In the "Orbital Mechanics" panel, Bob Mahoney and John Gibbons acted orbital mechanics out with a globe hanging from a microphone stand, hula hoops, and styrofoam noodles. They used lots of words too, of course. :-)
In this image, Bob Mahoney holds up two hula hoops to illustrate a higher orbit and a lower orbit of a hypothetical spaceship. One of the first things he demonstrated on this panel were gravity-assisted fly-bys, that are, in his words, "an almost magical way" for your spaceship to speed up, slow down, or to change direction. He invited two volunteers from the audience to act it out.
First he reminded us that a spacecraft approaches a planet on an asymptote. This gave him an opportunity to use a phrase "grab my asymptote", as he handed Patrick (one of the volunteers) a long styrofoam noodle, the kind children use in the pool. (Well, I think that's what it was, but I may have been sitting too far from the stage to see clearly.)
Left to right: an unidentified guy, Bob Mahoney, and Patrick demonstrate asymptotes of a hyperbolic trajectory on which a spacecraft approaches a planet.
Then he directed Patrick to go to the middle of the stage and walk slowly on a curve, and the shorter guy (this visualization would have been more effective if the other guy would have been a child) approach him. Then Patrick, under Bob's direction, gave a hand to the other guy, and swung him past. (I don't have a picture of that, since I didn't capture the right moment.) This is how the spacecraft gains speed when it flies past a planet. Here is a Wikipedia article on that. If the craft approaches the planet in a direction opposite to the planet's orbital motion, the spacecraft would slow down. Flying past a planet can also help it change direction. It gets all this "for free", without burning fuel. Of course, the energy boost doesn't violate any conservation laws: the momentum transferred to the ship slows the planet down by an infinitesimal amount.
(This, of course, is not a technical explanation, but this panel wasn't technical. It was a visual explanation to convey the basic concepts.)
There are more things you get "for free" in space, and they were part of the discussion on another panel, "Back to the Moon". That discussion involved such arguments as "it's cheaper fuel-wise to go from Earth-Moon Langrange point L1 to geosycnhronous orbit and back to L1, than from a lower orbit to the geosycnhronous orbit" (a quote from Ken Murphy). I didn't make much effort to follow it, because, to be fair, I never found near-space exploration to be very exciting. It's so difficult just to get off of this rock, and any objects worth going to are so incredibly far that we have very little hope of reaching them at velocities that are currently possible in space travel. So I always found this topic a bit depressing. But then Ken Murphy, a panelist on "Back to the Moon", said something really neat. This might have segued from the discussion of Lagrange points, which, as we know, are orbital points where a small object could remain stationary with respect to two larger objects (such as Earth and Sun, or Earth and Moon). According to Ken Murphy, gravitational wells of various planets create "grooves in spacetime" such that you could sent out a probe, and it would go down those spacetime paths and come back to you -- like a marble on a board in an old marble game from the eighties. Perhaps he meant something like these kinds of boards? What a neat image.
Ken Murphy also said -- and again, I forgot the context in which he argued this -- that NASA modules should be dockable and snapable, like USB or PCMCIA cards, so that any module would be able to dock with any other module. The analogy between very different scales -- computer components versus spacecraft -- immediately brought to my mind the iconic image of a coke can-sized spaceship from Charles Stross' "Accelerando". As we might recall, it contained hardware on which uploaded personalities of space travelers ran. Indeed, one can easily visualize a USB key as a spaceship containing millions of virtual astronauts running on its hardware. But that's a different panel. Such images repeatedly come up in "Stump The Panel", and there WILL be a post on the latter, too!
The second part of the "Orbital Mechanics" presentation concerned fun things you could do in space with gravity-gradient stabilization and tethering. The main idea is simple. Bob Mahoney reminds us that objects in a higher orbit are flying at lower speeds, while in a lower orbit they are flying at higher speeds. Imagine that a spaceship's long axis is aligned with the radius of the spaceship's orbit. Bob Mahoney demonstrates it in this image, holding a ruler above the globe. A you see, he is not holding it precisely aligned with the radius of the globe, but the idea is clear. Then the far end of the spaceship will be in a higher orbit than the near end. Meanwhile, the spaceship is moving at a speed at which its center of mass is moving. Thus the far end is going faster than it should for its orbit, whereas the low end is going too slow for its orbit. The outer end of the spaceship is pulling it outward, while the lower end is pulling it down so, if you line it up right, the spaceship will stay in orbit without you having to burn fuel to maintain that orbit. This is called gravity-gradient stabilization.
If the two ends are separated, centrifugal force will propel the upper end into a higher orbit, whereas the lower end will drop into a lower orbit. This has all sorts of applications, says Mahoney. If you unroll a rope with a ball attached to each end, the upper end will try to go off outward, and the lower end will try to fall inward, so the rope will stay taut without you having to do pretty much anything. This makes it possible for objects to stay in orbit just by being tethered to one another. I think Mahoney was talking about tethered satellites. They are described in this Wikipedia article. And if you tether a conductive wire to your space station and drag it along, you'll get electric current in it. Drawing current off of it will act as a brake, and the space station will drop into a lower orbit.
In practice there are complications with this concept. Vibrations in the tether might cause it to oscillate like a violin string, and that would lead to waves developing in all three dimensions. Then you might get, quote Mahoney, "the dreaded skip-rope effect". But there are ways to counteract it.
The purpose of this panel was to present to a layperson the basics of orbital mechanics, and ideas of various neat ways we can make physical forces work for us in the orbit. There are plenty of ideas here for a writer. I, for one, had never heard about spacecraft tethering, but that's what great about SF conventions -- you accidentally stumble onto things it had never occurred to you to look for.
Pictures from ArmadilloCon 2009 are in my photo gallery.