You also have to factor the Spirit of Children Believing or whatever.
Still, these do not override the laws of physics.
In other words, it is impossible (both mathematically and otherwise).
For Santa to lug around presents for the whole world, he'd have to:
-Assuming each child receives roughly two pounds worth of presents and 500 million stops worldwide (from people and cultures who believe in Santa--and each of these having at least one good child), he'd have to lug around over 500,000 tons of presents (about 4.8 times the weight of the Queen Mary 2--the largest cruise ship currently in service).
Eight reindeer wouldn't suffice; if a single reindeer can haul, say, 500lbs on a sled (which evenso is probably stretching it), that puts the amount of reindeer (which weigh a couple hundred pounds a piece) up to at least 2,000,000.
500,000 tons plus the weight of the reindeer (200,000 tons) plus the weight of the actual vehicle (unknown, but for thee purposes let's figure 100,000 tons), plus the weight of Santa himself (overweight but less than 3/8 ton). So, we're looking at least 860,000 tons of weight to be carried to start.
-This is, of course notwithstanding the space issue...
-That 860,000 tons is going to cause a lot of atmospheric friction. Meaning that as Santa travels, the reindeer, sled, presents, and Santa himself will burn up in the atmosphere on re-entries. Why? To travel that fast without any direct force would require a vacuum (e.g. space).
-Cover the entire world in 31 hours (counting changes for timezones and the Date Line). The Earth rotates around its axis roughly 15 degrees every hour. This means that Santa has to travel nearly 700 miles a second (3,500 times the speed of sound) to meet this target (with an assumption of 500 million stops), and the average stop time is no more than one fifth of a millisecond.
The Ulysses solar space probe by contrast travels at roughly 30 miles per second, and the Apollo spacecraft cruised at 5 miles per second.
-Couple the last two points. Why do you think it's necessary for spacecraft re-entering the Earth's atmosphere to have a full heat shield? Any heat shield around the reindeer would kill the reindeer and thus render the whole system null.
Santa would never make it to Australia, much less the U.S. His spacecraft would burn up under all that friction.