With billions of children around the world anxiously waiting for their presents, Father Christmas (or Santa) and his reindeer must be traveling at breakneck speeds to deliver them all in one night.
But did you know that light from an object traveling at high speeds changes color? This is thanks to what’s called the Doppler effect – the way speed affects the length of waves, such as sound or light.
When light changes color due to speed, we call it redshift or blueshift, depending on the direction. If we could catch the color of Rudolph’s famous red nose with one of our telescopes, we could use the Doppler effect to measure the speed of Father Christmas.
Here’s how that might work – and why this effect is also a crucial tool in astronomy.
How far do Santa Claus and his reindeer need to travel?
Strap into your sleigh for some light Christmas maths. I’ve updated a method proposed in 1998 to work out how fast Rudolph and Santa Claus need to travel to deliver all the required presents (you can find my working here).
There are approximately 2 billion children under the age of 14 years in the world. Approximately 93% of countries observe Christmas in some way, so we’ll assume 93% of all children do.
We know Father Christmas only delivers presents to those who truly believe. If we assume the same percentage of believers by age group as found in the United States, that leaves us with approximately 690 million children.
With about 2.3 children per household worldwide, he has to visit roughly 300 million households.
Spreading those households evenly across 69 million square kilometers of habitable land area on Earth (taking oceans, deserts, Antarctica, and mountains into account), Father Christmas has to travel 144 million kilometers on Christmas Eve. That’s nearly the same as the distance from Earth to the Sun.
Luckily, Santa has time zones on his side, with 35 hours between dropping off the first and the last present.
Let’s say Father Christmas uses half his time to zip in and out of each household, which gives him 17.5 hours total or 0.2 milliseconds per household. He uses the other 17.5 hours for traveling between households.
My hypothesis is that he needs to travel at a whopping 8.2 million kilometers per hour, or 0.8% of the speed of light, to drop off all the presents.
How can we measure Father Christmas’ speed with Rudolph’s nose?
Let’s say we want to actually measure the speed of Father Christmas’ journey to see if it matches the hypothesis.
A standard speed camera wouldn’t do the trick. But we have telescopes on Earth that can measure the color of something by using spectroscopy.
Father Christmas’ lead reindeer, Rudolph, has a famously ruby-red nose. If we could observe Father Christmas with telescopes, we could use the color of Rudolph’s nose to measure his speed using the Doppler effect, which describes how speed affects wavelength. That’s because Rudolph’s nose wouldn’t look quite so red if he were traveling at high speeds.
What is the Doppler effect? A good example is the sound of an ambulance. When it goes past you on the street, its sound is higher pitched as it approaches, and lower pitched when it drives away. This is because as the ambulance travels towards you, the sound waves are compressed to a shorter wavelength, and a shorter wavelength means a higher pitch.
The same thing happens with light. If a source of light is traveling away from you, the wavelength is stretched out and becomes redder or “redshifted.” If the source of light is traveling towards you, the wavelength is compressed, and the light becomes bluer or “blue-shifted.”
Rudolph the redshifted reindeer
Red-colored light has a wavelength of 694.3 nanometres when it’s “at rest,” which means it isn’t moving. That would be the measurement of a stationary Rudolph.
Let’s say Father Christmas would prefer to deliver presents fast, so he can relax with some milk and biscuits at the end of the night. He gets his reindeer to run much faster than I hypothesized, at 10% of the speed of light or 107 million kilometers per hour.
At this speed, Rudolph’s nose would be blueshifted to bright orange (624 nanometres) as he was flying towards your home.
And it would be redshifted to a very dark red (763 nanometres) as he was moving away. The darkest red human eyes can see is around 780 nanometers. At these speeds, Rudolph’s nose would be almost black.
Source : https://studyfinds.org/sants-speed-christmas-rudolph-red-nose-reindeer/