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Re: [Phys-l] Rocket Science



R. McDermott wrote:

Well, they sure as heck aren't going to rendezvous!

I'm glad that's obvious to you ... but it is amusing to note that
it wasn't obvious to the guys who planned the Gemini 4 mission.
They treated rendezvous as a distance=rate*time problem, utterly
failed to rendezvous, and used up a whole lot of fuel in the attempt.

I'm told the Russians flew *two* missions where they tried and
failed to rendezvous (although I don't know the details). That's
gotta be embarrassing.

The Gemini / Apollo program was a triumph of engineering, of skillful
and courageous piloting, and of the art of managing a huge project.
But science was at best an afterthought. This example suggests that
no matter how many smart engineers you have, it would pay to hire a
few scientists.

... I don't
think we have an easy way of determining what happens during that maneuver
without more detail.

We don't need more detail. We already have on the table a
well-posed initial value problem.

I know of two reasonably easy methods of solution. Maybe not
high-school easy, but still mainstream physics:
1) Virial theorem, and/or
2) Timestepping the equation of motion on a computer.

There are other methods that might be just as easy, but I haven't
personally tried them so I can't say for sure.

John M. wrote:
I get something like 360 km--the original 90 plus an additional 270.

That's what I got. A factor of 2 from the KE-versus-velocity law, and
a factor of 3/2 from the Kepler 1-2-3 law. And of course the virial
theorem.

I have to wonder if I would have gotten the right answer if I hadn't
already heard the Gemini-4 story. It's tricky, because the "obvious"
answer is so seductive. If it looks like a distance=rate*time problem,
why should you even question it? Why bother to double-check? It's a
lesson in humility and skepticism: always be alert to the possibility
that the obvious answer is wrong.

I'd like to think I would have simulated it. This is a pretty strong
lesson in the value of simulations. Don't tell me it couldn't have
been done in 1965; the Spacewar game (running on a PDP-1 circa 1962)
would have told you what you needed to know about maneuvering in a
gravitional well. Nowadays you could code it using a spreadsheet in
less time than it takes to talk about it.

I don't know how many times I've simulated the "conventional wisdom"
and found it to be a bunch of baloney.


I wrote:

Vis vobiscum.

That's Latin for "May the force be with you."

Note that "vis" and "virial" are two forms of the same word. See
e.g.
http://humanum.arts.cuhk.edu.hk/Lexis/Wheelock-Latin/lat14.txt

Note that translating this word is a nightmare; depending on context
it could mean strength, power, force, or even something resembling
kinetic energy (in the expression "vis viva").