It’s another year and another Star Wars Day—May the 4th be with you. Following my tradition, I’m going to take some element from Star Wars and do some cool physics. For this year’s post, I’m going to look at the end of The Empire Strikes Back. The great thing about using this movie is that it’s so old—more than 40 years—that I don’t have to worry about spoilers. I mean, if you haven’t seen it by now, are you really going to watch it?
So, here is the scene: Leia, Lando, and Chewbacca use the Millennium Falcon to escape from the Imperial forces on Bespin. On their way out, they grab Luke (he was literally just hanging around). Once they get off the planet, of course, Darth Vader is there to intercept them with his Star Destroyer. Lando says, “Oh, no biggie. We will just make the jump to lightspeed and skip out of this system.” Well, that doesn’t work. The Imperials have disabled the hyperdrive.
R2-D2 is the real hero here. He’s onboard the Falcon talking to the Bespin central computer—you know, just sharing lubrication techniques and dropping some gossip on the silly things C-3PO says. The central computer comes back with a rumor: The hyperdrive has been turned off. So now R2 knows what to do. He rolls over, and with the flick of a switch—boom. There goes the Falcon, right off into hyperspace. Hopefully they’re looking where they’re going and won’t hit a planet or something.
Now for the cool physics. When the starship makes the jump to hyperspace, R2 goes flying backwards inside the Falcon. It’s as though he was on a turbocharged bus when the driver hit the gas, and he’s not seatbelted in. If we take the inside of the bus as the reference frame, then we will need to add a fake force to account for the acceleration. I mean, it’s not necessarily a fake force. According to Einstein’s equivalence principle, there’s no difference between an accelerating reference frame and a gravitational force.
So, in the reference frame of the accelerating Falcon, there appears to be a gravitational-like force that pushes in the opposite direction as the acceleration. The magnitude of this force on R2 would be equal to his mass multiplied by the acceleration of the spaceship. If R2 has completely frictionless wheels (or at least very low friction), then as the Falcon accelerates forward he would accelerate backwards with respect to the ship’s frame. That’s a good thing—because I just need to measure R2’s acceleration as seen from inside the spacecraft.
This means we get to do some video analysis. If I know the size of stuff inside the Falcon, then I can determine the position of R2 in each video frame. Also, with a known frame rate I can get the time for each of these positions. For the distance scale, I’m going to use the height of R2-D2 and the frame rate that is embedded in the video (so that it plays back at the correct speed). My favorite tool for getting this data is Tracker Video Analysis. (It’s free.) Of course, there are some small issues with this analysis. The camera pans and zooms—but I can compensate for that motion by looking at how R2 moves with respect to the wall. With that, I get the following plot of position vs. time: