Stellar Oscillations across Spiral Arms

Jim, rather than turn this thread into a tutorial on orbital mechanics, I'll just refer you to some excellent resources.

The "Escape Velocity" section of the Orbits page at UCLA illustrates very clearly what I've been saying.

Some other useful sites are:
Satellite Orbit Data Calculator
Orbital Mechanics
Science@NASA
Liftoff to Space Exploration
Explore the Solar System
Kepler's Law Calculator

There is a very useful Escape Velocity Calculator at Geocities; unfortunately, it doesn't make clear the distinction between escape from the surface and escape from some other location. Where they say to type in the radius of the body you wish to escape from, they mean type in the radius from which you wish to escape. Apparently, they're as confused as you are.

Where does all this confusion come from? I believe it started with CBS Snooze coverage of the Apollo missions by Walter Cronkite. Since he was addressing a wide audience of mostely ignorant housewives, he spoke of the "escape velocity of 25,000 mi/hr", as if it didn't matter where you were or where you were starting from. It was confusing enough, anyway. Perhaps because of Cronkite's enormouse prestige, many brilliant scientists even today, who know better, have fallen into that same way of speaking---either out of deference to an ignorant audience or out of laziness.

PhilJ, I understand what you are saying quite well. It is very easy to get bogged down in details and lost in the fog. I try to avoid doing that by focusing in on what is important and setting aside the other stuff-in this case the capture process.

Jim,
Quite right! I apologize [] for helping to drag this thread farther astray from the original topic. That's what I get for jumping in without first following your link to the C. Johnson article . [)] I'll need some time to digest it before commenting.

P.S.: That "groups.beta.google...." link, by itself, is wider than my page at 1280 x 1024 resolution. [!] Read Posting hyperlinks under News and Information.

PhilJ, I got on at a point during the development of this thread when the capture of bodies by other bodies was started and not at the start. How does that relate to the main topic of this thread? It seems the threads always start at one topic and drift into other topics.

Oops! Can't blame you for that long URL in the post, by Peter Nielsen, which started this thread. It links to a Google Groups discussion of a rather interesting and scholarly paper, by C. Johnson, about stellar motions that deviate from simply drifting uniformly around the galactic core. I must confess, I haven't read all of it. [|)]

There are computer models which, with the help of a supercomputer, display collisions between galaxies in 3D, simulating billions of years in a few minutes. Two simple oval galaxies collide and the result is spiral-arm galaxies. I saw that on TV several years ago; it might have been Nova, on PBS. I wonder if C. Johnson got his idea from watching such a simulation.

Johnson speaks of "oscillations in both directions", which some posters have found to be unclear. I think he might mean both radial and axial directions, relative to the galaxy. In otherwords, stars near the center of the spiral arm simply follow an oval path around the galaxy, while a star near the outer limits of a spiral arm follows a flattened spiral around that longer oval path.

It's not easy to draw such a complex picture in words, but I'll try:

Start with a long cylindrical solid, full of stars, rotating about its longitudinal axis. The stars near the outer surface of the cylinder move rapidly, while those near the axis are nearly stationary.

Now, taper the ends of the cylinder, more or less to a point. Place two or more copies of that object so they radiate perpendicular to a central axis. Then twist the whole arrangement about that central axis so the objects spiral outward, with their original cylindrical axes in a plane. Finally, flatten the whole thing in that plane; i.e., flatten it parallel to the axis about which it is twisted.

So the motion of a star near the outer edge of the original cylinder will follow a flattened oval path relative to its "arm of the galaxy", while the center of that oval follows a much longer oval path around the core of the galaxy. The path of such a star around the galaxy would then be a flattened spiral, following a long oval.

Here's another way to describe the path of an individual star: Wrap a wire around a pipe to form a coil; remove the pipe and stretch the coil around a large circle, connecting the ends of the wire to each other. Then flatten the whole thing.

I'm not sure if that's what C. Johnson had in mind, but it works for me. The question is, does this obey the laws of physics. Only a supercomputer model can say for sure.

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This led into a discussion of whether such a galactic model makes it more or less likely for interstellar comets to be captured by our solar system. For that to happen, the comet would have to start with little more than the threshold energy (or velocity) for escape.

Now it seems to me that most of the stars in our arm of the galaxy ought to be moving according to the same general scheme, as described above. If so, I would expect our closest-neighbor stars and interstellar comets to have not-so-great velocities relative to one another. Alternatively, there is the traditional view of all the stars following more or less parallel oval paths around the galaxy, which suggests even less relative velocity for close neighbors. If, on the other hand, it's every star for himself or herself (like a busy street in Mexico), then our telescopes should be spinning in an effort to follow them. [V]

I don't think we can answer this question with Keppler's laws and a slide rule. We'll have to hand this problem over the supercomputers and many-body models, and trust their results. [^]

PhilJ, It will do nothing to simply hand the issue over to a supercomputer if you give it the wrong program or whatever. The way a comet can come to have enough energy or velocity to get into the gravity field of the sun is if it(the comet) came from a supernova event. TVF says data indicates comets arrive in the gravity field in cycles. It seems logical the eruption of of a SN in the past might eject mass and some of it would come our way. Wouldn't you have to tell the computer that before it could predict anything? Its a trash out-garbage in sort of process it seems to me.