in at 40 km/s.

Taking it one step further, we will consider the payload of toys. Let's say each child gets an average size lego set of 2 lbs (0.9 kg), and net load towed by the reindeer comes out to 102.6 million kg, not including the mass of the sleigh and Santa (negligible by comparison). To bring such a mass to the velocity specified, Santa's reindeer would need to exert 4.15 x 10^19 J, not even considering the additional energy required to overcome the gargantuan drag force. Friction would create another issue, but that's outside the scope of this consideration.

In short, due to the ridiculous requirements laid out above, it is unlikely that Santa exists.

Thanks to the blogs of Linda Harden and Joachim Verhagen for inspiring this analysis.

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