Known Space: The Future Worlds of Larry Niven

The following is a "slides and notes" version of a talk, written by Andrew E. Love Jr, a long-standing subscriber, and frequent contributor, to the Larry Niven mail list, and presented by him as part of the 2007 Balticon science program. Since all graphics are full size, this page may take some time to load.

Note from Andy: First, I'd like to thank Larry Niven for writing stories that reward careful attention (and support fun math) - it was a special treat for me to present this talk with Larry in attendance. Second, I'd like to thank Mark Firestone for converting the Powerpoint to html. This talk is all about using Niven stories to spark interest in (and provide examples of) physics - so if you're a teacher who'd like to use my examples, you may (but please give me credit). If you find an error please let me know. If you like this talk, you may be interested in my own page, which contains study guides and other information about using science fiction in education - it's URL is (somewhat unimaginatively): http://communities.msn.com/AndysUsingScienceFictionForEducationPage/homepage. I use some of the same examples (mostly from the works of Larry Niven) that I use in this talk below, but in a somewhat different fashion. If you're interested in the use of SF in the classroom you should also check out http://aboutsf.com/, and particularly, the study guide archive http://www.aboutsf.com/lessons/contents.php and the Speculation Speakers database.

Good evening. My name is Andrew Love. In my work at Johns Hopkins University’s Applied Physics Laboratory I give presentations on a variety of technical topics, but since 2000 I’ve given talks about science every year at Balticon. I’ve also participated in a lot of panel discussions about the use of science fiction to teach and inspire. This time, I’m combining the two ideas, talking about the science in a few of our guest of honor’s stories and how that science can be used as a jumping off point for learning and teaching about science in general. In the process of creating this talk I’ve had the fun of “doing the math” and uncovering some issues I’ve never heard anyone else mention before – so I hope you enjoy hearing the talk as much as I enjoyed writing it.

One more thing – it’s important to recognize that it doesn’t take a doctorate in physics to understand most of this material – I only have a master’s degree myself, after all, and all the concepts I’ll be discussing require only high school physics to understand and only slightly more advanced mathematics to actually do the calculations. Feel free to jump in with questions whenever I’ve been unclear.

It can be difficult for children to understand some basic physics concepts because life on earth is full of friction and gravity, but by using an SF story as a frame, students can develop a useful intuition about Newton’s laws, etc. in the friction-free, gravity-free environment (example: the scene in Heinlein’s Rolling Stones when the twins are pulling a load of freight with a rope (while in space)) and can also learn about scientific methods – like the method that the characters in Heinlein’s “Lifeline” come up with for testing Pinero’s lifespan-measuring device.

I’m reminded of how Richard Feynman was educated about science by his father – with made-up stories about the things they saw around their neighborhood, and careful observations about what they saw. You can read more in Feynman’s book What Do You Care About What Other People Think?, but don’t pick it up if you have a deadline coming up soon – because it’s hard to put down. In addition to being a good playground for simplified physics, a good story illustrating an interesting concept can inspire thinking that grows deeper and more illuminating with every new fact you learn – as you will see.

I should note that I’m not overly interested in finding errors in the stories I talk about – if it’s necessary to remark on an error to make my point, I will, but I’m more interested in the way that stories covey scientific principles, which is generally fairly insensitive to numerical errors.

Originally, I was going to use a lot of different examples from different authors throughout the talk, but there is so much to discuss in Ringworld that I’ve focused almost entirely on it, and uncovered a few facets that I’ve not seen discussed before. If there’s time I’ll mention a few other books and/or stories before listing some resources for learning and teaching via SF, and as always, I’ll close with a final thought.

I’m sure all of you are familiar with Niven’s Ringworld, which he described as halfway between a normal planet and a Dyson sphere (Freeman Dyson, the mathematician who established that Feynman’s and Schwinger’s approaches to quantum electrodynamics were equivalent, suggested in 1959 that a technological species would eventually need all its sun’s energy, and that it could get that energy by surrounding the sun with an immense number of planetoids, so that all the light from the sun was captured, but nowadays, people usually use the term to mean a solid sphere surrounding the sun). Ringworld is a less audacious concept than a Dyson sphere but it’s still so immense a construct that most minds boggle even after quite a lengthy exposure to the idea. Basically, Ringworld is a huge ribbon circling a star; the inside of the ribbon is habitable. An example of the scale of the Ringworld is this: on Ringworld, there is an ocean large enough that a full scale map of earth is a tiny archipelago separated from other such island groups by an ocean voyage of up to a half million miles, or twice the distance from the earth to the moon.

