It’s another year and another Star Wars day – May 4th with you. Following my tradition, I will take some element of Star wars and do some fresh physics. For this year’s post I’m going to watch the end of The Empire Strikes Back. The advantage of using this movie is that it’s so old – over 40 years old – that I don’t have to worry about spoilers. I mean, if you haven’t seen it yet, are you really going to watch it?
So here’s the scene: Leia, Lando and Chewbacca are using the Millennium Falcon to escape the Imperial forces on Bespin. Coming out, they grab Luke (he was literally hanging out). Once they leave the planet, of course, Darth Vader is there to intercept them with his Star Destroyer. Lando says, “Oh, no problem. We’re just going to go light speed and jump out of this system.” Well, it doesn’t work. The Imperials have disabled hyperdrive.
R2-D2 is the real hero here. He is on board the Falcon talking to Bespin’s mainframe – you know, just sharing lubrication techniques and gossiping about silly C-3PO things. The mainframe returns with a rumor: the hyperdrive has been turned off. So now R2 knows what to do. He turns around, and with the flick of a switch – boom. He will Falcon, immediately in hyperspace. I hope they watch where they’re going and they don’t hit a planet or something like that.
Now for the cool physics. When the ship makes the jump into hyperspace, R2 flies back inside the Falcon. It’s like he’s in a turbocharged bus when the driver hits the accelerator, and he’s not belted. If we take the inside of the bus as our frame of reference, then we will have to add a false force to account for the acceleration. I mean, it’s not necessarily a bogus force. According to Einstein’s principle of equivalence, there is no difference between an accelerated frame of reference and a gravitational force.
So in the frame of reference of acceleration Falcon, there seems to be a gravitational force pushing in the opposite direction to the acceleration. The magnitude of this force on R2 would be equal to its mass multiplied by the acceleration of the spacecraft. If R2 has completely frictionless wheels (or at least very low friction), then as the Falcon accelerates forward, it would accelerate backward relative to the ship’s frame. This is a good thing, because I just need to measure the acceleration of R2 as seen from inside the spaceship.
This means that we can do video analysis. If I know the size of the 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 will use the height of R2-D2 and the frame rate embedded in the video (so that it plays back at the correct speed). My favorite tool to get this data is Video Analysis Tracker. (It’s free.) Of course, there are a few small issues with this scan. The camera pans and zooms, but I can compensate for that movement by watching how R2 moves relative to the wall. With that, I get the following graph of position versus time: