The Physics of Star Wars’ BB-8 Bouncing Around the Millennium Falcon
Every time a new clip is released for Star Wars: The Force Awakens, I find something new to analyze. I really need to stop, but I can’t. In this video we see BB-8 getting tossed around inside the Millennium Falcon. Now for an analysis.
What would make BB-8 ride up the side wall of the Falcon? The answer is the same force that pushes you against the car door when you make a turn: nothing. There is no force that pushes you in this kind of motion. In fact, the car door pushes you when you turn but nothing is pushing you into the door. Why is this so? Let’s start with the Momentum Principle. This says that the net force on an object changes the momentum of an object.
This relationship between forces and changes in momentum (or if you prefer—you could say acceleration) only works when everything is measured from a non-accelerating reference frame (inertial reference frame). Looking from inside the Millennium Falcon as it accelerates is clearly accelerating (non-inertial reference frame). However, there is one way to make the Momentum Principle work in these accelerating frames—add a fake force.
Yes, you already do this in your car. When you are taking a turn, you think of some force pushing you into the door. This is a fake force. The magnitude of this fake force would have to be the mass of the object times the acceleration of the frame and the direction would be in the opposite direction of the acceleration of the frame.
With that in mind, we can assume there is a fake force on BB-8 in this clip. As she moves up the wall, I can include the following forces.
These forces are just guess. There are lots of problems with an analysis of this scene.
- Which way is “down”? Is this even on a planet, or is it in space?
- How hard is the wall pushing on the droid? Maybe BB-8 is just barely touching the wall.
- Do the forces in this accelerating frame add up to the zero vector so that BB-8 is either stationary or moving at a constant speed, or is she accelerating?
It’s a tough question. However, I can still make some guesses—so I will. First, I can estimate the dimensions of the inside of the Falcon (using the helpful images at The Full Scale Falcon project). Second, I can use Tracker Video Analysis to correct for the motion of the camera with respect to the background. This is what it would look like if you were just standing the in the spacecraft during this maneuver.
Now, marking the location of the droid in each frame I get the following for the horizontal and vertical motion (with respect to the Falcon-reference frame).
But what can we gather from this? Fitting a quadratic function to both x and y plots, I can estimate the acceleration in the Falcon-frame (although they don’t occur at the same time). In the x-direction, I get an acceleration of about 10 m/s2 (remember how to find the acceleration from a quadratic fit) and an acceleration of about 6 m/s2 in the y-direction.
I think both of these values are significant in that they aren’t really greater than the free fall acceleration on Earth (9.8 m/s2). Why does that matter? Well, what if you wanted to record this in a studio? You could take a Millennium Falcon set and rotate it around with an actual real BB-8 droid and see how she moves and falls. This would be a real video and not a computer generated scene (CGI). We already know that the BB-8 droid is real and not CGI, so this would just be more evidence that this scene could be created in real life. I think that’s cool.
Homework: If you want some homework to go along with this post, see if you can model the motion of BB-8 rolling up the wall using GlowScript. Do it quick before I find time to create this. Also, what would the motion of the droid look like when the Falcon pulled out of a dive or did a loop near an asteroid?
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