It’s one other 12 months and one other Star Wars Day—May the 4th be with you. Following my custom, I’m going to take some element from Star Wars and do some cool physics. For this 12 months’s submit, I’m going to take a look at the tip of The Empire Strikes Back. The wonderful thing about utilizing this film is that it is so outdated—greater than 40 years—that I haven’t got to fret about spoilers.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 look at 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 approach out, they seize Luke (he was actually simply hanging round). Once they get off the planet, in fact, Darth Vader is there to intercept them along 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 true hero right here. He’s onboard the Falcon speaking to the Bespin central pc—you recognize, 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 wanting the place they’re going and received’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’s as if he was on a turbocharged bus when the motive force hit the fuel, and he isn’t seatbelted in. If we take the within of the bus because the reference body, then we might want to add a pretend drive to account for the acceleration. I imply, it is not essentially a pretend drive. According to Einstein’s equivalence principle, there is not any distinction between an accelerating reference body and a gravitational drive.
So, within the reference body of the accelerating Falcon, there seems to be a gravitational-like drive that pushes in the wrong way because the acceleration. The magnitude of this drive on R2 can be equal to his mass multiplied by the acceleration of the spaceship. If R2 has fully 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’s a superb factor—as a result of I simply must measure R2’s acceleration as seen from contained in the spacecraft.
This means we get to do some video evaluation. If I do know the scale of stuff contained in the Falcon, then I can decide the place of R2 in every video body. Also, with a recognized body price I can get the time for every of those positions. For the space scale, I’m going to make use of the height of R2-D2 and the body price that’s embedded within the video (in order that it performs again on the appropriate velocity). My favourite software for getting this knowledge is Tracker Video Analysis. (It’s free.) Of course, there are some small points with this evaluation. The digital camera 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: