Let’s just check this solution real quick.
- What about the units? On the left, tension is in units of Newtons. On the right side of the equation, F-pull is in Newtons and the denominator is unitless (mass divided by mass). So that’s good.
- What about limits? What if mass B is super tiny? As the mass of block B goes to zero, the denominator goes to a very large number which makes the tension almost zero. That makes sense.
Going back to the scene from The Expanse, it’s basically the same thing, with Bobbie instead of the string. Also, we can see a way that the forces pulling her apart can be more reasonable. If the acceleration is small and the mass of the Razorback isn’t too great, she should be able to hold on (which she does).
Now for an analysis of the scene. Is it possible to estimate the mass of the two spacecraft? Maybe. Although the Belter ship and the Razorback are fairly close in length (probably between 20-30 meters), they likely have very different masses. The Belter ship is wider and bulkier and made for normal space travel. The Razorback was built as a racer.
I can actually get a better estimate of the size of the Razorback. Since they show a doorway, I can assume that it’s about 2 meters tall (seems reasonable for a door). Using this as a scale, the entire length of the ship would be around 20 meters. I can also measure the width at the rocket end at about 5.7 meters. Now let’s pretend like it’s a pyramid with a square base (it’s not). The volume of this would be the area of the base (5.7 times 5.7) multiplied by one third of the height. This would put the total volume of the Razorback at 217 m3.
Yes, I can use this volume to estimate the mass. The trick is to use the density. Oh, you don’t know the density of a spaceship? Well, neither do I. But I could use a REAL spaceship as an example. What about the Space Shuttle Discovery? This has a mass of 110,000 kg. Then I can use the length and width to calculate the volume and density.
Finally, by using the Space Shuttle density, I can determine the mass of the Razorback. Yes, it’s a rough estimate—but it’s still better than nothing. Just in case you want to challenge my numbers, I put all the calculations in this python code.
There you have it—a Razorback mass of 13,000 kilograms. Now, instead of estimating the thrust force on the Belter ship, I’m going to instead estimate its acceleration. If you look at the time between when the gangplank detaches from the Razorback and the moment Bobbie grabs it, it’s about 4 seconds, and the distance traveled is close to 1 meter. Assuming the ship starts from rest and has a constant acceleration, I can use the following kinematic equation: