Aerrow’s Space Sling
Hey everyone!
Today we’re diving into celestial mechanics and three wonders in Atmos’ orbit. The most spectacular of which is, of course, Radarr’s insane launch towards the Exopod! :D
Why insane, you ask? Because suddenly Radarr’s pulling off an ORBITAL TAKEDOWN! >:D But, as we all know, Radarr actually took the Exopod out of orbit and then returned home safe and sound. And now we’re going to simulate it all and figure out how he actually pulled it off. Buckle up your space skimmers and let’s blast off to orbit!
Theory
1. What is an Orbit?
To understand how Aerrow and Radarr behave in orbit, we need a little theory. Let’s take an apple and throw it. The faster we throw it, the further it will travel, but sooner or later it will fall to Earth. And at this point, we need to ask the right question: can we throw the apple fast enough so that it orbits the Earth and comes back to us? It turns out we can. To do this, we need to throw it at the first cosmic velocity. If nothing happens to the apple after the throw, it will fly around the Earth forever, endlessly falling towards it. This is an orbit, an endless fall to Earth. Let’s visualize it.
The first cosmic velocity is the speed at which the apple will be in a circular orbit. In this simulation, the distance from the Earth to the apple is 50 pixels. The first cosmic velocity for this height is 5.77 pixels per unit of time. In reality, the first cosmic velocity is 28,400 km/h at the surface, and at the ISS orbit, it’s already 27,300 km/h. That’s a huge speed that only a rocket engine can achieve. Don’t throw apples into orbit…
2. Orbital Maneuvering
Now let’s find out how the apple behaves in orbit. Let’s see what happens if we give the apple a braking and accelerating impulse.
In the first simulation, we give an impulse against the apple’s motion. Its orbit began to lower and reached a minimum height at the bottom of the screen, turning from circular to elliptical. But look what happened to the speed. It started to increase and reached a maximum at the minimum height.
In the second simulation, we give the apple an impulse in the direction of motion, and everything happened exactly the opposite: the orbit began to rise and reached the greatest height at the bottom of the screen, also turning into an elliptical one. At the same time, the speed began to decrease and reached a minimum at the maximum height.
On Earth, we’re used to the fact that if we need to speed up, we need to accelerate, and if we need to slow down, we need to brake. In orbit, everything is upside down: if we need to speed up, we need to brake, and if we need to slow down, we need to accelerate. The space driving test will be very difficult… :'D
3. Hohmann Transfer
Now let’s find out how the apple can transition from one circular orbit to another. The Hohmann transfer is the least energy-intensive way to do this. First, the apple needs to be given an impulse to enter a transition elliptical orbit, which we have already seen, and then give another impulse at the top or bottom of the transition orbit to enter a circular orbit at a new height. Let’s visualize it.
To rise to a higher orbit, you need to give 2 accelerating impulses, and to descend to a lower one, you need to give 2 braking ones. In canon, Aerrow complained about not having enough fuel for such distances. In real life, it’s exactly the same: in addition to astronauts, the spacecraft has to carry fuel. This increases its weight and requires even more fuel for maneuvering, which is why it’s always extremely insufficient for space flights. For example, the minimum distance between Earth and Mars is “only” 60 million km, and at a speed of 11 km/s, this distance could be covered in 2 months. However, it’s impossible to get to Mars faster than 6 months because the ship has to make an economical but very long Hohmann transfer, and not fly the shortest route. Physics, you heartless thing…
Well, on that cheerless note, we’re done with the boring theory and move on to the practice.
Scene Analysis
So, I’ll say right away that I will not elaborate on my assumptions about the size of Atmos, what its gravity is, at what altitude this flight took place, and most importantly, to what altitude the Atmosian atmosphere extends. Therefore, all further simulations will take place in Earth orbit at an altitude of 250 km. Formally, this is still the mesosphere, not the exosphere, as stated in the canon, but it doesn’t really look like they’re climbing that high. If the authors ever share these details, let me know, and I’ll re-model with them. But until then, we have what we have. ¯\_(ツ)_/¯
1. Taking the Exopod Out of Orbit
Let’s start with the simplest thing. As we remember, Radarr hit the Exopod with a crowbar, after which it shot down Ravess’ ship and did this:
For this to happen, we need to change the Exopod’s orbit so that it enters the Earth’s atmosphere. That is, lower the lowest point below 90 km, then due to air resistance, burning will begin, and the fall will be inevitable. There are only 2 ways this could be done, and the crowbar, which Radarr couldn’t somehow harm the Exopod with, is unfortunately not one of them:
Brake the Exopod
Accelerate towards the Earth
Let’s visualize both of these methods. We see that, as in the canon, in both cases the Exopod falls ahead of Radarr.