So what’s it like on Ringworld? It’s a big place - the surface area is about 3 million times the Earth’s. Shadow squares (see diagram) provide a day-night cycle of 30 hours, but when the sun is not shadowed, it’s always directly overhead - it never rises or sets. Unlike in a Dyson sphere you can see the stars, but the biggest feature of the sky is the Arch, the other side of the Ring from where you are. Somehow (spoiler-warning!), the Ringworld became inhabited by primates half a million years ago or so and now there are dozens of species of human-like but non-human creatures filling the Ring, some intelligent, some not.

In several places in the book, the tangential velocity is given as 770 miles/sec, but 740-760 miles/second fits the given period of rotation and the given surface gravity better than 770 does. However, this difference doesn’t affect much really, except in trivia contests I suppose.

It’s widely understood that pseudogravity can be produced by rotation, but it’s educational to use Ringworld as a way to demonstrate why. If a person holding an object a distance h above the surface of the Earth and drops it, it hits the ground after this amount of time – the square root of 2 times the height divided by g (so it takes about 1 second for an object to fall 16 feet). On the Ring, when the object is dropped, the motion is determined by the following equations – the object doesn’t move at all in the y direction, while the object retains its motion in the x direction. The square of the total distance from the center is the sum of squares of the x and y values – and what we care about is the moment when the square of the distance equals R squared. Solving for t gives the square root of 2 times (R*h), so the equivalent acceleration of gravity on Ringworld is v squared over R. Similar calculations comparing how high an object gets when you throw it upward with a given velocity give the same answer for equivalent gravity. Note that we’ve approximated the answer – so as h becomes a significant fraction of R, Ringworld gravity stops being so similar to Earth’s. For example…

One way the approximation fails is a bias to the antispinward – if an object is launched straight up at 8 miles a second, it will land about 100 miles antispinward, and if the object is launched aimed slightly spinward, it will reach about 36 miles higher than if launched antispinward. This is also a demonstration of the difficulty in taking off from Ringworld. At 8 miles/second a rocket would leave earth easily, but on Ringworld at the same velocity a projectile crashes. We’ll explore the comparison between Earth and the Ring in more detail in the next few slides.

I got a little carried away with calculating the differences between a planet’s gravity and the pseudo-gravity on Ringworld. Here’s a plot of the time a rocket would spend in flight if launched straight up with various initial speeds - not too much different with low speeds.

But quite different at only slightly higher speeds. As the launch velocity approaches 7 miles per second, escape velocity is reached for Earth – an infinite time of flight.

The same goes with maximum height achieved by the rocket. Not much difference at first…

But a lot different as the launch speed increases… One interesting not-obvious implications of the Ringworld’s layout are the lack of natural resources. Resources are lacking because Ringworld just isn’t that thick and was not formed by geological processes - there are no oil wells to tap or veins of metal to mine. If civilization falls, it will be tricky to revive. This is a chance for students to think about hydrological and other cycles – how are the lifecycles of lakes, rivers and ecosystems different on Ringworld than on Earth?

Another non-obvious implication is that it’s very difficult to leave or return to the Ring – on Earth, launching at escape velocity in any direction that doesn’t intersect the Earth results in escape from Earth – but on the Ring, it’s necessary to achieving the equivalent escape velocity is not sufficient, and worse, landing on the Ring safely is very difficult indeed; to avoid a disastrous collision it is necessary to match the surface velocity of 770 miles per second. In the novel, the heroes crashland but this is not recommended for anyone without an impervious stasis field wrapped around an invulnerable spacecraft.

Note that an object in orbit around the Sun while near Ringworld would be moving at a very different speed than the Ring; that’s because…

The Ringworld is not in orbit.

