How the Phyzards stole Christmas

Ho ho ho! Merry Chrysler Christmas! Santa has had a little “accident”, not involving me and a shovel, however I as luck would have it, purely by coincidence, happened to be in the North Pole. After persuading the elves it has become definitive: I’ll be filling in today to fill your hearts with Christmas joy. So, we at the Phyzards come to you bearing the greatest gift of all: Scientific Accuracy. Now all I have to do Is spread this gift to all the children in the world in one night. Likely I have also “repossessed” his trusty sleigh, so flying around would be no problemo as the elves here say. 

Sadly, I’m not both rotund and an old bearded man (make of that wat you will) and as such doen’t know Santa’s magical ways of flying this apparatus. Fret not! For physics will sure guide me to the best method to fly around while staying in the dead (or alive) of night. 

Now, I will set out with all of his iconic reindeer to save(?!?) Christmas! Go forth Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzle (Why is there a Pokemon here?), and Rudolph. 

As we all know, Santa is seriously slaying in his sleigh, but how would it work? Given the sleigh’s…. sleigh appearance we can easily tell that it doesn’t work with lift like our punnie planes do. Furthermore, the presence of the toys it usually caries, and this year physics textbooks, means that it probably isn’t less dense than air. 

While it does get pulled by reindeer I have also concluded that they too can not fly. Donner’s willful participation in this experiment is very appreciated. However, they do add horsepower (deer power) which can drive the sleigh. This makes me have the sneaking suspicion that they sleigh uses momentum to fly around the earth and not actual flight. 

I can safely say that the reindeer are there to provide a small driving force to counteract any resistance encountered along the way and to course correct. Props to Santa for not entirely ignoring air resistance while designing his sleigh. 

In this way the sleigh is nothing more or less than a satellite, which takes little energy to stay in the air. Except for launching it into the air it mostly uses its own momentum and earths gravity to orbit around it, making them very energy effective. When an object has a large mass it requires more force (and energy) to accelerate it and as such to cause it to move in a different direction. 

This, of course, is just a side effect of that one law of a certain physicist that keeps haunting me in my dreams, and who was coincidentally born on Christmas Day: Newton. Maybe he is is the secret identity behinds Santa, who knows?

Let me show you elaborate about that momentum thingy, when you have a satellite the object is moving so fast around the earth that by the time gravity has pulled it in the direction of the ground it’s moved far enough ahead that “down” to earth is different (not in the getting real sense, although that is also allowed). If you choose the velocity of the object to be exactly the point where the downward pull is large enough to make the object go in circles, but not strong enough to make it crash, you can have a satellite. 

Funnily enough the mass of the satellite isn’t important to what the Goldilocks zone, which is because the downward correction force is gravity, which is also dependent on mass. While a greater mass does cause the downward force to need to be greater, earth’s got it covered because this force, gravity, increases at the same rate. So, the velocity at which these satellites have to travel at depends solely on the distance between the centre of mass of het earth and the satellite. 

In the case of Santa’s sleigh this would be very close to ground lever, maybe a couple of kilometers above it (or Freedom-miles <Eagle emoji>). Otherwise we couldn’t get that shot in every Christmas movie where some kid sees santa flying over, and no one believes him until, maybe, the ending.  The earths radius dwarfs (or elfs) the range of altitudes meaning we can just assume that the distance between the centre points stay a crisp 6 371 000 metres. 

But now I bring you, my trustworthy partner in “Saving Christmas”, to may secret stash of plans, which I have been cooking up for some time now. However, I must admit that not all of these are as safe and sound as the jingle bells on this very sleigh. Unfortunately, they might crumble like a gingerbread house when held under scrutiny by quite basic physics. Give me this opportunity to illustrate to you what won’t work, which also intern allows you to get a better grasp on exactly how we can apply this merry knowledge. 

The simplest plan of action, Plan A, is also quite deceptive. And just so you know: I did not create this one when I had a little too much eggnog and a few too many cookies. This plan requires the sleigh to stay in the area of the earth that is currently at midnight, which of course changes as the day goes on allowing me to bring Christmas and physics joy to all. 

My biggest objection to this plan is that it would take 24 hours to have finished the entire path, which does mean that is is going to be a long day for me. Luckily, as I hinted at before, this plan wouldn’t work.

Even though it appears to us measly humans at the ground that the sleigh is going a whopping 464 m/s that entire time, which isn’t even enough to not crash I might add (skill issue on Santa’s part), on a cosmic reference frame it doesn’t appear to be moving at all. For the satellite like behaviour it would need to be in some kind of orbit around the earth, but it’s in fact simply dangling there in place, except for earths orbit around the sun that is.

You can tell that we have to look at it from the perspective of the sun because while the earths surface is moving (where we are observing from), the earths centre of mass isn’t. So we see a large movement, but that movement is actually us, not the sleigh (compared to the rest of the Milky Way, which Santa presumably frequents because it resembles his favourite drink). 

Even the simplest of scenarios require us to always thing about how we relate things to each other. In This case that means that it doesn’t actually have any momentum compared to the earths centre of mass, meaning that it would plummet no different than Santa falling down a chimney. 

My next plan entails correcting for that problem. You see, if I start at the dawn-side of the world and then move towards the dusk-side during a 12 hour period I would also have moved over the entire earth. From a cosmic view (I have achieved enlightenment) the dark side of the earth mostly stays in one area, however what part of the earth is in the dark side changes as the earth rotates. So, I have in fact traveled from a cosmic perspective if I go to one corner of the dark side to the other, dusk to dawn. 