In this simulation, the scale is 1 km per 1 pixel. No, Radarr is not 4 km tall; otherwise, he wouldn’t be visible. :D The simulation shows that we only need a braking force of 50 m/s or a push towards the Earth at a speed of 200 m/s for the Exopod to enter the atmosphere and burn up. With braking, the descent took 35 minutes, and with a push, 18.
If Junko were there instead of Radarr, I would have no doubt that he could throw the Exopod with his hands at a speed of 200 m/s, while Uncle Newton isn’t looking, of course, and stay in his orbit. There was also the idea that Stork could do it, since headcanons state that he is very strong, but @rin-henricov completely and irrevocably refuted it. In light of these circumstances, I have no choice but to assume that behind the scenes, Radarr still braked the Exopod with the engine in his cradle. ¯\_(ツ)_/¯
And of course, after braking, he had to give an accelerating impulse to stay in orbit and not fall with the Exopod. If Piper wasn’t controlling Radarr’s every action behind the scenes, then he’s a very clever lemur. :D
It should also be considered that when the Exopod shot down Ravess’ ship, a signal came from the control panel to activate the maneuvering engines, which sent it into the atmosphere. It sounds like incredible luck, but since no one saw these engines being turned on, and the situation is presented in such a way that Radarr dealt with the Exopod, this option seems implausible. ¯\_(ツ)_/¯
2. The Space Sling
So, let’s increase the difficulty! And this is what we’ve all been waiting for! :D Without further ado, let’s watch Aerrow zoom past the Exopod.
We’ll assume that the Exopod is moving exactly in a circular orbit. We estimate that Aerrow is moving faster than it by about 50 m/s and load the simulation. With your permission, I will reduce the scale to 1 meter per pixel, which, of course, will remove the Earth from the frame, but otherwise they will all merge into one point, and nothing will be visible. ¯\_(ツ)_/¯ Also, in the frames, we see that the distance between Aerrow and the Exopod was about 100-200 meters, so we’ll assume that Aerrow launched Radarr fast enough not to fly away too far. Assumption upon assumption, but what won’t you do to save Atmos. ¯\_(ツ)_/¯
Well, the moment of truth! We launch Radarr at a speed of 55 m/s directly towards the Exopod. Three, two, one… Radarr, go save the Atmos!
Um… okay, guys… you didn’t see that… :'D
So, why didn’t anything work? As you all probably already understand, Aerrow is not just overtaking the Exopod, but is on different orbits. Even 50 m/s is enough for Aerrow’s orbit to be 100 km further; and since he just launched him in the direction of the Exopod, he, in addition to the impulse, also transmitted to him the angular momentum of his orbit, which led to the divergence. If Aerrow wants to launch Radarr towards the Exopod, he must extinguish the angular momentum by launching him a little below the Exopod at a slight angle. By a slight angle, I mean a very slight angle. Only 0.036 degrees. No more, no less, otherwise Radarr will miss again! >:D We make the corrections and repeat.
Yesss, bullseye! :D
BUT!
Firstly, what is 0.036 degrees at a distance of 250 meters? It’s like barely moving your finger up close, and at that distance, you shouldn’t even tremble! Only Finn’s marksmanship would allow this to be done, but even that’s not certain. And, most importantly, would the technology allow verifying such an angle? Aerrow is a true virtuoso, I can’t say anything. ¯\_(ツ)_/¯
Secondly, as you have already seen, Radarr won’t just stop at the Exopod. He has to accelerate and equalize speeds, otherwise he will fly away. And equalize very, very accurately. At an angle of 0.0255 degrees. Because otherwise…
Thirdly, I won’t be filming this again, but if you accelerate NOT at this angle, after only 15 minutes, Radarr’s cradle flies more than 100 meters away from the Exopod. ¯\_(ツ)_/¯ Radarr needs to equalize not only speeds but also angular momentum; otherwise, this launch is very likely to become a one-way ticket. And even in this case, he would have to return and adjust the position of the cradle at least once. What can I say? It seems that Radarr is no less a virtuoso than Aerrow. Well, or Piper very diligently advised him behind the scenes, who knows. ¯\_(ツ)_/¯
Fourthly, as you already understand, from Radarr’s point of view, launching against the direction of the space skimmer is braking. And what does braking in orbit lead to? That’s right! It leads to a decrease in orbit! That is, if Aerrow makes even a slight mistake, calculates the throw even slightly incorrectly, he will send Radarr straight into the atmosphere! He would have to very accurately calculate the force of the throw so as not to drop Radarr onto Atmos, and…
And in all good conscience, Piper should have just SCREAMED at the top of her lungs into his radio about THIS as soon as she saw what he was doing, and not… Okay, calm down, now is not the time. More on that at the end of the post. >:D
In the meantime, let’s move on to the last point to find out where Aerrow actually flew.
