A scientific investgation, Providence unknown. Illustrations by John Dalziel, there used to be more but I don't seem to have them, dang! Read on....
But there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not completely rule out flying reindeer which only Santa has ever seen.
But since Santa doesn't (appear to) handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total - 378 million according to Population Reference Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes. One presumes there's at least one good child in each.
This is due to the different time zones and rotation of the earth, assuming he travels east to west (which seems logical). This works out to 822.6 visits per second.
This means that for each Christian household with good children, Santa has 0.001s to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house.
Assuming that each of these 91.8 million stops are evenly distributed Around the earth (which, of course,we know to be false, but for the purposes of our calculations, we will accept), we are now talking about 0.78 miles/household, a total trip of 75.5 million miles - not counting stops to do what most of us must do at least once every 31 hours, plus feeding etc.
So Santa's sleigh must be moving at 650 miles/second, 3 000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a pitiful 27.4 miles/second. A conventional reindeer can run, tops, 15 miles per hour.
Assuming that each child gets nothing more than a medium-sized Lego set (2lb), the sleigh is carrying 321 300 tons, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300lb. Even granting that "flying reindeer" (see #1) could pull 10 times the normal amount, we cannot do the job with 8, or even 9 reindeer. We need 214,200. This increases the payload - not counting the weight of sleigh - to 353,430 tons. This is four times the weight of the ocean-liner Queen Elizabeth II
This will heat the reindeer up in the same fashion as a spacecraft re-entering the earth's atmosphere. The lead pair will absorb 14.3 Quintillion joules of energy. Per second. Each. In short, they will burst into flames almost instantaneously, exposing the reindeer behind them, and creating deafening sonic booms in their wake. The entire reindeer team will be vaporised within 0.00426 seconds. Meanwhile, Santa will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250lb Santa (seems ludicrously slim) would be pinned to the back of his sleigh by 4,315,015 lb force.
If Santa ever did deliver presents on Christmas Eve, he's dead now....