How Much Energy Does It Take to Blow Up a Planet?

As Obi-Wan says when he drops in on Grievous: Hello there! In the present day is Star Wars Day. (Might the 4th be with you.) Which suggests I get to publish one other physics evaluation of a scene from one of many Star Wars films. Final yr, I appeared on the acceleration of Jedi in all of their jumps—together with Jar Jar, as a result of why not?

This time it’s The Rise of Skywalker. The Last Order needs to show everybody within the galaxy a lesson. So, on orders from Emperor Palpatine, a Xyston-class Star Destroyer fires a brilliant highly effective beam from area and blows up the planet Kijimi. Similar to that.

I do know what you’re pondering: How a lot power wouldn’t it take to explode a planet? In fact, it’s simply a tutorial query. I’m positive you’re not a Sith lord with dangerous intentions, so I’ll present you easy methods to determine this out. However even when this isn’t an actual factor, it’s nonetheless enjoyable to calculate.

Video Evaluation of the Explosion

To begin, we have to estimate the pace of the planetary shards as they’re blasted into area. We will try this with the Tracker video evaluation app. The thought is to select a number of particular items and map their place in every body of the video.

This place is measured in pixels, however we are able to convert it to distance by scaling it to a recognized object within the scene. Then we are able to get time information from the body charge—24 frames per second on this case. Assuming the scene is filmed at common pace (i.e., not gradual movement), we all know that every body represents 1/24th of a second. With place and time information, we are able to the compute the pace.

To repair the space scale, I’m going to make use of the dimensions of Kijimi itself. How large is that this planet? Who is aware of? I am going to simply say it has a radius of 1 Okay, the place Okay = the radius of Kijimi. Sure, it appears foolish to outline the unit when it comes to the factor we’re measuring, however we try this on a regular basis in science. (Earlier than individuals knew the precise distance from Earth to the Solar, they set it equal to 1 “astronomical unit.”) Don’t be concerned, it’ll work out ultimately.

There may be another concern. We will actually solely measure the pace of stuff transferring perpendicular to the digicam—i.e., within the image aircraft. Why? Suppose a bit is type of angling towards the digicam. In every body, it will transfer barely to the facet and get barely greater. But when I solely plot its pixel place, I’ll underestimate the space traveled and thus the pace.

With that in thoughts, I picked three fragments that begin on the fringe of the planet (as seen from the digicam) and journey outward in numerous instructions. The Tracker app then gave me this plot of distance traveled (the radial place of every object as measured from the middle of the planet) versus time:

You’ll be able to see that they principally plot out as straight traces, and the slope of every line (change in place/change in time) is the radial velocity in items of Okay per second. The inexperienced and blue objects have very comparable speeds of round 0.three Okay/s. The purple one begins off at 0.24 Okay/s then falls to about 0.08 Okay/s. That’s most likely an error by the software program; it’s onerous to trace objects in a discipline with a bunch of different stuff flying round.

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