## Ringworld 40th Anniversary: Learning Physics with Ringworld

Less than a year after the first time I read Ringworld, I was studying it, as a part of a between-semester mini-course on science fiction and philosophy (a very interesting course, by the way). Since then I’ve used Ringworld as an object of study many times, but I have been teaching (and learning) physics instead. Here’s why:

Science fiction is often used as a playground for idealized physics. A science fiction story can take place naturally in an environment where there’s no friction or air resistance, which gives readers who have lived all their lives with those forces the chance to develop intuitions about the laws of physics which exist without them. Heinlein provides one excellent example in the The Rolling Stones when Castor and Pollux are instructed to start their freight on its return to their ship with one gentle heave on the cable holding the freight—because the constant pulling that is required on Earth to continually overcome friction/air resistance would result in a disaster if attempted in space. Ringworld, however, is better than that—by postulating one perfect element (the incredibly strong material that makes up the Ringworld floor (called “scrith” in the sequels to Ringworld)) Niven has created an object that anyone armed with basic physics can analyze surprisingly deeply, for fun and edification.

Here are some examples:

1. Starting with the most famous—“The Ringworld is Unstable!” It’s easy to show that if the Ring ever gets off-center from the sun, the sun will pull more on the close side than on the far side, and the Ring will get even more off-center, resulting in an ever-increasing race to collision. With a computer, it’s possible to figure out exactly how fast this process will go and it turns out that the amount of off-centerness will double in about 57 days, up to the point when the off-centerness reaches about 30 million miles or so; after that the Ring will accelerate even faster toward the Sun. Even if the Ring is off-center by as little as an inch to start with, in a little over six years, it will have collided with the Sun.

2. Ringworld Seasons—if the Ring is placed so the plane of the Ring is above or below the Sun, the Ring will oscillate much like a pendulum bob oscillates, resulting in seasons, as the distance from the Sun and the angle of the Sun’s light as it strikes the Ringworld changes. These seasons will differ from seasons on Earth in several ways.

• On Earth, seasons result primarily from changes in the angle of the Sun’s light relative to the Earth’s surface (which affects how much energy reaches the Earth’s surface), while on the Ringworld, seasons result both from changes in the angle of the Sun’s light and on the distance to the Sun. When the plane of the Ring is centered on the Sun, the Sun will be directly overhead at every point on the Ring, and the Sun will be 93 million miles away from every point on the Ring; when the plane of the Ring is above or below the Sun, the Sun will be more than 93 million miles from every point on the Ring, and the sun’s light will impinge on the Ringworld surface at an angle (see the illustration at The Oscillating Ringworld).
• On Earth, seasons are not worldwide. While the northern hemisphere experiences summer, the southern hemisphere experiences winter, every point on the Ring will experience winter or summer at the same time.
• Finally, on Earth, the seasons occur once during the revolution of the Earth around the Sun. On Ringworld, the Ring has summers and winters twice during an oscillation above and below the Sun—there is a summer every time the Ring is at its closest point to the Sun, and a winter every time the Ring is furthest from the Sun.

The severity of the seasons on Ringworld depends on the maximum deflection of the Ring from the plane of rotation, but the period will be about 375 days unless the maximum deflection is very large (the fact that the Ring’s sun has about the same mass as Earth’s Sun, and that the Ring’s radius is about the same as that of the Earth’s orbit, makes the natural oscillation of the Ring very close to Earth’s year).

3. The Ring isn’t flat—though the Ringworld floor material may resist deformation, the Sun’s tides still affect the material (dirt, water, etc.) on top of the Ringworld floor, pulling all material towards the centerline of the Ring, and it’s possible to calculate how high the clump in the middle will be (about 1300 meters), and what the maximum slope of the loose material would be (at the edges of the Ring, it would be about two-thirds of an arc-second). Now think about how the tidal effects of the Sun would change if the Ringworld was set to oscillating to create seasons as discussed above—the Great Oceans would slosh over the length of a year, and rivers might change their direction with the seasons as well. All those effects would act as friction and eventually damp out the Ring’s oscillations—but it would be an interesting place to live until the Ring settled down.

4. The soil, water and people are held on the inner surface of the Ring by the pseudo-gravity caused by the Ring’s rotation; space stations and amusement park rides are small enough that the deviation between normal planetary gravity and the pseudo-gravity caused by rotation is pretty obvious, but the Ringworld is huge—and a student could have a good time calculating how advanced Ringworld natives’ gunnery or rocketry would have to be before Ringworld’s pseudogravity would start to measurably differ from Earth’s gravity.

There’s plenty more fun to be had—it’s possible to calculate how the Ring would vibrate if struck very hard, as Peter Taylor shows at Ringworld Modal Analysis Results, or to make some calculations about how well the Ringworld holds onto its atmosphere (it’s got walls a thousand miles high and a gravity gradient much different than Earth’s, making determining the answer a challenge). Other interesting questions like how well Ringworld can recycle its materials are less amenable to calculation from first principles, but just as worthwhile to think about. Here and there you may find errors in Niven’s calculations or design, but I won’t tell you where to look. I hope this sampler provides a good starting point for any explorations of the wonders of the Ringworld and how they illuminate aspects of the real universe that you care to make (for more, see Teaching Physics And More With Niven).

Andy Love is an electrical engineer and science fiction fan with an
interest in using science fiction for education; in 2001, he won the
Analog-sponsored “Webs of Wonder” for his website on that topic, and he frequently uses Niven stories in his examples of the “Science in Science Fiction” in presentations to a variety of audiences. Some of Andy’s writing about the Ringworld and about the science in science fiction can be found online at these links along with a downloadable document here.

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