Star Wars Celebration VII

The Science of Star Wars: Aristotle, Newton, and R2-D2

By Rhett Allain

Associate Professor of Physics at Southeastern Louisiana University


Have you heard the joke where Aristotle, Newton, and R2-D2 walk into a bar? Neither have I, but it could be the beginning of a classic!  Although the joke doesn't exist, these three can give some great insight into the idea of force. In this case, I am not talking about "The Force" - created by Midi-chlorians - but the other kind of force. Let me use these three people (R2 is a person for our purposes) to look at common ideas about force and how it relates to motion.

Aristotle's ideas of force and motion

Aristotle Let me start with a question. What does a constant force do to an object? Aristotle's answer is that forces cause motion. A constant force would make a constant motion (constant speed). Of course, he had more details than that but that is his basic answer. Is this a good answer? Well, probably 90% of the population would agree with him. In fact, when Aristotle said this (and he probably wasn't the first one to think about forces) his ideas would be held as the truth for around 2,000 years.

The most important thing to think about with Aristotle's ideas of force is that they seem to agree with common sense. If I push a book on my desk, the book will move. If I stop pushing the book, obviously it will stop. If I push harder, it moves even more. So, the idea that force causes motion and makes things move is supported by common observations that we see.


Newton's ideas of force and motion

Isaac Newton First, it wasn't just Isaac Newton that came up with this new way to look at force, but he is typically given credit (think Newton's Laws of Motion). Newton's answer to the constant force question would be that a constant force makes an object CHANGE its motion. Change is the key word (can't you tell?). Consider the following situation: A bowling ball is sitting on a smooth floor. If you keep tapping it with a stick, the ball will speed up. If you stop hitting it, the ball will just roll at a nearly constant speed. The force (the stick) causes the ball to change its speed.

Why is the Aristotle idea different from the Newtonian idea? The key is friction. Friction is a force that is almost always around, but people can easily forget about it. Back to the pushing book example. The reason the book stops when you stop pushing it is because there is another force on it that causes it to change its motion. The bowling ball doesn't have this problem so much because it is fairly massive with a fairly small frictional force. It turns out to be not so easy to observe situations where the frictional force doesn't really matter. This is why Aristotle and 90% of the population have the same ideas about force and motion.

What about R2-D2?

Flying r2 d2 SPOILER ALERT: R2-D2 flies in Star Wars Episode II. Maybe you think, " So what?"  Well, what if I look at the way he flies using ideas of Aristotle and Newton? First, let me make a few assumptions about the way he flies.

  • R2 uses some type of thruster and not some other technology. Oh, I understand that you could argue until the end of time over this assumption. The point is... there are things that look like thrusters that come out of his legs when he flies. I assume this is important for flying.
  • In the video scenes I will discuss, R2 flies at a fairly constant speed. Actually, this really isn't too much of an assumption. I actually went and did some video analysis of R2 flying and it does appear to be at a constant speed.
  • For flying I am going to assume near-Earth-like gravity. This should be an ok assumption because you see people jumping around and it looks mostly like jumping on Earth.
  • Earth-like atmosphere. Not sure how much evidence I have for this assumption, but I going to use it anyway.
Now, to look at flying R2. Here is a diagram of what R2 looks like while flying at a constant speed.

Flying r2 d2 1


What is important about this diagram? It shows the rocket thrust pointing both down AND backwards. So, from this there must be at least two forces on R2. Here is a force diagram where the arrows represent the size and direction of the two forces (in this case, gravity and the thrust).

Flying r2 d2 2


Here is the deal. If the thrust is like that, then part of it would balance with the gravitational force. The horizontal part would cause R2 to accelerate (change his speed). But I already said R2 does not accelerate. So, that leaves me with two options:

 

  • Option 1: Newton was wrong and Aristotle was correct. A constant horizontal force makes R2 fly at a constant speed.
  • Option 2: There is some other force in the horizontal direction that makes the total force zero. This force would have to be something like air resistance.
If I go with option 2, then there is something to say. Looking at the angle, it will say how much of the thrust is going down against gravity and how much is going against air resistance. I am not going to bore you will all the details, but I actually did this calculation.

If R2 flies using Newtonian ideas of force (just like everything we see in this world), then the only way R2 would have the thrusters at that angle would be if R2's mass was extremely small - like 100 grams. This comes about because R2 only needs a small force to push him through the air. Since the thrust is at an angle, R2 would only have a small thrust pushing up to balance the gravitational force.

Real World Example

There is something very similar to a flying R2-D2, the human jetpack. If you ever watch a video, you will notice that to move at a constant speed, the rockets face down, not down and back. Here is a shot of a rocket guy flying (from wikipedia).

Rocket man


So why is R2 flying wrong? The short answer is that the animation was created by someone from the 90% of the population that thinks about force like Aristotle. Please don't take this as an attack on the animator, it is a simple mistake to make. Just think, Aristotle was a pretty smart guy and he got it wrong. Not only that, but look at all the people after him that also got it wrong. Finally, who would even notice the flying R2 is wrong. Yep. It's me.

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