Written by Harry Jang (Gyeonggi Academy of Foreign Languages'19)
Edited by Jaemin Yoo (Korea International School '19)
━━ August 12th, 2018 ━━
How long did Darth Sidious actually fall?
*SPOILERS AHEAD*
Chances are, unless you’ve literally spent your life beneath a rock, you have most likely seen the Star Wars series and been amazed. Possibly one of the most widely acclaimed and universally loved series in film history, it is by now an integral part of most childhoods. We all know how it ends - Darth Vader, turned back to the light side by his son’s faith, turns against his old and twisted master, Darth Sidious, and throws him from his throne room the Death Star II - after which, purportedly, he falls down to the reactor core at the center of the station, and explodes and dies in a massive burst of dark energy. But wait, you say. The Death Star II is 200 kilometers in diameter (From the Star Wars wiki). The reactor core is at the massive station’s center, and Darth Sidious’ throne room is at the very top of the planet-killing station. Falling that kind of distance must take ages, no? And yet, the film would have us believe that once thrown, impact and death occurred only a few seconds later. In the following exploration, we will see why this could not have really been the case with the assistance of physics, and hopefully find out what really transpired in that crucial moment, a long time ago in a galaxy far, far away.
Gravity
Little explanation, I believe, is necessary to explain what gravity is; most of us probably have a pretty solid intuitive understanding of gravity. It’s a force - one of the four fundamental forces of nature*, and the one that we are probably most familiar with, for the simple reason that it keeps us perpetually anchored to the surface of the Earth. However, less commonly understood is the mechanism by which it operates; with some wisdom from our friend Isaac Newton, we will see what exactly gravity is and how it works.
Gravity is a force. This means, by Newton’s 2nd Law (F=ma), it involves a mass, and an acceleration. Since gravity is a force, it will accelerate a mass that is within its sphere of influence, or within the gravitational field. But when I stand on the surface of the Earth, you ask, I’m not accelerating - I’m standing still, right where I am. Where does this acceleration go? Well, by Newton’s 3rd law, every action will have an equal and opposite reaction. When you press against a wall, the reason you do not plough through the wall and go forward is because it exerts back on you something called a normal force - in that it exerts a reactive force perpendicular to the applied force, or in the normal direction as sometimes called in physics. The same principle applies with gravity. As gravitational force pulls you down, against the ground, a normal force is created that pushes you upwards with the same force. These will cancel out (because they are equal and opposite), thus you stay in one spot. When there is no such object to exert a normal force - in other words, when you are in midair - there will be no normal force to cancel out the gravitational force, and thus the gravitational force will pull you down (you will fall).
(If you are doubtful, go ahead and calculate the values - multiplying the gravitational constant by the mass of the earth, and dividing by the square of the radius will invariably yield this value.) This is also the reason why objects of differing mass will fall, when near the surface of Earth, at the same speed, given no air resistance.
Gravity, and Air Resistance
That’s all very well, but on Earth – and on the Death Star – gravitational force will not be the only force around. Fortunately for us (and unfortunately for those who need to calculate this), we have an atmosphere, and this leads to the occurrence of air resistance, which will provide an opposing force to the direction of movement.
While the object falls, the it will continue to accelerate due to the gravitational force, until the velocity v grows to such an extent that the drag force will cancel out the gravitational force, and the system will attain dynamic equilibrium – while it is in motion, there will be no net force, and the falling object will fall at a constant velocity. This is known as the terminal velocity. A falling person will reach this velocity in just a few seconds, so we can assume that when Darth Sidious is thrown down the reactor shaft, he falls at this velocity for the majority of his descent.
The Real Story
This has massive consequences for the events of the movie. The station has a radius of 200,000 meters. At a rate of 52.92 meters per second, it will take Darth Sidious 3779.7 seconds to reach the center, assuming no further deceleration occurs (although this will inevitably be the case, since realistically the gravitational field loses strength and thus allows drag to decelerate the mass further). As such, the derived values we have now are minimum values, and the actual values are most likely going to indicate a longer time than 63 minutes, or an hour and 3 minutes. Based on our laws of physics and the movie’s purported chain of events, Darth Sidious was dropped from his throne room atop his gargantuan space station, where he should have fallen for more than an hour, after which he would have hit the reactor core at a terminal velocity of 52.92m/s . Either that, or Darth Sidious was dramatically thrown from his throne room, and died (and exploded, for some reason) in a matter of seconds when a draft of air presumably blew him sideways into a wall. Kind of anticlimactic either way, really.
*Four fundamental forces of nature: Gravitational force, electromagnetic force, weak nuclear force, strong nuclear force, listed in order of strength. All forces within our physical world are, at a fundamental level, composed of these forces.
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Bibliography:
“Death Star II.” Wookieepedia, starwars.wikia.com/wiki/Death_Star_II.
“Drag (Physics).” Wikipedia, Wikimedia Foundation, 1 May 2018, en.wikipedia.org/wiki/Drag_(physics).
“Gravity.” Wikipedia, Wikimedia Foundation, 8 May 2018, en.wikipedia.org/wiki/Gravity.
OpenStax. “Physics.” Lumen, Open SUNY Textbooks, courses.lumenlearning.com/physics/chapter/5-2-drag-forces/.
Pelcovits, Robert A., and Joshua Farkas. Barrons AP Physics C. Barrons Educational Series, 2016.
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To contact the author, email Harry Jang at harry.jang21@gmail.com
To contact the editor, email Jaemin Yoo at jmyoo19@student.kis.or.kr
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