Every part of the earth (in ideal circumstances) always goes from day to night after 12 hours or the other way around. If the sleigh travels that entire night area, in the opposite direction of earths rotation, it would have covered the entire earth. 

12 hours and and about 20 million metres in traveled area, half the earth circumference, gives us the 464 m/s. How in Santa’s name do we get the same result for this as for standing still from the perspective of people on the surface of the earth?

Let me explain, because this is mostly just a funny by product of that it is conceptually the same thing, but in different reference frames. For a bystander on earth plan A seems like the sleigh is moving a circle around the earth for 24 hours, or half an earth in 12 hours. While in plan B it appears to the sun that the sleigh is moving around half the earth in 12 hours, or the entire earth in 24 hours (if the drives keeps on flying because they feel like it). 

I’ll show you that difference lies in what happens when you view them from the others perspective. We know that with plan A it looks like the sleigh is standing still if you look at it from a cosmic view, but the exact opposite happens when you look at plan B from the down to earth view. In this case the velocity of earths rotation is added onto that of the sleigh, because, if you remember, the sleigh is moving counter to the earths rotation (what a wannabe contrarian).  

However, as stated before, the 464 m/s isn’t sufficient speed to maintain our desired equilibrium between gravity and momenten. I have also been advised not to repeat another Donner scenario, meaning that I am not allowed to put this one to the test. 

In my darkest moment, afraid that I will never “save” Christmas by bringing physics to all, I turned to a dark evil: Kind of avoiding the entire problem of not going too fast, and reasoning the other way around. The elves are on my tail, for no particular reason, so we will hastily continue to plan C. 

What if, instead of looking how the sleigh can stay in the dark side and then calculating the velocity I do the reverse? To stay in earths orbit at approximately ground level, 100 or 1000 metres isn’t that much on earths scale, it would need to travel at 7906 m/s from a cosmic perspective. This is a large number, and makes my caveman brain happy. 

One little itty bitty caveat though: If we just fly around the earth like plan B the sleigh will be in daytime before you know it and our nighttime charade will be up.   

The one orbit around earth we can go at this speed without ever entering the day zone is on the dawn-dusk line. This line creates a circle with the same radius as the earth, because it is precisely half way between the point facing and facing away from the sun. So, if I and my little sleigh keep on flying over this zone we’re all good, just pretending that dawn-dusk are as good as night time. 

With this in mind I present to you my masterfully created plan C, adore it in all its glory! 

As you can see in my battle plan, the sleigh is so fast that it will make a total of 8,5 loops before the night is up, which also allows for me to reach most households. These 8,5 loops are spread out over the entire earth by the fact that the earths surface is moving under the sleigh. While the sleigh has a straight path which repeats the part of the earth under it changes. These loops are sufficient because it splits the earth in 17 longitudal areas. 

If we avoid the oceans (sorry for flint who lives under the A of Atlantic), this should be enough. The rest of it is quite self explanatory, just the previously explained plan C, so just gawk at it in awe. 

While the path traveled appears straight from space it becomes kind of weird and curvy if viewed from our mere mortal perspective. This is because the velocity at which you’re spinning varies depending on how close to the poles your are. In this case it’s not just that the sleighs movement look different from different reference frames of the earth and space, but also for different places on earth.

This plan might just work, now the only part left is actually taking off. 

My time of departure has finally arrived. Although, the world doesn’t appear to be taking a liking to me (what a shame) as I suspect that these reindeer aren’t capable of reaching the velocity which I desire (and is necessary for me to not die) any time soon. 

After putting Donner through the wringer one more time, probably the last time for good anyway, I can tell that reindeer can provide 190 W of power. With a total of 8 reindeer this gives us 1520 W, which isn’t much of anything to work with, but I digress. 

Alas, I can no longer ignore the elephant in the room, or should I say the massive pile of presents in the room. To calculate how long it takes to reach a certain velocity, mass has to be taken into account. Assuming each of my wonderful textbooks have a mass of about 500 grams, and one for every child, we get a total of 1 billion kilograms. Sounds quite reasonable to me, for this utterly ridiculous situation that is.

You see, after putting the elves to work on the calculations I have come to a prospect quite grim. It would take six hundred thousand years before I reach 7906 m/s. The upside of this is that after waiting this monstrous amount of time, the event of witnessing the sleigh’s orbit would eclipse all of human history before that point and thereafter. Also all of the children who have been waiting for their toys this whole time would have long since passed away, but who cares about that.

The waiting time is so absurd that Santa will catch up to me. Sorry for not mentioning by the way, but it wasn’t totally by his choice that I took over. This means I have to skedaddle before he turns me into a snowman. Would you, reader, be so kind to inform Santa about what happened to Donner and that his other reindeer need to go to the gym more?

That was it for my dive into the physics behind Santa’s sleigh, and it turns out that he does use magic after all. What a bummer, I hoped he would really put the cool in winter. He also wasn’t a huge fan of me “stealing Christmas” as he put it: It looks like I’m getting coal this year. 

I used the opportunity of this blog mostly to tell about reference frames and satellites, which is why I didn’t really go into detail on what other possibilities exist. Please go ahead in the comments to discuss other possible methods, and I will try to respond with my thoughts. 

However, most importantly: We at the Phyzards wish you very happy holidays! And we’ll see you next year 🙂