The Physics of a Spinning Spacecraft in The Expanse

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The Expanse ought to simply change their put up credit for every episode to incorporate an inventory of homework questions. Critically—there are such a lot of nice issues to discover on this onerous science fiction present.

In a current episode, one of many massive spaceships (the Navoo) rotates as a way to create synthetic gravity (that is probably not a spoiler). How about some questions and solutions about this big spinning spaceship?

How do you make synthetic gravity?

Let me get proper to it. You might be in all probability someplace close to the floor of the Earth and there’s a gravitational power between you and the Earth pulling you down. However right here is the loopy half—you do not actually really feel this gravitational power. Because the gravitational power pulls on all elements of your physique, you do not really feel it. What you truly really feel as “weight” is the power from the ground (or seat) pushing up on you. We name this the “obvious” weight.

Here’s a case the place you possibly can see how this works. Go to an elevator and get in. Press the “up” button. When the door closes, the elevator begins to speed up upwards. How do you’re feeling? Anxious? Bored? Heavy? Sure, you’re feeling just a little bit heavier than regular—even when only for a short while. To ensure that your physique to speed up upwards, there should be an upward web power. This implies the power of the ground pushing up should be higher than the load flattening. The precise weight does not change, simply your obvious weight. Like I mentioned, you do not actually really feel the gravitational power.

OK, get out of the elevator and get in a spaceship. It does not matter if this spaceship is in orbit round a planet or touring between planets. All that issues is that the movement is solely because of a gravitational interplay (with the planet or with the solar). In that case, everybody inside will solely have the gravitational power and they’ll really feel weightless. So, how do you make “weight”?

One resolution to this drawback is for the spacecraft to speed up. An accelerating spacecraft means the individuals may also speed up and an accelerating particular person wants a power pushing on them The power pushing on the people turns into the obvious weight—similar to in an elevator.

That is the way in which most spacecraft create “weight” in The Expanse. They use their thrusters to speed up in order that they’re both rushing up or slowing down. However both means, there’s a power on the people inside and so they really feel “weight.” If the spacecraft accelerates at 9.eight m/s2 (which is similar worth because the gravitational power on the floor of the Earth) then the people inside would really feel similar to they do on Earth.

However wait! There’s one other option to speed up a human inside a spacecraft—make the human transfer in a round path. Since acceleration is outlined as the speed of change of velocity and velocity is a vector, simply altering course is an acceleration. The magnitude of the acceleration whereas touring in a circle depends upon each the velocity and radius of the circle.

Since it is a rotating object, it is typically higher to speak concerning the acceleration when it comes to the angular velocity (ω) in radians per second. Oh, the course of this acceleration (as a vector) is in the direction of the middle of the circle. This implies you can also make a rotating spacecraft wherein the people stand on the within with their heads in the direction of the middle of rotation and so they can really feel “weight.”

Increase. That is precisely what occurs with the Navoo in The Expanse. Oh, there’s truly a plot level in that solely the Navoo can create synthetic gravity.

What does the Navoo do when it is not rotating?

Nice query. For all of the earlier episodes, the Navoo didn’t rotate. They created synthetic gravity similar to everybody else—that they had rockets speed up the spacecraft. Oh, you need to observe that always the spaceships are flying backwards as a result of they do not truly fly in house. Flying implies utilizing air to create elevate and that is not what is going on on right here.

If you wish to go from level A to level B, this is what you do. The 1st step: Flip in your thrusters and velocity up your ship with an acceleration so that you’ve synthetic gravity. Step two: Midway there, flip the spaceship round in order that it’s dealing with reverse the course of journey. Now activate the thrusters once more in order that the ship slows down—sure, that is nonetheless an acceleration and you’ll nonetheless have synthetic gravity.

Now for the issue with the Navoo—it is only a small drawback. Let me draw this ship as a large cylinder.

Check out these two individuals (labeled A and B). For particular person A, they’d expertise faux gravity when the ship is rising in velocity or reducing in velocity—that point when the thrusters are on. However for particular person B, they’d have “gravity” when the ship is rotating.