Orbital speed, v, for a circular orbit at any given radius, R, is the square root of GM/R where G is the universal gravitational constant (6.67300 × 10^(-11) m^3 kg^(-1) s^(-2)) and M is the mass of the Sun. For the Ring this velocity is about 18 miles per second; since the velocity of the ring is about 40 times that, the Ring is in tension (meaning that absent the structural strength of the Ring, each part of it would pull away from the rest of it (and away from the Sun)). If the velocity of the Ring is less than orbital velocity, then the Ring is in compression, meaning that absent the structural strength of the Ring, each part of it would be pressed further together (and further into the Sun of course). If the velocity of the Ring is exactly orbital speed, then each portion of the Ring , under neither compression nor tension – even if the Ring was made of wood or butter, it would retain its shape, with respect to the forces due to the Sun and its rotation anyway (or would it – see later slides).

Exercise for the student of materials - how strong must the Ringworld’s material be?

Students are often confused about the cause of seasons on the Earth, assuming that the cause is changes in the distance to the Sun, not changes to the length of the day and the angle of incidence of the Sun’s light. The Ringworld provides a way to explore causes of seasons.

At first it seems as if Ringworld wouldn’t have seasons. After all, on Ringworld, the length of day is constant. While this could be changed by adjusting the distance between the shadow squares (note that the shadow squares aren’t in orbit around the sun either - they’re connected by improbably strong wires and are spinning faster than necessary to stay in orbit), it’s hard to imagine getting a useful amount of day length change over a long period and the mechanism to do so would be pretty complicated. Changing the distance to the sun is also possible (but see what happens two slides further), but since the Ringworld rotates with a period of 8 days or so, seasons would be very short. And it would seem that the angle of incidence of the Sun’s light would have to be constant – but that turns out not to be the case.

Here’s how to introduce seasons to the Ring in a natural way. If we move the Ringworld so that the Sun is no longer in the plane of the Ringworld, gravity will act as a restoring force. With no friction, oscillation occurs and goes on indefinitely, changing the angle of incidence of light on the Ring - Seasons! The equations for the period of the oscillation aren’t very complicated. There is a gravitational force on the Ring and an equal and opposite force on the sun. The Ring mass is about 1/1000th of the Sun, so the Sun’s oscillation is a thousand times smaller than the oscillation of the Ring. The period turns out to be about 377 days, giving a reasonable length to the seasons (this analysis relies on a small angle approximation, but would be reasonably accurate for angles up to 10 or so degrees). Note that the period of 377 days is just the same as the period for a planet moving in the Ringworld’s orbit. There are only so many ways to combine the gravitational constant, the mass of the sun and the mass of an object to get an answer in units of time, so it’s not surprising that the same answer turns up in a few different places. By the way, the mass of the Ringworld is actually significant even compared to the huge mass of the sun, so for the calculation of the oscillation’s period I need to include both masses, instead of neglecting the smaller mass, which can be done in most planetary orbit calculations.

An oscillation of 10 degrees gives significant seasonal effects, for two reasons – insolation would vary by 1.5% due to the angle (the same effect that causes seasons on Earth), and 3% due to the changing distance from the sun (the effect that students assume causes seasons on Earth), adding up to a variation of about 5%, which is comparable to the change in insolation over a year due to earth’s orientation ( another exercise for the student!). Note that there are two winters and two summers in each cycle - an “up winter,” a “down winter,” an “up-going summer” and a “down going summer”.

Unfortunately, there are a couple of serious problems with this idea – as I will show you.

Now for the first bad news. Although moving the Ring so the sun is out of plane leads to a nice gravitational restoring force, moving the Ring so the sun is off center doesn’t. This can be demonstrated without calculating the whole force on the Ring, just by calculating the forces due to gravity from small arcs of the Ring. On the near side, the arc contains a mass proportional to (R-x) and the effect of this mass is divided by a distance of (R-x) squared. On the far side, the opposite arc has mass proportional to R+x and the effect is divided by (R+x) squared. These two effects don’t balance - any slight offcentering will get worse and worse. Note that a Dyson sphere is much better off. The mass contained in an arc at distance (R-x) is proportional to (R-x) squared, so when this is divided by (R-x) squared to get a force that exactly balances the force due to the opposite arc. The sun can be placed anywhere inside the sphere and will feel no force toward any particular part of the sphere. In Ringworld Engineers Larry Niven revealed that the Ringworld has attitude jets along its edge which convert solar wind into thrust, making the Ringworld stable by providing a restoring force that increases properly as the off-centering gets bigger. The only problem is that someone has stolen most of the jets.

