SciFi: The unexpected problems with gravity

Artificial gravity in science fiction falls into three categories:

  1. Applied Phlebotinum works via made-up technobabble. Examples include the gravity plating in Star Trek.
  2. Spin gravity is where inertia wants you to keep going in a straight line, but centripetal force from your outer hull keeps pulling (or pushing) you towards your axis of rotation, creating what feels like centrifugal force. Examples include the titular space station in Babylon 5, and in real life fairground rides and your car doing a sharp turn at speed.
  3. Acceleration gravity is similar to spin gravity, in that what you're feeling is the reaction of your hull against the inertia of your body, but is based on your engine constantly accelerating you. Examples include many of the ships in The Expanse, and in real life rocket launches and drag racing.

If you want to write hard science fiction, you will ignore Applied Phlebotinum. Spin gravity may be fine, but will probably have a noticeable Coriolis force in practically sized ships and stations; notably, in the film 2001: A Space Oddesy, the spin-gravity habitation ring of the Discovery One was so small you could expect people to get dizzy from the Coriolis force messing with your sense of balance if you turn around, bend over, or other everyday motions (Arthur C. Clark was reportedly well aware of this, and overruled in the name of cinematography). This can be challenging to get right, but you may want to do it anyway.

If you don't want to use spin or space magic, you only have acceleration gravity: In principle, there are plenty of atomic rocket designs could get you Earth standard gravity for most interplanetary trips out to about Jupiter, and some of the fancier fusion designs (let alone antimatter) could give you 1 gee to all the rest. Unfortunately, speed is a serious problem.

Consider Mars. Launch from Earth always requires you experience more than Earth gravity (the natural gravity adds to that of the acceleration), so let's approximate this trip as 1 gee of linear acceleration rather than 1 gee subjective experience.

The distance from Earth to Mars varies from 4 light minutes to 20 light minutes. The turn-around point is half that, take the high end and you get 10 light minutes. The time taken to get there is given by s = 1/2 at^2, i.e. 10 light minutes = 1/2 (9.8 m/s^2) t^2 ⇒ sqrt((20 light minutes)/(9.8 m/s^2)) = t = 191600 seconds (about 2 days 5 hours), peak speed is v = at = (9.8 m/s)(191600 s) = 1.88e6 m/s.

Nuclear fusion starts getting noticeable when the ions have an average speed of about 2e6 m/s, and the speed of the solar wind is enough to make up the difference on sunward flights.

The other problem is the density of the solar wind — space, despite being very empty, is not completely empty. While it varies depending on solar activity, location, and nearby magnetic fields, the interplanetary medium near Earth is around 5 particles per cm^3, which is 5e6 per m^3; at a peak speed of 1.88e6 m/s, every square meter of the hull's cross section to motion will be hit by (5e6 particles per m^3)(1.88e6 m/s) = 9.4e12 particles per square meter second. If they are all hydrogen atoms, the kinetic energy per second of this is 27.8 millijoules (does anyone say 'kinetic power'? They should. The kinetic power is 27.8 milliwatts). This does not sound like much, but there is no difference at all between hitting a proton at this speed and sitting next to something radioactive emitting protons at that speed, so this 27.8 mW is in the form of somewhat penetrating radiation — at best the front of your ship will absorb it, filling internal voids with hydrogen gas and eventually flaking off (a process like this is already used industrially to produce very thin sheets of expensive materials such as computer-grade silicon); at worst, a small fraction of this will undergo spontaneous nuclear fusion with your hull, producing much harder radiation. The only good news here is that fusion is difficult precisely because this is a low-probability event, and the fusion power flux will be less than the directly absorbed power flux from the IPM.

If your ship is flying out to 90377 Sedna, you have slightly worse problems; the interplanetary medium gets significantly thinner (inverse-square law), but particles/second is proportional to speed (which is proportional to time when acceleration is constant), and kinetic energy per particle is the square of the speed, so under constant acceleration, the IPM power flux is (roughly!) proportional to your total distance from the sun. As it's mostly in the form of a plasma, your ship design could use a magnetic field to deflect most of it; you might expect the downside of this to be that the magnetic field will massively increase your ship's drag, and indeed it will, but you're starting from such a low threshold that even a massive increase is negligible — solar sails, even M2P2 magnetic sails, have very small total forces despite trying to explicitly maximise this very effect.

And all that's ignoring the effect of hitting a 1 milligram fleck of dust at 1.88e6 m/s — the kinetic energy of which is roughly equal to 420 grams of TNT.

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Original post timestamp: Sat, 17 Jul 2021 12:04:34 +0000

Tags: fusion, space, spaceships, writing

Categories: Fiction, mathematics, Science, SciFi, Technology

© Ben Wheatley — Licence: Attribution-NonCommercial-NoDerivs 4.0 International