So, the place is the bridge—the place the place they management the spacecraft? The actual reply is that they in all probability ought to have two separate bridges. There could be a bridge for “thruster-mode” and a bridge for “spinning-mode.” Right here is the issue. Within the present, it seems like there is only one bridge. However actually—it is only a small element and it does not actually trouble me. I am simply pointing it out for enjoyable.

How lengthy wouldn’t it take to get the Navoo rotating?

Within the present, they present the Navoo rotating as much as spinning velocity. Here is all the information I can get from this a part of the episode (together with some dimensions of the Navoo).

It takes 30 seconds for the Navoo to rise up to spinning velocity. OK, I get it. This may not be the precise time, however within the episode it looks as if they present the entire spin up time. I am going with 30 seconds.The Navoo has a radius of zero.25 kilometers and a size of two km.On the finish of the spin up, they declare that they’re at “one ten g”. I assume that is 1/10th g, however these are belters. Belters have this accent that could be a lot like Eliza Doolittle earlier than she was reworked into My Honest Girl. If you do not get that joke, you need to critically watch that film—it is nice.

Let’s begin with the one ten g (I will begin speaking like a belter). If the people within the “drum” (the cylinder a part of the ship) have an obvious weight of zero.1 g (zero.98 m/s2), then I can calculate the ultimate angular velocity through the use of the radius of the drum.

With the values for the acceleration and radius, I get a rotation velocity of zero.063 radians per second or zero.6 rpm (so not very quick). However observe that the Navoo does not want an excellent quick rotation price since it’s so large. Only for enjoyable, listed below are the dimensions and rotation charges for another science fiction spaceships.

If you’d like get this spaceship rotating at zero.063 rad/s in 30 seconds, the angular acceleration could be zero.0021 radians/s2. Sure, that appears small—however bear in mind, this can be a large ship. How a lot vitality wouldn’t it take to get this factor rotating and what concerning the energy output? I’ll go away these as homework questions. You’ll have to estimate the mass and the second of inertia for the Navoo (or you would assume it is a hole cylinder).

However wait! There’s extra. We truly see the Navoo rising in rotational velocity within the present. I can use Tracker Video Evaluation to get the angular place of the aspect of the ship as a perform of time and from that discover the angular acceleration. Right here is the plot of angle vs. time.

Becoming a quadratic perform to this information, I get an angular acceleration of zero.00038 rad/s2. Sure, that is considerably smaller than the acceleration based mostly on the 30 second time interval from the present—I am truly stunned. I might have anticipated the angular acceleration from the visible of the rotating drum to be greater than calculated in order that you would truly see it rising in rotation velocity.

OK, how about one other homework query? With the angular acceleration from the video, how lengthy wouldn’t it take to rise up to a rotation price to provide zero.1 gs?

What concerning the particles within the heart of the drum?

There’s one other view of the rotating spacecraft from contained in the “drum.” The middle of the Navoo is mainly empty with all of the individuals on the within wall—however on this case there are a bunch of objects “floating” within the center after some incident (I will not say what occurred). Because the Navoo begins to rotate, you possibly can see this “floating” stuff do two issues. First, they seem to rotate due to the relative view from contained in the rotating spacecraft. That is legit and what ought to truly occur (I really like saying “truly occur” for science fiction stuff). Second, the inside particles begins “falling” in the direction of the outer partitions of the rotating drum. This half is fallacious.

Why would not the particles “fall” below the affect of the factitious gravity? It would not fall as a result of it is not rotating. The particles does not rotate across the axis of the ship as a result of nothing pushes it to get it spinning. The remainder of the stuff within the ship is linked to the flooring and partitions. There are rockets that enhance the rotational velocity of all the stuff linked to the ship, however that does not occur for the floating particles. No rotation means no synthetic gravity.

Oh, however finally this inside floating junk would fall. Because the ship rotates, it’s going to finally push the air within the heart to additionally spin. This spinning air will really feel like a wind and the wind would slowly push this particles into the wall-floor (unsure what to name the inside aspect of the drum). However nonetheless, it is a cool trying impact—even when not correct.

General, this can be a nice present—and it will get a lot of the science proper!

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