There are roughly 2.2 billion children in the world today. How could Santa Claus visit all of them in one 24-hour period for Christmas?

The land-surface area of the earth is roughly 148,940,000 square kilometres. Assuming the population of the earth is spread out evenly, this gives roughly 14.77 children per square kilometre. Again assuming an even spread, this means that each child across the land-surface of the earth is about 260m away from the next child.

This gives Santa a linear distance of approximately 573 billion metres to cover in one night. If Santa travels this distance, he will need to maintain an average speed of 6,637,000 metres per second- roughly 2% of the speed of light.

Of course, this assumes Santa travels continuously and does not stop at each child, as he would be required to do.

For Santa to stop at each house, he would need to maximise his speed between children, to give him sufficient time to deliver presents. If Santa were to cover the linear distance at the fastest possible speed (the speed of light, 299,792,000m/s), he could do so in 31 minutes and 53 seconds. This would give Santa the balance of the 24 hours- 23 hours, 28 minutes and 7 seconds (84,488 seconds) to stop and deliver presents.

With 2.2 billion children, this would leave Santa with 0.0000384 seconds per child to deliver presents- 38.4 microseconds, or around 1/65,000th of a blink of an eye.

This is clearly an impossibility.

The effects of relativity are inconsequential, as while time would appear to stand still for Santa, from an observer in the children’s perspective, time would pass normally. The only impact from relativity would be that Santa would age 31 minutes and 53 seconds less than the rest of the world during Christmas Eve.

Additionally, we need to factor in acceleration. Let’s give Santa 30 minutes to accelerate at the start of Christmas Eve, and 30 minutes to decelerate at the end of Christmas Day. This leaves Santa with just 23 hours to cover his target distance now, which means he has to average 6,925,640m/s. To reach this speed over a 30 minute period, Santa needs a constant linear acceleration of 3,848 metres per second per second, or roughly 392 Gs.

This rate of acceleration would instantly turn Santa into a fine meat paste.

A human astronaut can survive (and maintain consciousness) out to a rate of roughly 10 Gs, or approximately 100 metres per second squared. Assuming this rate of acceleration, and allowing Santa to begin acceleration prior to Christmas Eve, he could start at around 5:30am on the 23rd of December and maintain constant linear acceleration for the following 18 1/2 hours (roughly 66,370 seconds).

However this leads us to another dilemma. The space shuttle, upon launch, reaches comparable rates of acceleration. However, to do-so, it requires booster rockets with over 1,000,000kg of rocket propellant in them. Burning this propellant over 120 seconds provides this level of acceleration. To maintain acceleration for 66,370 seconds would require a vast amount of fuel.

The space shuttle weighs approximately 2,000 metric tonnes. Assuming each of the world’s 2.2 billion children receive 1kg of presents each from Santa, Santa’s sled would need to carry a mission payload of 2,200,000 metric tonnes, or roughly 1,100 space shuttles. The fuel requirements (never mind structural engineering requirements) to launch and accelerate Santa’s sled would be astronomical- and this, again, would assume constant motion for the duration of Christmas Eve, rather than the continual deceleration and acceleration which would actually be required.

Therefore there is no practical way Santa Clause, as an individual and engaging with a reality governed by relativistic physics (i.e. limited by the speed of light as the maximum possible velocity) would be able to deliver presents to all the world’s children in 24 hours.

Stepping into the bounds of more theoretical physics, the only plausible faster-than-light-speed travel currently being discussed is by folding space-time between two points- ‘warp’. However Santa’s vehicle travelling at warp- instantly moving over the space between individual children- over 24 hours still runs into the problem that there is insufficient time to actually offload and deliver presents, as outlined above. Even assuming instantaneous displacement due to warp, Santa still only has 39.3 nanoseconds per child to deliver presents.

Generously assuming that Santa requires ten seconds to deliver presents per child (kits are prepacked and in delivery order so they can be rapidly offloaded upon arrival at each new destination), Santa would require 22 billion seconds, or 697 years, to complete his task.

To complete this task in one night, a minimum of 254,630 teams operating 254,630 warp-speed delivery vehicles, maintaining an average rate of 1 delivery every 10 seconds, would be required. Each vehicle would need to complete 8,640 deliveries, which would mean warping space 8,640 times. The energy requirements believed necessary to warp space-time are tremendous, so the fuel and energy costs of operating such a fleet would bankrupt the planet in no time at all.

Again assuming that each child receives 1kg of presents from Santa, each delivery vehicle would need to carry a mission payload of 8.64 metric tonnes- roughly the weight of a small bus. Factor in the weight of a warp-drive and the fuel necessary, and these would be very, very large vehicles indeed. Certainly far too large to be able to warp directly into an average living-room to complete delivery. Warping the delivery vehicle to outside each home might be more feasible, but rapidly increases delivery times, which in turn rapidly increases the necessary fleet size necessary to complete delivery in a single 24-hour period to the point of ludicrousness.

Finally, the resources required to build and maintain such a large fleet would require a city of millions focused solely on this task. No such city exists at the North Pole.

I can think of no physically plausible theory that supports the idea that Santa Claus delivers presents to the world’s children.

Alternatively, a global team of roughly 2 billion sets of parents each purchasing a small number of presents and all delivering them within that 24-hour period, while improbable in terms of spontaneous organization, is a feasible logistical delivery mechanism.

Clearly you’ve never heard of Santa’s little helpers! He doesn’t deliver all the pressies himself, he has a team! Factor that into the calculations. Am about to have a child and I’ve lined up lots of dreamsworks evidence pointing to Santa’s existence.

Or, the Doctor helps him travel through time to every house in the world.

Parents giving credit to a fat man who breaks into their house once a year or the Doctor helping out the children of the world? Obvious answer is the Doctor!