By the way, Pournelle and Sheffield's "Higher Education," which I enjoyed quite a bit and noticed a cute touch (spoiler space below) - one of the questions that the space-faring students have to answer is this:

A solid ring made of strong material is attached by strings (like spokes) to a rotating massive object (and therefore is rotating at the same rate as the massive object). When all the strings are simultaneously cut, what happens to the ring. The answer is, of course, that the ring will shortly collide with the object in the middle – for the same reason that Ringworld is unstable. I wonder if this is a deliberate reference to Ringworld.

This is, by the way, the way that James Clerk Maxwell determined that Saturn’s Rings could not be solid – since a solid ring would be unstable.

Let’s talk a little more about stability, since I mentioned it.

A system is in equilibrium when there is zero net force (all the forces balance), but to be stable more is required – when a stable system is disturbed slightly, it tends to return to the equilibrium, while an unstable system does not. For example, a pencil balanced on its point is in equilibrium, but is not stable. A ball in a bowl is in equilibrium and stable.

This chart shows different kinds of stability. The lines are potential energy functions. The oscillating Ringworld is as stable in the vertical direction as a ball in a bowl is. Any perturbation simply causes an oscillation or changes the magnitude of the oscillation – and if there’s any friction in the system, the effect of the perturbation eventually dissipates leaving the Ring centered.

In the horizontal direction though, the Ringworld is completely unstable – the slightest perturbation causes a complete disaster as the Ring tends to get more and more off center.

The Dyson sphere is neutrally stable. Any perturbation just moves the Sphere slightly but gives it no tendency to move further along or to return to the original position – like a ball on a table.

Finally, attitude jets would make the Ringworld is meta-stable - it will recover from small perturbations, but be vulnerable to a large perturbation. Most systems in the real world are metastable; they will stay put, if they’re not pushed too far - just like most people.

It’s worth noting that if the impact of light on the shadow squares causes a greater outward force than gravity produces an inward one, then the shadow squares are stable horizontally but unstable vertically. Because the dominant force is outward, not inward, all the signs reverse making stable situations for the Ringworld into unstable ones for the shadow squares and vice versa.

Because a system can be stable with respect to disturbances in one direction, but not in another, it’s useful to show the potential energy as a surface, not a curve. This chart shows the classic “saddle-shaped” equilibrium, stable in one direction but not another, just like the Ringworld. In addition to the Ring, this chart describes inertial navigation systems – a slight initial horizontal velocity error will cause 84-minute oscillations, requiring slight damping to control, while a slight vertical velocity error will grow without limit unless heavily damped. 84-minutes, by the way, is the natural period of an earth-radius pendulum, the natural period of horizontal velocity errors in an inertial navigation system, the period of a ground level Earth satellite, and the period of motion for an object in a tunnel from New York to London, New York to Beijing or New York to Chicago – it’s also a dessert topping and a floor wax.

Here’s the real Ringworld potential function, calculated by integrating the total force on the Ring - note the rapid drop off. That’s why even with attitude jets, the Ring is probably only metastable - a big perturbation might overwhelm the jets’ ability to restore the Ringworld to its proper place.

One particularly neat thing about the Ringworld is that it’s a great way to introduce the concepts of angular momentum, moments of inertia and the like. Force, mass, acceleration, momentum, velocity, and kinetic energy each have analogous terms in rotational mechanics – torque, moment of inertia, angular acceleration, angular momentum, angular velocity and angular kinetic energy. You can solve problems using either set of terms, but usually, for any particular problem it’s much easier to do the work in one set of terms than in the other. Ringworld, however, is different – it’s nearly as easy to calculate the kinetic energy of the Ring (due to its rotation) as the mass of the Ring times 770 (miles/second)2, or to calculate the moment of inertia of the Ring around Axis 1, and calculate the kinetic energy as the moment of inertia times the angular rate of rotation squared.

