I’ve received a few enquiries in response to my post “Coriolis Effect In A Rotating Space Habitat”, concerning something I didn’t address at the time—what happens to the trajectory of objects moving parallel to the axis of rotation. (Though I did mention this topic in passing in my post about the Coriolis effect in general.) So that’s what I’m going to write about here. And after discussing that, I’ll talk a bit about the trajectory of rolling objects, which is another thing science fiction writers sometimes get wrong.
If you’ve arrived here directly, then you’re probably going to need to at least read the original Coriolis Effect In A Rotating Space Habitat post before returning here (there’s a link at the end of that post that will get you back); in fact, going all the way back to my Coriolis post could be useful, and you might even want to cast an eye over Saying “Centrifugal” Doesn’t Mean You’re A Bad Person. They’re all relevant to the topic of habitats that generate artificial gravity by rotating.
My previous post on this topic provided a lot of diagrams of the trajectories of objects moving in the plane of rotation of the habitat. That’s because there is no Coriolis pseudoforce acting on any velocity parallel to the rotation axis. To illustrate this, let’s go back to two diagrams from previous posts, which portray the trajectory of a dropped object.
First, we have the view of a stationary observer outside the habitat:
The dropped ball retains the rotation velocity it had at the moment it was released, and follows the red trajectory. The person who dropped the ball meanwhile continues to rotate with the station (I’ve marked four successive positions of ball and rotating observer.)
From the rotating observer’s point of view, the ball’s trajectory looks like this:
The rotating observer invokes two pseudoforces to explain this. One is centrifugal force, pulling the ball directly towards the floor; the other is Coriolis force, which (under anticlockwise rotation) deflects the ball to the right whenever it has any velocity in the plane of rotation.
Now, before going any father, lets name the different directions in our rotating habitat. We have spinward and antispinward, which are in the direction of rotation and against the direction of rotation, respectively. We have up and down, which are towards the axis and towards the floor of habitat, respectively. Centrifugal force is always directed down. Any movements in any combination of these directions (which lie in the plane of the screen in my diagrams) will be deflected by Coriolis force—rightward if the rotation is anticlockwise, leftward if the rotation is clockwise. The direction parallel to the axis of rotation (in or out of the screen in my diagrams) is axial, and movements in this direction experience no Coriolis deflection.
AXIAL MOTION
Now imagine that the observer in the diagrams above has not dropped the ball, but has instead fired it axially towards you—straight out of the plane of the screen, parallel to the rotation axis. There are no new forces invoked by this extra direction of movement—the ball will fall to the floor at the same rate, under centrifugal force, and will experience the same deflection in the plane of rotation, caused by Coriolis force. So with the ball coming directly towards you, its trajectory will look exactly the same as in the diagrams above. If you are rotating with the habitat, the ball will fall downward and antispinward as it moves towards you. If the ball is fired towards you very quickly, then it won’t have time to fall very far, or be deflected very far, and it will probably hit you, just a little below and antispinward of target. If it is fired very slowly, it will fall to the floor before it gets to you, landing some way antispinward of its launch point. At intermediate velocities, it will whisk by on your antispinward side before hitting the floor behind you.
And this is true of all the diagrams I produced for previous posts. In any of them, you can imagine that the object has some axial velocity, without that changing the trajectory you see projected on to the plane of rotation (which is the plane of the screen). If the object has a large axial velocity, it will travel a long way parallel to the axis before it completes the trajectory illustrated; if it has a low axial velocity, it will complete the evolution I’ve shown without travelling very far parallel to the axis.
For example, imagine that you and the observer are standing some distance apart, with purely axial separation. The observer wants to hit you in the head with a thrown ball. To do that, he needs to launch the ball with some axial velocity (so that it moves towards you), and an upward velocity (so that it doesn’t fall to the floor before it reaches you). Those components are familiar from throwing a ball in a real gravity field on Earth. But in a rotating environment, he also needs to throw the ball to antispinward, so that the Coriolis deflection will bring it around in a loop as it travels. From your point of view, as the ball comes sweeping towards your head, it will appear to follow one of a family of curves that look like this:

