“Yes, Virginia,” wrote Francis P. Church, editor of the New York Sun, in 1897, “there is a Santa Claus.”
But when Virginia got a little older and took high school physics, her doubts returned. Big time.
Let’s see how she thought about the matter.
Virginia used round numbers, as befitted someone who had yet to encounter advanced mathematics. She started off with the idea that Santa had 29 hours to complete his appointed rounds. She came up with 29 by figuring that Santa had to visit within the six hours during which children could be assumed to be sleeping–say, between 11 p.m. and 5 a.m. (If you don’t think kids get up on Christmas morning at 5 a.m., you don’t have kids or it’s been too long since you were one.)
So Santa has a six-hour window. But the earth rotates through its 24 hour-long time zones, of course. Therefore Santa has 24 hours plus five more. Imagine if Santa took one hour to cover each of the first 23 zones. Then, when he started the last one, #24, he would have six hours to cover it. Thus 29 total.
Virginia was pretty sure that “29” was harder to work with than “30,” so she rounded up to 30.
Next, she used a really round number: 2 billion. She figured that that’s the number of Christians in the world plus others who would celebrate Christmas. Maybe more people than that would celebrate it, in fact, but she didn’t want to make it harder for Santa than she had to.
Then she figured that, given that many people live in families and other domestic groupings, Santa could visit, say, 3 people at a time on average.
Two billion people, then, divided into groups of three meant that Santa would have to make about 667 million visits on Christmas Eve and he had to do so in 30 hours. Thus Santa had to make 22 million visits per hour, or 6200 visits every second. (667M visits / 30 hours (or 3600 seconds per hour) = 6200 visits per second)
Let’s suppose each of the families is, on average, a mile apart. Virginia’s math was certainly not equal to the task of figuring out how far Santa in fact would have to travel to visit everyone, given that many were clustered in cities and some were scattered over, say, the wide open spaces of the Australian outback, the American west, and the Canadian and Russian north. So she settled on one visit per mile. This gave her the convenient calculation that Santa would have to move at an average of 6200 miles per second (mps).
And that meant that Santa couldn’t do it.
The g forces to accelerate almost instantly to a speed that averaged 6200 mps would certainly have pulled the antlers (and everything else) off the reindeer. And long before Santa and his team had in fact reached anything like 6200 mps, atmospheric friction would have vaporized them.
Virginia put down her pencil and cried into her hands. That nice newspaper editor probably didn’t know much math–you know how journalists are–but she did, and she just couldn’t believe anymore.
Can anyone help Virginia by showing her an error in her assumptions or calculations? Or is Santa doomed?
(This is not a trick question. I’d really like to know!)