It is one other yr and one other Star Wars Day—Might the 4th be with you. Following my custom, I will take some aspect from Star Wars and do some cool physics. For this yr’s submit, I am going to take a look at the top of The Empire Strikes Again. The beauty of utilizing this film is that it is so previous—greater than 40 years—that I haven’t got to fret about spoilers. I imply, if you have not seen it by now, are you actually going to observe it?
So, right here is the scene: Leia, Lando, and Chewbacca use the Millennium Falcon to flee from the Imperial forces on Bespin. On their manner out, they seize Luke (he was actually simply hanging round). As soon as they get off the planet, after all, Darth Vader is there to intercept them together with his Star Destroyer. Lando says, “Oh, no biggie. We’ll simply make the bounce to lightspeed and skip out of this technique.” Nicely, that doesn’t work. The Imperials have disabled the hyperdrive.
R2-D2 is the true hero right here. He’s onboard the Falcon speaking to the Bespin central pc—you understand, simply sharing lubrication strategies and dropping some gossip on the foolish issues C-3PO says. The central pc comes again with a rumor: The hyperdrive has been turned off. So now R2 is aware of what to do. He rolls over, and with the flick of a change—growth. There goes the Falcon, proper off into hyperspace. Hopefully they’re trying the place they’re going and gained’t hit a planet or one thing.
Now for the cool physics. When the starship makes the bounce to hyperspace, R2 goes flying backwards contained in the Falcon. It is as if he was on a turbocharged bus when the motive force hit the gasoline, and he is not seatbelted in. If we take the within of the bus because the reference body, then we might want to add a faux power to account for the acceleration. I imply, it is not essentially a faux power. Based on Einstein’s equivalence precept, there isn’t any distinction between an accelerating reference body and a gravitational power.
So, within the reference body of the accelerating Falcon, there seems to be a gravitational-like power that pushes in the other way because the acceleration. The magnitude of this power on R2 can be equal to his mass multiplied by the acceleration of the spaceship. If R2 has utterly frictionless wheels (or at the very least very low friction), then because the Falcon accelerates ahead he would speed up backwards with respect to the ship’s body. That is a superb factor—as a result of I simply have to measure R2’s acceleration as seen from contained in the spacecraft.
This implies we get to do some video evaluation. If I do know the dimensions of stuff contained in the Falcon, then I can decide the place of R2 in every video body. Additionally, with a recognized body charge I can get the time for every of those positions. For the space scale, I will use the peak of R2-D2 and the body charge that’s embedded within the video (in order that it performs again on the appropriate velocity). My favourite software for getting this information is Tracker Video Evaluation. (It is free.) In fact, there are some small points with this evaluation. The digicam pans and zooms—however I can compensate for that movement by taking a look at how R2 strikes with respect to the wall. With that, I get the next plot of place vs. time: