In the original trilogy, there are three planetary sized objects that blow up (explode). First was Alderaan, the home world of Princess Leia. Boom. Next was the original Death Star. Boom. Finally, the second Death Star was destroyed by the Rebel Alliance (it was supposed to be a trap). Boom.
But wait! These are no ordinary planetary sized explosions. Instead, all of these blow up and produce this expanding ring of stuff. I really don't know why they do this. Maybe this is due to a high speed internal rotation of the core. I could understand some type of high speed spinning thingy inside the two Death Stars, but Alderaan? Maybe Alderaan has a secret core power source inside so that they can keep the surface looking all natural. I'm just guessing here. Oh, we all know that there would be no sound from these explosions in space, right?
Ok, here is the question. How fast do these rings move? Let's get right to it. The first thing you are going to need is a video analysis program. Why not use the free and awesome Tracker Video Analysis? I have a couple of tutorials to help you get started with Tracker, but I think this screencast is the best intro. Basically, you use the program to mark the pixel location of something in a video for each frame. If you know the size of the pixels, you can get position (and velocity) data for that object.
I already have the videos of these three explosions (from my previous analysis of the blaster speeds in Star Wars). All I really need is the scale of the objects (Death Stars and planet). I've looked at the size of the Death Star when I estimated the size of a correctly scaled Lego Death Star. From this, the first Death Star has a diameter of 160 km and the second one was bigger with a diameter of 900 km. What about Alderaan? If I had to guess, I would just say it's Earth-sized, Wookieepedia lists it with a diameter of 12,500 km - which is essentially Earth-sized.
Now for the data. Here is a plot of the position of the expanding ring of "stuff" for the three explosions.
You can't even see the explosions from the two Death Stars, they just don't get very far. Ok, let's talk about the Alderaan explosion first. It looks crazy, right? I fit a quadratic function to the first part of the explosion. Since the acceleration looks fairly constant, I can write:
At t = 0 seconds (which is after the explosion but when I started taking data), the explosion ring would have a speed of 3.3 x 107 m/s. That's super fast. Actually, the speed of light is around 3 x 108 m/s, so this ring starts with a speed of about 0.1c (where c is the speed of light).
Why would this exploding stuff accelerate? Well, I guess it could be due to a gravitational interaction with all the stuff still near the planet. From the fit, this would give it an acceleration of 1.5 x 107 m/s2. If this is from a gravitational force, the field would have this same value (but I would use units of N/kg). But that's a crazy high field strength. The gravitational field on the surface of the Earth is 9.8 N/kg and on the surface of the Sun it is 274 N/kg. If the ring is slowing due to a gravitational force, there must be something massive in there. In fact, using the gravitational force I can get an estimate for this mass.
If the mass is constant (debris mass), then as the ring expands the gravitational field should decrease (I am leaving off some details, but this post goes over Gauss's Law for gravity). So, there is a problem. What value of r should I use? Let me just pick a reasonable value to get an estimate. With an r of 2 x 107 m, I get a mass of 9 x 1031 kg. This is 47 times more massive than our Sun. What does this mean? I don't know.
But wait! There's more! A little bit later, the exploding ring increases in speed to a value of 7.5 x 107 m/s (0.25c). Why would it do that? I don't know.
Ok, now for the two Death Star explosions. Here are their plots without the Alderaan data.
From this, the first Death Star exploding ring moves at 5.2 x 105 m/s and the second Death Star is at 1.56 x 106 m/s. Of course the second Death Star has to be bigger and better at everything.
Star Wars Day Homework
I think it should be a tradition to have homework questions on Star Wars Day, so here you go. Yes, Star Wars Day is May 4th (May the 4th be with you).
- This one has been done before, but it's worth redoing (don't google the answer until after you calculate it). How much energy would you need to gravitationally destroy a planet like Alderaan? By gravitationally destroy, I mean how much energy would it take to move all the mass of the planet a very far distance from the other mass.
- Alderaan's exploding ring is moving pretty fast. The parts of the ring moving towards the observer would have a blue doppler shift so that it would look a little bluer. The part of the ring moving away from the observer would look redder. Estimate the change in color for different parts of the exploding ring.
- Assume that Alderaan has a mass similar to Earth. What should the acceleration of the ring be as it explodes?
- The video shows an exploding Alderaan ring with a constant acceleration (even though the ring gets bigger). If this acceleration is due t mass, calculate the rate that mass is added to the system.
- The exploding ring seems to have a constant density even though it is expanding. Estimate the rate of change in mass as the ring expands.
- Create a reasonable explanation for why both Alderaan and the two Death Stars produce these exploding rings.
That's still not enough? There are some more question from my Reddit Inspired Star Wars Homework post.
Homepage Image: Lucasfilm
