Dot Physics

WALL-E Gravity and Air

I finally saw the movie WALL-E. Good flick, I liked it. There was, however, one part I must comment on. You know I can’t help myself. I feel like the shark Bruce in Finding Nemo. I try not to attack, but there is a tiny drop of blood in the water. Here is the scene that I want to talk about:

I guess I should give a spoiler alert. Although, I will not talk about the plot of the movie.

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In this scene, WALL-E is hitching a ride on this space craft. The space craft is entering a hanger deck of a space station. While the hanger door is still open, WALL-E is clearly hanging on so that he won’t float away (no gravity or maybe everything is in orbit around a planet). As soon as the door shuts and possibly the hanger becomes pressurized, WALL-E falls off the top of the space craft suggesting that there is some type of gravitational force.

Yes, the people in the movie clearly have advanced technology. However, the scene seems to agree with the common idea that if there is no air, there is no gravity. What you say? Really? Yes, this is really a common idea. You can see this idea when you ask people why astronauts are weightless in orbit. Some will say it is because the astronauts are beyond the atmosphere where there is no gravity. I talked about what causes astronauts to float around in a previous post. It is not a lack of gravity.

This idea about gravity and air can also be seen when talking about the moon. It is not uncommon for people to say that there is no gravity on the moon because there is no air on the moon. Of course this is wrong for a couple of reasons. First being that there IS gravity on the moon. If you ask a person how astronauts walk on the moon if there is no gravity, the answer is “heavy boots”. I saw this somewhere on the internets, but I didn’t believe it until I actually got these answers from students. Heavy boots trumps no gravity.

Ok, I know I will get a comment.

“Why do you hate WALL-E? I thought that movie was great. You are spending too much time analyzing a movie. Can’t you just let a movie be a movie?”

There, I beat you to it. And since someone is going to get upset anyway (remember, I said I liked the movie), I will point out one more thing in WALL-E. Here is a shot from the scene where the space craft is leaving Earth:

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In this scene, the spacecraft has to break through all the Earth-based space debris. The first problem is that the unused satellites are just sitting there. If they were to stay in orbit, they must move. Maybe the WALL-E creators are sticking with the no air means no gravity idea. At least they are consistent.

The other problem with that scene is the sheer amount of junk in orbit. Suppose that was 300 km above the surface of the Earth (the orbital distance of the space shuttle). What is the volume of of this space (say it is 100 meters thick – which is tiny). The volume of this shell would be:

i-26507192de3f51ebade708cab4aacb58-vshell-2.jpg

Where r1 is the radius of the Earth plus 300 km = 6.678 x 10 6 meters and r2 is 100 meters more. This gives a volume of 5.6 x 1016 m3. See – that is a lot of space. How many pieces of junk could fit in this? Let me give an overly large estimate that each piece of junk gets (on average) a cube of 100 m x 100 m x 100 m (1 x 106 m3). How many pieces of junk would there be? Well, I can just take the amount of space available divided by the space for each piece of junk and I get: 5.6 x 1010 pieces. If Earth launched one spacecraft a day, that would take 153 THOUSAND years. Just saying.

One FINAL Thought – as an exercise for the readers

Here is the real question I had during the movie (and I don’t know the answer) oh wait…..

SPOILER ALERT

This question may give away more on the plot. Anyway, I tried to warn you. In movie, there is a large space craft that is essentially maintained by robots for more than 700 years. The humans don’t really do anything. The question is, if there is an energy source, is it possible for robots to maintain order in such a way forever? Would this violate any laws of thermodynamics? Is it possible to build some robots that are able to continue repairing themselves and cleaning stuff forever? I don’t know.

Comments

  1. #1 meichenl
    January 5, 2009

    I’ll try to give an argument that does not answer your final question directly, but could at least serve as the beginning of a discussion.

    Suppose you have a certain amount of information which you want to remember exactly, so you make a digital record of it with n bits. However, every minute, each bit of information has some small chance p of being flipped randomly. Over a long time, you accumulate errors and your record evolves into completely random mush.

    Now imagine you foresaw the previous disaster, so you decided to build three records of information. They begin identically. Again, every minute, each bit has some small probability p of being flipped. So, at the end of each minute, you compare all three records. If a bit flipped, you’ll have one record that disagrees with the other two. That way, you catch the mistake, and can manually flip it back.

    Unfortunately, after some extremely long period of time, you will have a case where the very same bit flips in two different records in the same minute. When you do the comparison at the end of the minute, the record with the correct bit will be outvoted, and you’ll lose some of your information for the first time. But if this happens once, give it long enough, and it will happen again and again. So after many ages, you’ll again have mush for data.

    Assuming the rate of random errors is fixed, you can slow the degradation of your data by
    1) making more copies
    2) checking more frequently
    Say you make c copies of your data and check on it with a frequency f. The sad news is that for any given probability P that no degradations have taken place, we can find some function t(c,f,n,p,P) that gives a time t such that if you wait for t minutes, the probability that you will lose some of your data exceeds P.

    In other words, if you want things to remain exactly the same for infinitely long, even an infinite supply of free energy won’t save you. Eventually, you’ll have to forget.

    However, there could be a way around this. What you need to do is continually increase the number of copies of data you have as a function of time (or continually increase the frequency of your checks as a function of time). If you continually make more copies of your data as time goes on, you may be able to get your probability of an error to converge to some value less than one as t -> infinity. However, to implement this strategy, the number of copies of the data you’re capable of storing would have to be unbounded (or the frequency with which you conduct checks on your data would have to be likewise unbounded.)

  2. #2 Rhett
    January 6, 2009

    @meichnel

    Thanks for the insightful comment.

    Rhett

  3. #3 Rob
    January 7, 2009

    Or continually decrease the probability, p, that a given bit has flipped by technical improvements in the storage medium and the protection afforded to it.

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