Tuesday, May 11, 2021

Could Bobbie really hold 2 spaceships together in “The Expanse”?

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Let’s just check this solution very quickly.

  • And the units? On the left, the voltage 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 it’s good.
  • And the limits? What if mass B is tiny? When the mass of block B goes to zero, the denominator goes to a very large number which makes the voltage almost zero. It makes sense.

Returning to the scene of The extent, it’s basically the same, with Bobbie instead of the chain. Also, we can see a way that the forces that separate it can be more reasonable. If the acceleration is low and the mass of the Razorback isn’t too large, it should be able to hold up (which it does).

Now for an analysis of the scene. Is it possible to estimate the mass of the two spacecraft? May be. Although the Belter ship and the Razorback are quite close in length (probably between 20-30 meters), they probably have very different masses. The Belter Ship is wider and bulkier and made for normal space travel. The Razorback was built like a racer.

I can actually get a better estimate of the size of the Razorback. Since they show a door, I can assume it is around 2 meters high (that seems reasonable for a door). Using this as a ladder, the total length of the ship would be around 20 meters. I can also measure the width at the end of the rocket at about 5.7 meters. Now let’s pretend it’s a square pyramid (it isn’t). The volume of this would be the area of ​​the base (5.7 times 5.7) multiplied by a third of the height. This would put the total volume of the Razorback at 217m3.

Yes, I can use this volume to estimate the mass. The trick is to use 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 Space Shuttle Discovery? This has a mass of 110,000 kg. Then I can use the length and the width to calculate the volume and density.

Finally, using the density of the space shuttle, I can determine the mass of the Razorback. Yes, that’s a rough estimate, but it’s still better than nothing. Just in case you want to dispute 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 push force on the Belter ship, I’m going to estimate its acceleration instead. If you look at the time between when the catwalk detaches from the Razorback and when Bobbie grabs it, it’s about 4 seconds and the distance traveled is close to 1 meter. Assuming the ship starts at rest and has constant acceleration, I can use the following kinematic equation:

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