3. Aerrow and Radarr’s Rendezvous
So, ladies and gentlemen, to describe the full complexity of what you see in these frames, I will give a small analogy: have you ever tried to jump out of a window and land exactly in the cockpit of a supersonic aircraft? You probably haven’t? We return the scale back, remove the Exopod so that it doesn’t flicker before our eyes, and see where Aerrow will fly if he does nothing.
He will fall behind Radarr by 840 km after 1 orbit. Not bad, right? :D
So, repetition is the mother of learning: Aerrow and Radarr are on different orbits after separation. So meeting them is a classic celestial mechanics problem of transitioning from one orbit to another.
In real life, if we wanted to do this, we would have to perform two Hohmann transfers: first to an intermediate synchronization orbit, then at the right moment rise from it to his orbit, and only then could we slowly approach Radarr. But it would take many hours and many orbits, and we don’t have that much time - in canon, Aerrow caught up with Radarr after 1 orbit. And Atmos has poor communication in orbit, so classical methods are not suitable for us. ¯\_(ツ)_/¯
The situation seems hopeless, but there is a way. Aerrow must maneuver. For ease of perception, I slow down the simulation and show in video format with comments what and when Aerrow must do to meet Radarr.
So, what did we see here? This is a simulation, and it took me 4 impulses to return Aerrow to Radarr’s orbit. It could have been done in 2, but that was enough for me. The fact is that it took me a whole day to select the impulses, and each of them must be very accurate so that Aerrow doesn’t miss. And, I won’t hide it, while I was trying, I dropped Aerrow on Earth several times. ¯\_(ツ)_/¯ And it is also important to note that in the simulation, you can subtract the velocity vector and put Aerrow into the correct orbit, but in reality, the equipment has limitations, and many more impulses would be needed, and Aerrow would have to keep his eyes glued to the radar for an hour and a half of this flight. And he returned as cheerful as if he had taken a walk. And it is also important to note that I was doing this at home over a cup of tea, and I had an unlimited number of attempts. And Aerrow had to do this there. In orbit. On the first try. This is literally heaven and earth.
And now the most important thing. Since there was no communication with Aerrow during this flight, this means that he performed this maneuver completely independently. Without Piper’s hints, without anything. And no, Piper only calculated that he should turn on the engine 1 time at a certain moment - and it is impossible to get closer in 1 orbit with 1 impulse. Do what you want, but I only know one person who would 100% be able to do all this, put him at the helm of a space skimmer.
To say that the authors did not model this flight and could not have known all this can be said at any moment. But this is not our method; we are looking for opportunities, not excuses. And after modeling, I have no choice but to declare that Aerrow and Radarr, if not the same as Jimmy Neutron, are at least comparable geniuses. And now, SUDDENLY, I have something to say that… well, I can even call a headcanon in a certain sense. ¯\_(ツ)_/¯ But first, a few words about Piper.
Where Did Piper Go Wrong?
So, ladies and gentlemen, I propose to look at the plan that our beloved Piper came up with for Aerrow.
Looking at THIS, I… I just really want to ask: Does Piper understand that she is sending friends into space, not a warhead? .. :'D No, of course, I believe that she actually planned a safe rendezvous but incorrectly determined the altitude and entered the wrong speed, but this plan… And she was only lamenting when she saw WHAT her friend was going to do, and not screaming into the radio with all her might that he could drop Radarr… No, just say that it’s a blunder of the artist and that Piper actually understands what she’s doing… please, I beg you… :'D
Okay, enough joking. Let’s move on to the headcanon. ¯\_(ツ)_/¯
Why Did Piper Want to Leave the Squadron?
Suddenly, we descend from orbit to the “Storm Warning” episode. As we remember, Piper had a fight with Aerrow because he didn’t follow her plans and decided to see how they would do without her. And then she decided to leave for real but quickly changed her mind.
So, the headcanon is, what if Aerrow really is a genius? What if he runs through thousands of such plans in his head right during the mission, while Piper is painstakingly thinking about one single plan? Then it’s no wonder that he doesn’t want to follow them - he simply sees many options that are at least as good, and maybe even better! For example, some option is no worse, but… more fun. It’s strange to write this after analyzing a space flight, but anyway. ¯\_(ツ)_/¯
And that’s all for today! As usual, I don’t claim to be the ultimate truth; I just analyze what the authors drew to the best of my knowledge. Thank you for your attention; if anyone has mastered this brick of text, please don’t beat me up too hard for the errors if you find any, and see you soon!
