As Christmas approaches, children around the world will be eagerly awaiting a visit from Santa and his reindeer.
But with around two billion children on the planet, Santa really has his work cut out for him tonight.
Scientists have calculated that Santa would need to travel 89 million miles (144 million kilometres) to deliver presents to all the good girls and boys around the world.
That is the equivalent of flying his sleigh all the way from Earth to the sun in a single night.
In order to leave some time for delivering presents, this means Santa would need to travel at 5.1 million miles per hour (8.2 million kmph), or 0.8 per cent of the speed of light.
That incredible speed might also explain why Joly Saint Nick is able to fit his belly down a narrow chimney.
According to Albert Einstein’s theory of special relativity, objects travelling with Santa’s sleigh will become compressed in size as they near the speed of light.
But most strange of all, scientists say that, at this speed, Rudolf’s famous nose wouldn’t appear red at all.
Dr Laura Nicole Driessen, a radio astronomer from the University of Sydney, made these festive calculations based on a formula created by particle physicists from Fermilab in the 1980s.
First Dr Driessen estimated the number of children that Santa would need to deliver presents to.
There are approximately two billion children on Earth, but Christmas is only celebrated in some way in 93 per cent of countries we can assume that seven per cent of children don’t need presents.
But, of course, even among those who celebrate Christmas not every child is good enough to warrant a visit from the man himself.
Writing for the Conversation, Dr Driessen says: ‘We know Father Christmas only delivers presents to those who truly believe.
‘If we assume the same percentage of believers by age as found in the United States, that leaves us with approximately 690 million children.’
And with about 2.3 children per household worldwide, Santa will need to stop at a minimum of 300 million homes tonight.
‘Spreading those households evenly across 69 million square kilometres of habitable land area on Earth,’ says Dr Driessen.
‘Father Christmas has to travel 144 million kilometres on Christmas Eve. That’s nearly the same as the distance from Earth to the Sun.’
That would be a very tall order if Father Christmas only had the 10 hours between 20:00 and 06:00 the next day when children in the UK are sleeping.
Thankfully, he gets a few extra hours thanks to Earth’s rotation.
If the children are evenly distributed around the globe, then Sata has at least 24 hours to travel from the make his way all around the planet.
And, with the 11-hour difference in time zones between one side of the world and the other, Santa has a total of 35 hours from the first child falling asleep to the last waking up.
Dr Driessen says: ‘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 travelling between households.
‘My hypothesis is that he needs to travel at a whopping 8.2 million kilometres per hour, or 0.8 per cent of the speed of light, to drop off all the presents.’
But if Santa wants some time to eat a mince pie and put his feet up and the end of the evening, Dr Driessen suggests he might have to travel significantly faster.
To deliver everything nice and fast, Santa could travel 10 per cent of the speed of light – or 66.5 million miles per hour (107 million kmph).
However, at these speeds, things would start to get very weird for Father Christmas.
Thanks to the theory of special relativity, from our perspective Santa and anything travelling with him would appear to be much skinnier than usual.
Even though Einstein predicts that Santa would gain more mass as he gets faster, as he nears the speed of light he would get compressed in the direction he’s travelling – letting him slip down a chimney with ease.
Dr Katy Sheen, a physicist in the geography department at the University of Exeter, has previously suggested this could also be why Santa always looks the same age.
As objects near the speed of light, time moves slower from their frame of reference than in ours which means that Santa would age slower while travelling.
Yet, thanks to something called the Dopler Effect, the strangest effects would occur if we were to look out for the bright light of Rudolf’s nose.
This is the same effect which means that an oncoming ambulance’s siren sounds higher pitched than it does once it has passed.
As the object races towards us, the waves are compressed making the pitch higher and as it moves away the waves stretch out to produce a lower tone.
The faster something is moving the more pronounced this effect becomes which means that Rudolf’s breakneck flight will create an extraordinarily strong Dopler effect.
Red-coloured light has a wavelength, the distance between one peak to the next, of 694.3 nanometres when its source is at rest.
Flying at 10 per cent of the speed of light, we would see this light shift radically in either direction.
Dr Driessen says: ‘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 nanometres. At these speeds, Rudolph’s nose would be almost black.’
That means no one on Earth would ever really get to see Rudolf’s famous red nose.
WHAT IS THE DOPPLER EFFECT?
The Doppler Effect is a well-understood physical phenomenon which is also seen in astrophysics as the universe expands and creates ‘redshifting’ but is more commonly seen in sirens.
For example, when a blaring ambulance or police car shoots past with its sirens on, they seem high-pitched as they approach you and then lower-pitched as they speed past.
This is due to the compression of sound waves as they come closer, and they then stretch out as they grow more distant.
A stretched-out sound wave has a greater wavelength, and therefore a lower frequency, resulting in an increasingly lower pitch.
In astronomy, scientists use this effect to measure the speed of distant stars and planets.
When light sources in space move away from us, their wavelengths are stretched out into the red end of the spectrum.
Likewise, when something is moving towards us the light wave is compressed and the light shifts towards the blue part of the spectrum.
By looking at this red and blue shift, we are able to work out how something is moving relative to Earth.
For example, by measuring the red-shift of distant supernovae the Hubble Space Telescope and James Webb Space Telescope have helped to calculate how fast the universe is expanding.
Astronomers have also used this effect to work out whether a star is orbiting another.
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