These are exactly the same curves that are required if the observer simply wants to toss the ball in the air and catch it. Except, this time, he has added an axial velocity that brings the ball into contact with your head just as it has completed its loop in the plane of rotation.
This is tricky. If he throws the ball with high axial velocity (so it reaches your head quickly) he needs to direct it only a little upward and antispinward—it will follow the short, interior loop as it comes towards you. If he throws the ball with low axial velocity, he needs to prolong its time in the loop, so he must throw it with a higher antispinward and upward velocity—the long, outer loop in the diagram.
We’re used to this, in the vertical direction—we throw balls fast and low or slow and high. But the inhabitants of rotating environments will need to adjust the antispinward component of their launch velocity, too, if their thrown ball is to arrive on target. And the antispinward and upward components will vary independently from habitat to habitat, according to how their sizes and rotation speeds differ. Games like cricket and baseball will (quite literally) take on a whole new dimension.*
Notice that Coriolis only appears if there is some velocity in the up/down or spinward/antispinward directions. That’s unavoidable with an object moving along a free trajectory (like a thrown ball) because all objects in a rotating reference frame will experience an apparent centrifugal force that accelerates them downward.
ROLLING MOTION
But what happens if you just roll an object along a horizontal surface? Science fiction writers occasionally invoke a sideways Coriolis deflection in this scenario, so that a rolling ball will follow a curved path across the floor, for instance. (I noticed Alastair Reynolds doing this in The Prefect, which I reread recently, but he’s only the first writer who springs to mind—there are many.) However, it doesn’t work that way.
If we roll a ball in the purely axial direction, then it will not be influenced by Coriolis forces at all, because it is not moving either up/down or spinward/antispinward. If we roll a ball antispinward, then the Coriolis force will act upward—the ball will become lighter, and may therefore experience less friction and roll farther, but it won’t experience sideways deflection. Likewise, a ball rolled to spinward will experience downward Coriolis, will become heavier, and may roll less far. But again, no sideways forces are generated. And that’s true of any combination of axial and spinward/antispinward velocities for an object rolling on a horizontal surface—its apparent weight may change, but its direction won’t.
That’s also true if we roll something down an inclined ramp facing in the spinward or antispinward direction. The up/down movement will generate a Coriolis force, but it will act to either lift the object away from the ramp (if moving antispinward) or press it against the ramp (if moving spinward)—again, no sideways component.
The only time sideways deflection of a rolling object occurs is if the object is rolling downhill in an axial direction, in which case it will experience the antispinward Coriolis force experienced by a dropped object. So general downhill rolling trajectories become complicated, with a combination of antispinward deflection and changing apparent weight continuously influencing how the rolling object and the ramp interact with each other.
Crown green bowls is played on a surface with a slight dome in the middle, and bowls that are biased in their weight distribution. Think how much extra fun that would be, in a rotating habitat.
* Bowlers and pitchers already use the aerodynamics of a spinning ball to shape laterally curved trajectories. What they might be able to do with Coriolis stirred into the mix defies imagination (at least, my imagination for the time being).
or

And some more in the plots from a 1921 article produced by the Royal Navy’s Hydrographic Department, which was later reproduces as “


Now, Stefansson’s “colony” was established in September 1921, but he kept his territorial aspirations a secret, at first. The fact that he claimed Wrangel for Britain was not revealed until March 1922, in an article in the New York Times













You’ll see it gives sunrise and sunset times to one-second precision, which is entirely spurious—the refractive state of the atmosphere is so variable that there’s no real point in quoting these times to anything beyond the nearest minute. I just couldn’t bring myself to hide the extra column of figures.
Between the solstices, the latitude at which the sun is overhead varies continuously from 23.5ºN (in June) to 23.5ºS (in December), and then back again:











The higher the index of refraction, the closer the light comes to bouncing straight back where it came from—retroreflection.
In practice, retroreflective beads generally have a reflective coating at the back, which allows the reflected light to be coloured and scattered over a reasonably wide viewing angle, and also allows the use of cheaper glass with a lower refractive index. In this form, they’re used to coat the surface of road signs and those reflective safety garments that appear to “light up” in the headlights of your car.



































When I was a solitary, bespectacled and distinctly
If I turn and kick outwards, the same shift and rotation occurs, and my foot swings rightwards relative to my body again.
Face in the direction of spin, or against the direction of spin—it’s always the same rotation and shift.
In fact, it doesn’t matter where I stand on the roundabout, or which direction I kick in—the same rotation and shift is always there, so the kick always deviates in the same direction, and by the same amount.
As it turns out, the magnitude of the Coriolis acceleration depends on only two things—it increases the faster your reference frame rotates, and it increases as you move faster relative to the rotating frame. And the direction depends on only one thing—it is always at right angles to the direction of movement, and it pushes rightwards in anticlockwise-rotating systems, and leftwards in clockwise-rotating systems. (And, of course, if you lay underneath my anticlockwise roundabout and looked up at it from below, it would be rotating clockwise to you, and all the deviations in my diagrams would be leftwards.)






If you cut the corners off that triangular prism, you have a hexagonal prism, which is the shape of the ice crystals that cause sun dogs.
Light goes in at one face, is deflected by refraction, and leaves by another face, being deflected again. There are various ways of describing the light path through prisms of various shapes, but I’m only going to talk about this one, in which the light enters one face of the hexagonal prism and leaves through what’s called an “alternate” face—the next face but one. Let’s call this route through the crystal the parhelion path, for ease of reference. And I’ll call the two relevant faces the entry face and the exit face.

It turns out that means the flat crystals must be between about 0.025mm and 0.25mm across—smaller, and they never get themselves orientated in the turbulent air; larger, and they tend to rotate end-over-end around a diagonal axis, rather than falling flat.