The moment of inertia for Ringworld is approximately 4.5x1049 kg*meters*meters, and the kinetic energy associated with the rotation of RW is therefore 1.5 *1039 kg*(meters/second)2. This amount of K.E. is equivalent to a rest mass of a quarter of the moon. For comparison, one gallon of gasoline masses about 3 kg, and thus has a rest energy of 2.5*1017 kg*(meters/second)2 which is enough energy to accelerate a 1000-kg automobile to more than 5% of the speed of light, so imagine the energy in one-quarter of 7.35 ×1022 kg

By the way, this talk of angular dynamics raises the issue of another kind of stability – the stability of a rotating object with respect to small perturbations in the spin axis. It turns out that because the Ring is rotating around axis 1, it is stable with respect to perturbations of that axis – if you tried to spin the Ring around one of the other axes, it would wobble and eventually end up rotating around axis 1 (and I wouldn’t want to be living on it during the transition!)

The overall shape of the Earth depends on the interplay between gravity and centrifugal force – the top figure shows a rotating spherical Earth. If you calculate the force along the tangent line at any point, you’ll find a net force towards the equator – so a loose object placed there will move towards the equator. In the long term, every object on Earth is loose – stone is just not strong enough to resist the continual force reshaping it. In the steady state the shape of the earth distorts just enough to eliminate the force along the tangent to the surface at every point; the normal force will vary from point to point, with a maximum at the pole and a minimum at the equator, but because the tangential force is everywhere zero, there is no further tendency for the shape of the planet to change.

The International Astronomical Union’s definition of a planet (the same definition that excludes Pluto) includes hydrostatic equilibrium as part of the definition of a planet. If an object is not massive enough for its gravity and rotation to reshape it (overwhelming the strength of its materials), it’s not a planet.

The same effect will reshape the Ring – even though the gravity of the Sun at the surface of the Ring is quite small, the force toward the center of the Ring will tend to create a “hump” of soil and water. When I first realized that Ringworld would have this kind of curvature I thought I had found a way to navigate on the Ring – because an instrument like a sextant could be used to measure the local slope (by observing where the Arch was with respect to the stars) wherever you were on the Ring, telling you where you were. I also was concerned that this curvature would ruin the scene where one character can see both rim walls at once. However, when I did the calculations, the maximum slope turned out to be very small indeed (making use of a sextant problematical), and the rise in the middle was only 1.3 km, which would not interfere with seeing the 1000-mile-high Rim walls. However, this solar tide effect does affect the idea of “bobbing” the Ring for seasons. Here’s why.

P.S. Note that I didn’t calculate the effect of the gravity of the Ringworld floor material, or of the soil, rock, water, etc. on the Ring. It’s easy to see that the effect of each of these would be to increase the size of the hump, though.

Ringworld might at first seem like an ideal frictionless oscillator – it’s in a vacuum after all, and it’s made out of material that doesn’t distort (except under very extreme circumstances). However, the material on the Ring is not so ideal, so the solar tides that lead to the “hump” in the middle would result in forces that would tend to move the material on the Ring over the course of the seasonal oscillation, leading to friction, and dramatic effects like rivers that flow in different directions depending on the time of year.

The friction would tend to damp out the oscillation of the Ring, so Ringworld seasons would not be automatic – there would have to be a driving force continually adding energy to the oscillation to keep it going, and you’d have to be willing to tolerate the other strange effects, like oscillating rivers.

Earlier, I mentioned the gravity of the Ring itself. The complete calculation requires some calculus, but there’s an easier calculation to get an upper bound – the gravity due to an infinite plate is given by this formula, which for the Ring would give this result (note that for an infinite plate, the gravitational effect is the same regardless of how far from the plate you are). This is a pretty small gravity for an object that weighs as much as Jupiter, but while Jupiter’s volume is about 1.4*1015 km3, the ring is spread out over a volume 10 billion times larger.

