How Rocket Wrecks the Ravagers With Physics

I’ve watched Guardians of the Galaxy Vol. 2 multiple times, but I never noticed this awesome physics scene before. Rocket, the cyborg raccoon, is being chased through a forest at night by Ravagers, and he sets a bunch of traps, including some sort of antigravity mine or repulsor device. When the pursuers approach, he hits the button and they fly up into the air, then tumble back down.

Of course, being Rocket, he can’t just do it once. We get this great view over the treetops, with Ravagers being tossed helplessly up and down, over and over. Boom: It’s a perfect scene for some video analysis. It’s like they made it just for physics classes.

Exoplanetary Motion

As always, we start by figuring out the forces. Once the dudes are beyond the influence of Rocket’s device (whatever it is), there is only one significant force acting on them: the gravitational interaction with the planet. It’s the same kind of downward tug that you feel on Earth as your weight.

OK, we know that on the surface of a planet, this gravitational force has a constant magnitude, equal to the local gravitational field (g) times an object’s mass (m). We also know that a constant force (F) causes objects to accelerate at a fixed rate, and the force equals the product of mass and acceleration (a). Putting those two things together, we get ma = mg:

Illustration: Rhett Allain

Canceling out m, we find that the acceleration is equivalent to the gravitational field: a = g. (For that reason, it’s often called the “acceleration due to gravity.” I don’t like that term, since it implies the object has to be accelerating.) The point is, mass doesn’t enter into it. Big Ravagers, little Ravagers—they all accelerate downward at the same rate. On Earth that rate would be –9.8 meters/second². But judging by the four moons in the night sky, this is not Earth!

Are we saying they fall at a constant velocity? No! Objects in free fall, with only gravity acting on them, speed up as they fall. But they speed up at a constant rate.

We can also plot position as a function of time. Starting from a certain height y₀ and an initial velocity v₀, we can write the relation between vertical position (y) and time (t) using this famous kinematics equation:

Illustration: Rhett Allain

Since this depends on both time and time squared, it’s a quadratic equation; if we graphed it, it would trace out a parabola. So if we can get position and time data from the film clip, we’ll be able to fit a curve to the data and determine the vertical acceleration, a.

Video Analysis

Enough formulas, let’s get back to the movie! I’m going to run that video clip through the Tracker video-analysis app to get position-time data for one of the falling Ravagers. But first I need to make a choice. With any video analysis of motion, there are three things to consider:

The distance scale: If we know the size of something in the video frame, we can measure distances moved. Essentially it’s a conversion from size in pixels to size in meters.
The time scale: We can get this from the video frame rate. If it’s 30 frames per second (and we know it’s running at real speed, not slo-mo), then we know the time scale.
The acceleration of the object whose motion we’re studying.

If you have values for two of these three things, you can find the third. Usually, for videos taken on Earth, we can figure out the time and distance scales, and we use that to find the acceleration. But here it’s tricky. There’s no obvious way to get a distance scale—I surely don’t know the size of trees on some foreign planet.

So instead, I’m going to assume a value for the acceleration. This is feasible because we’re looking at the simple case of free-falling objects, where the only force involved is gravity. Specifically, I’ll assume the gravitational field on this planet is the same as it is on Earth, giving a vertical acceleration of –9.8 m/s². That can’t be too far off, since everyone moves around exactly as they would on Earth. (What are the chances, right?)

Here’s what we get. This is a plot of the vertical position for one of those Ravagers. I’ve used an arbitrary distance scale (for now) in made-up units of, er, u. Don’t worry, I will convert this to real units soon.

Illustration: Rhett Allain

The data looks roughly parabolic. That’s a good sign! The software fit the equation for me, and it gives a value of –2.11 in front of the t² term. That should equal the coefficient in the kinematic equation above, which is 1/2 times the acceleration. That puts the vertical acceleration at –4.22 u/s². Then I’ll just set this equal to our assumed value of –9.8 m/s² to convert the distance unit to meters:

Illustration: Rhett Allain

Illegal Motion

Now I have a better plot of the vertical position of the flying Ravagers. But something is still wrong with this trajectory. You can see the problem a little better by plotting the vertical velocity as a function of time. Here’s what that looks like.

Illustration: Rhett Allain

The slope of this line is the acceleration. If I fit just the first part of the motion, on the way up (the lime green dots), I get an acceleration of –12.5 m/s². The second part, on the way down (blue-green), looks pretty similar.

But what about at the top? If you look at the graph in the middle, you’ll see that for about five frames, the hapless Ravagers have a vertical velocity of zero—the line becomes flat. They just float up there. At full speed it’s subtle, but if you go back and watch the clip knowing this, you’ll notice it.

Of course it’s just a movie, not real life (shocker, I know). But why would they just stop at the top of the arc? It could be that Rocket’s device alters gravity in some more complicated way that Earth physicists don’t yet understand … Or maybe it’s just poetic license.

They do that all the time in movies. The animators obviously used a physics model here for the basic trajectory, so the Ravagers move up and down in a believable way. You can see that in the constant acceleration (instead of constant velocity, which would be simpler to create)—that’s some nice attention to detail. But filmmakers often bend and tweak the model for effect.

In this case, I’m guessing they hung the Ravagers up there just so we, along with Rocket, could enjoy the sight of the bad guys—or in Guardians of the Galaxy, maybe we should say the worse guys—swimming helplessly in midair. It looks cool. I’m all for that.