In WALL-E, the Axiom entered hyperspace incredibly fast, and it looked identical to Star Wars. If I didn't know, I would assume the Axiom was very far from Earth and entered the solar system within seconds. Can someone correct me on this?
It's funny that you ask this question because I was literally watching the special features disc for Wall-E about 2 hours ago. It's one of my son's favorite movies.
They specifically mention that the Axiom is in orbit in the Kuiper Belt in the BnL extras section of the special features disc on the BluRay.
According to NASA, the Kuiper Belt is located "beyond Neptune" and extends to encompass Pluto's eccentric orbit. Since the Kuiper Belt is made up of individual objects, it's difficult to say exactly where it "begins" per se, but it seems to exist between 30-50 AU from the sun. In case you aren't aware, because I was not, 1 AU is the mean distance between the Earth and the sun which is about 93 million miles.
So...if you do the math on that you get a distance of roughly 2,790,000,000 miles if you assume that the Axiom was orbiting at the innermost edge of the Kuiper Belt.
Since we know that it takes sunlight an average of 500 seconds to travel 1 AU, this thing is traveling crazy fast. In a matter of seconds on film, the Axiom manages to travel 30 times the distance from the Earth to the sun. Let's assume this whole scene takes 15 seconds of film, this thing is moving something like 1000 times faster than light.
Of course, this assumes A LOT like the Axiom is actually right at the internal edge of the Kuiper Belt, the Earth happens to be optimally located in relation to the Axiom, and nothing like a large planet or the sun happens to be standing between them. I will mention, though, that the animators incorrectly placed the Kuiper Belt immediately beyond Saturn rather than Neptune in the BluRay's special features, so the intention may never have been for the Axiom to be orbiting as far from Earth as it actually would be.
If the Axiom were only traveling at the speed of light, and assuming that I've done my math correctly, it would take 4.16 hours for it to reach Earth from the Kuiper Belt. Not going to lie, though, math is not my strongest subject. If someone wants to check it, please feel free.
The Axiom, simply, is fast. But exactly fast did the Axiom go when it Hyperjumped to earth?
To figure this out. We need to know two things. How far it went and how long it took to get back to earth. The second problem is easy. In the film, the Axiom is in HyperJump for 11 seconds.
The first problem is not so easy. In the BnL extras the mention the Axioms intended destination is the Kuiper, however. Due to the directive A-113 which tells the Axiom to never return to earth. The Axiom is far outside the Solar System. As shown in the movie, it is actually orbiting the Horsehead Nebula. Which is 1,500 light years away.
This means the Axiom managed to travel 1,500 lightyears in 11 seconds. Which results in a speed of 1.29x10^18 m/s
Which means the Axiom traveled at 4,302,976,828c
In short, while in HyperJump, the Axiom travels 4•3 billion times faster than light.
The location of the Axiom is uncertain. It is statted that it could be located in the Kuiper Belt, or in IC 434, or in M16.
I believe it is M16 because, in the movie, we can see pillars, which are a reference of the pillars of creation which are located in the Eagle Nebula. Plus, even if they are both H II regions (I belive), the Eagle Nebula doesn't look as "red" as IC 434, it rather looks more purple.
If the Axiom is in fact around IC 434 or somewhere else, the process to determine its speed is the same, you only have to change the numbers.
The following calculations of part A will determine its speed if it was located in M16, in part B if it was around the Horsehead Nebula (IC 434), and part C, if it is around the Kuiper belt (we will consider at its farthest point, which is about 55 AU from earth.
I.1/ Introduction to the calculations
I.1.1/ general facts
- 1 light year is about 9 641 billion km.
- Speed (in km/h) = distance (in km) / time (hours)
- 1 AU = distance from earth to the sun, ~150 million km.
I divided the calculations in 3 steps:
Find the distance of the object where the Axiom is potentially located
I use the formula "Speed in km/h = distance in km / time in hours" to get a speed in km/h. In order to do this, it is necessary to convert distances into km, and time in hours.
Once we found the speed in km, we can determine its speed in seconds by doing this calculation : if 1 hour = "x" km. How much km in 1 second (0.00028 hours). So use 0.00028 hours (= 1 second) x the value in km that you found earlier, divided by 1.
To determine how much faster it is compared to the speed of light (c), it is necessary to understand that the speed of light is ~ 300 000 km per second. We simply use the number of km per second that we found in step 3 and divide it by 300 000. The result will tell you how much faster it is compared to c.
III.1/ Part A : M16
the distance of the Eagle Nebula is about 5610 light years. In km, that's approximately 53 076 210 000 000 000 km. In the WALL-E movie, they travelled this distance in about 26 seconds (from the moment when the computer countdown said "ZERO" to when we could distinguish the Axiom in earth high clouds). So, divide this huge distance in km by 26 seconds. 26 seconds is approximatly 0.0072 hours.
- So, 53 076 210 000 000 000 / 0.0072 = 7 371 695 833 333 333 333 km per hour (4 580 559 428 769 686 528 mph) To know how fast in goes in one second, we have to multiply the speed in km x 0.00028 hour which gives 26 327 485 119 047 619 046 428 km per seconds.
In conclusion of Part A:
The speed of light is 300 000 km per seconds The axiom's speed is 26 327 485 119 047 619 046 428 km per seonds, which is 87 758 283 730 158 730 times faster than the speed of light.
III.2/ Part B : IC 434
IC 434 is at a distance of about 1 500 light years, ~ 14 461 500 000 000 000 km. 14 461 500 000 000 000 km / 26 seconds (0.0072 hours) = 2 008 541 666 666 666 666 km/h x 0.00028 hours (1 second) = 562 391 666 666 666 km per seconds = 1.8 billion times faster than the speed of light.
III.3/ Part C : Kuiper Belt at its farthest (55 AU = 150 million x 55 = ~ 8.2 billion km)
8 250 000 000 km / 26 seconds (0.0072 hours) = 1 145 833 333 333 km/h. 1 145 833 333 333 x 0.00028 (to figure out in one second) = 320 833 333 km per second, which is about 1 064 times faster than the speed of light, which is the most "realistic" scenario.
We have to keep in mind that the exact location of the Axiom is not clearly precisly defined. Moreover, the movie takes place in a very far future, and we can speculate that, compared to how fast innovation and technological advancements are growing, it is safe to assume that we might develop new ways to "move in space". Of course, there are nowdays no evidence that there is a way to go "faster than the speed of light". In fact, the amount of energy needed to approach 1 c grows exponentially, and is potentially inifinte in order to get to 100% c.
The fastest machine built by humans today is the NASA Helios 2 space probe which went to a speed of about 252 792 km/h (70 km/s about 0,023% c).
The goal of this post was to try to determine approximately the speed of the Axiom depending of its speculated locations.
Even if we can be impressed of the technology involved in WALL-E, I think it would be also a good idea to analyse the implicits messages that Pixar may have tried to tell us.