The actual answer is pretty close to the estimate – but there are some interesting features to the answer. The picture shows two functions, the force towards or away from the Ring, in blue (evaluated along a line from the sun through the center of the Ring), and the force along the Ring (towards the centerline of the Ring), in red (evaluated at the edge of the Ring – half a million miles from the center). As expected, the force along the Ring is always toward the center of the Ring, and is pretty small unless you look very close to where the Ring is. The force towards or away from the Ring is usually towards the Ring, but near the Ring itself, there is so much mass nearby and “above” the surface that there is a small net force away from the Ring (the zero crossing is about 5000 km above the Ring). Note that the force towards the center due to the Ring gravity is about 10 times greater than that due to solar tides – so it looks like the mass on the inside of the Ring is curved a bit more than I calculated before – with a peak of 13 km, not 1.3 km, which doesn’t really affect our previous conclusions, except to make use of a sextant for navigation on the Ring slightly more possible). To be really complete, I should take into account the non-linear effect – as the material on the Ring gets clumped in the middle, there’s a tendency to get more clumped, but that’s for another day.

It’s worth noting that the drop-off of the gravitational force from an infinite cylinder is 1/r, instead of the one over r-squared of a point particle (or a spherically symmetric object). If I extended this figure, the changeover from a 1/r dropoff of gravity near the Ring to a one over r-squared dropoff further away; near the Ring, the fact that the Ring is not infinite in width doesn't matter so much, while far from the Ring, the fact that the Ring is not a simple point particle doesn't matter at all.

It’s always possible to take the analysis further – Peter Taylor, a rocket scientist from Texas, analyzed the vibrational modes of the Ringworld. One of the modes is shown here – the ellipses show how each point on the Ring would move if this mode of the Ring were excited. Peter’s website explains his calculation and shows several other modes. If you’re intending to move the Ring, or hit it hard, some thought about the vibrational modes is warranted definitely warranted.

I’m just going to touch on a few other topics of interest as time permits – as I mentioned before, I had intended to cover a few other authors, but it turned out that there were enough examples in Niven’s work to fill an hour and more, easily.

Here’s another big object: The Smoke Ring. It is a torus of gas circling an old neutron star, created from the atmosphere of the planet within the Ring. Its radius is about 26,000 kilometers and it gets light from the star that both it and the neutron star circle. It holds life. By the way, there is a gas torus around Saturn which one of Saturn’s satellites (Titan) orbits within (see Niven’s N-Space for details on how he was inspired to create the Smoke Ring).

Being so close to the high gravity of the neutron star, things in the Smoke Ring orbit the star pretty quickly. Niven gives a minimum period of 2 hours for an object in the Ring, while I calculated a typical period of a little less than 2 minutes. I suspect that this is rare error on the author’s part – to get a period of 2 hours with the given radius of the Ring, the mass of Voy would have to be about a 10,000th of the mass of the Sun, which is pretty unlikely. The mass of Voy is implied to be 0.5 solar masses which is about 10³³ grams.

The first time I gave this talk a student asked how a planet could have survived the supernova that created Voy - it’s in the book that the planet came later and also that Voy is old enough that it is not rotating anymore and therefore not sweeping a radiation beam through the Smoke Ring periodically. Good question, though.

One of the life forms common in the Ring is the Integral tree. It’s pretty big - people actually live on it. Now when people are simply in the Smoke Ring they’re in free fall, but what if they live on a tree? It turns out that tides give an equivalent to gravity.

The gravity of the neutron star is so great that the ends of the tree should be in significantly different orbits, but instead they’re constrained to orbit together. Therefore anything attached to the upper end of the tree is moving too fast for its orbit and thus feels an acceleration outward. Meanwhile, anything attached to the lower end is moving too slowly for its orbit and is accelerated inward towards Voy. The middle of the tree remains in free fall (otherwise the whole tree would accelerate into Voy or out of the Ring) - it’s in the right orbit after all. Another way to think about it is that the whole tree is being swung around Voy, which should result in a centrifugal force outward on any object on the tree, but the gravitational force of Voy cancels out the centrifugal force exactly at the center of the tree, too much on the inner tuft and not enough at the outer tuft.

The equation for the acceleration experienced by something attached to the tree is remarkably simple - it’s just 3 times square of the rotation rate of the tree around Voy times the distance of the object from the center of the tree. In other words, it’s just the force that would be felt if Voy didn’t exist, and the tree were being rotated around its center at the rate omega, plus the differential force due to change in Voy’s gravity over the length of the tree (Thanks to Peter Taylor for pointing out a factor-of-3 error in an earlier version of this talk).

Unfortunately while the book reports a maximum force of about 1/5 g at the ends of a tree, I get a force of almost 30 gees - probably because of the same miscalculation that caused the error in the period of objects in the Smoke Ring. However, that problem is easily resolved - just make the tree shorter. By the way, the same tidal force that creates pseudo-gravity for objects attached to the tree makes the orientation of integral trees very stable - each end of the tree is being pulled so that it lines up with the radial vector. If the tree ever got out of that orientation, it would oscillate a bit, but then settle down due to the damping effect of air resistance. I should note that man-made satellites orbiting the earth sometimes use tidal stabilization to remain oriented with one axis pointing towards the earth.

Remember this picture – it also shows the shape of the potential field experienced by an object in free orbit – while the center of mass feels no force, bits of the object that are slightly closer to the primary will feel a force towards the primary, and bits further from the primary will feel a force away from the primary, and that are at the same distance from the primary as the center of mass feel a force towards the center of mass.

If the object becomes tidally locked, the compressive force goes away but the stretching towards and away from the gravitating object is 50% greater.

This chart just shows the two previous potential surfaces together – it’s pretty, so I put it in the presentation. Note that at the very center the surfaces intersect.

And here’s a look at the magnitude and direction of forces for the orbiting and the tidally-locked. Note – because of the way I created these pictures, the maximum length of the arrows is fixed – so it isn’t clear that the longest arrows on the right indicate 50% more force than the longest arrows on the right

There’s an old saying in the Smoke Ring.

Is it true? Why? Imagine yourself in the Smoke Ring with a jet pack at your command.

If you apply a thrust eastward (in the direction of your orbit), you put yourself in a higher orbit (you move Out)
If you apply a thrust Westward (against the direction of your orbit), you put yourself in a lower orbit (you move In)
If you apply a thrust outward, you put yourself in a slower orbit, so you move West relative to everything else in your old, faster orbit
If you apply a thrust inward, you put yourself in a faster orbit and you move East relative to everything else in your old, slower orbit

If you thrust to the left or right, you move to an orbit that is at an angle to your original orbit, but which intersects your original orbit at two points, one of which is the point at which you applied the thrust - hence you come back to where to started after half an orbit.

The “old saying” compressed all that knowledge into a few sentences, and it’s a useful mnemonic for students learning about orbital mechanics as well.

These are some of the handiest equations for dealing with orbital mechanics in a science fictional environment. The total velocity of an object at any point in its orbit is equal to a constant times the difference between twice the reciprocal of the current distance from the primary and the reciprocal of the average distance from the primary. What this gives you (among other things) is the delta-v for transfer orbits. If you want to travel from earth to Mars, simply calculate the current orbital velocity of earth, and then the orbital velocity f an object currently at earth’s radius but with a maximum distance that just reaches Mars’ orbit. That gives you the dV to apply. Once you reach Mars the same equation gives the dV that will put the spacecraft in the same orbit as Mars.

What makes this equation particularly useful is that you can pick your units for your convenience. When I was taking courses I used units of astronomical units for r and a, and units of miles per second for velocity whenever possible, so that for calculations in the solar system I could determine GM by taking the earth case - all I needed to remember was the length of the year and the size of earth’s orbit and I could determine the earth’s orbital velocity, and since the distance term in my units was (2-1), GM was easy to solve for and easy to use for any subsequent solar system problem without the pain of memorizing G or M.

The applications to SF for these equations are pretty obvious, but one thing I’d like to highlight is that at any point in an orbit, increasing velocity increases your orbit’s semi-major axis, and decreasing velocity decreases it. The trick is that for any given orbit, a nearby orbit with a larger semi-major axis will have a smaller velocity (this time r is changed as well as a), so if you attempt to “catch up” with something in a higher orbit by speeding up, you’ll end up falling behind. As John Brunner said in Shockwave Rider, “see you later, accelerator”

Here’s a thought experiment for students. What if teleportation were possible, but the laws of conservation of energy and momentum still applied. Niven played with this idea in his “Flash Crowd” stories – a change in altitude requires causes of gain or loss of potential energy, which translates into heat gain or loss. Transfer to a different latitude or longitude results in a problem because the object being teleported retains the velocity it has due to the Earth’s motion at the location it’s teleporting from – which could mean being slammed into the wall at dozens of miles per hour at the new location (see http://groups.msn.com/AndysUsingScienceFictionForEducationPage/studyguide3.msnw for some calculations).

But the students could have some real fun figuring out the social implications of teleportation. Some are obvious (no airplanes or cars except for fun), some are less so, like the effect on crime, or the creation of “flash crowds” (a flash crowd is a crowd that appears whenever and wherever something interesting is happening. If we assume that teleportation is cheap and easy, a crowd can grow very quickly, since it draws on the whole world's population of possibly interested parties). We see “flash crowd”-like effects on the Internet now - “teleporting” to a web site is easy, so an overwhelming number of hits can happen to any site that is attractive (see the Risks forum for a mention of this http://catless.ncl.ac.uk/Risks/17.86.html#subj8). I highly recommend Niven’s article on the subject, by the way.

Niven references pop up in the news pretty often – recently, astronaut Edward Lu suggested that an asteroid could be deflected by using the gravity of a space probe station-keeping nearby – the same method used in A World Out of Time to move the Earth itself. Advantages of this method include minimization of strain on the object being moved (it would be unfortunate to damage the Earth, or to break up the asteroid before it is safely past the Earth) – the only strain is the tidal force which can be made very small at the cost of lengthening the time needed to move the asteroid (or the Earth).

I’ve got a study guide for this story at http://groups.msn.com/AndysUsingScienceFictionForEducationPage/studyguide2.msnw, at which I reveal the name of the deadly force and calculations associated with it.

If I’ve interested you at all in using SF for education, here’s some information about how to do so. First of all there’s “Reading for the Future,” a group of teachers, librarians, writers, parents, and fans (and, of course, people who fit into several of these categories) – there is a website and an email mailing list associated with this group. The magazine “Science News” has a web site “Science News for Kids” with SF content updated every week by Julie Czerneda.

Also there’s the AboutSF.com web site with SF lesson plans and a speaker’s database – if you’re looking for a speaker, the site will find those who are near by you. If you’re willing to speak, I encourage you to sign up there.

If you’d like to read more about science from the science fiction point of view, here are some good choices: of particular note are Borderlands of Science by Charles Sheffield, which explores the edges of our current scientific knowledge, with a view towards illustrating the many areas of science in which there are open questions just waiting for new scientists to a nswer (and waiting for new science fiction writers to exploit for story ideas), Turning Points, which includes Poul Anderson’s classic “How to Build a Planet” article and larryniven.org, the semi-official Larry Niven website (at which this talk will likely be archived). The Niven collections also include Niven’s non-fiction pieces about teleportation and megastructures.

Science fiction as we know it was born in magazines; therefore many classics of the field are short stories, or novels short enough to be published serially in two or three parts. Using short stories in the classroom makes sense for many reasons, especially when introducing SF to students with little experience with written SF. Short stories take much less investment of time than novels do, thus allowing the reader to experience different subgenres of SF and to distinguish between "I didn't like this story" and "I don't like science fiction".

This is a favorite quote capturing the idea that knowing the causes of something does not dilute one’s pleasure in seeing it. Oddly enough the Feynman book I mentioned at the beginning of the talk discusses the same concept – “I can appreciate the beauty of a flower. But at the same time, I see much more in the flower than he sees. I can imagine the cells inside, which also have a beauty. There’s beauty not just at the dimension of one centimeter; there’s also beauty at a smaller dimension”. Even though I had to skip several slides in my talk, I made sure to show this one.

Known Space: The Future Worlds of Larry Niven

Teaching Physics With Niven