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but on the same not do the engines actually stop spinning? I would have thought the air naturally moving through the off engine would cause it to spin too.

Yes and no. Turbojets and turbofans as well as fixed-pitch props do free-spin in the air. However, they do so at a very low rpm, usually in single-digit percent of their rated speeds. If anything, this is more of a detriment to performance because it actually acts as a big air brake. All turboprops (as well as some of the higher performance piston props) I know are equipped with variable pitch full-feathering propellers, so they actually do come to nearly a complete stop - this helps reduce their drag and increases performance in engine-out conditions. Turbojets and turbofans do have an in-flight minimum restart rpm. This can be achieved either by flying very fast, by cross-bleeding compressed air from the compressor of the working engine, or by using an auxiliary power unit (a small turbine engine designed to start the aircraft without ground assistance and to provide power when the main engines are off or failed) to feed compressed air to the air turbine starter of the failed engine.
Regardless, irrespective if the engine's internal turbo machinery remains spinning at some small fraction of rated RPM, the hot section of the engine cools off pretty quickly, since the heat source is gone and you've got very cold air going through there (not at a very high rate, but still after a few minutes of -50C air flow, it's going to be pretty much chilled). As a further example, here you have a Boeing 747-400 APU (a >1000 shp beast) starting up and going from zero to 100% rated output power in about 30 seconds. The APU is fully automatically controlled, the crew literally just flips a knob in the cockpit and that's it (here it is, near the center of the picture).

Apparently it was the turbine of an old 737-300 with the turbofan removed so one of the mech engineers told me.

Possibly an industrial variant of the CFM56. Don't know what they're called in industrial versions, I'm only familiar with GE's and some of RR's products. Industrial conversions of aviation engines do occasionally happen.

the engine was attached to a large gearbox. Maybe that's where the warm-up requirement came from

Not sure either. Gearboxes don't really need warmup either, they just need lubrication. It's mainly large castings (as occur in piston engines) that are susceptible to heat stress. Turbine engine oil has very low viscosity (far lower than automotive engine oil), so I don't think viscosity of the oil is much of a factor either... I dunno, maybe the manufacturer just wanted you to really baby the engine.

Cash cows are forever? Hardly. Tell that to buggy whip manufacturers at the advent of the automobile, or more to the point, tell that to IBM's Mainframe Division in 1978. All cash cows will eventually die as they fall out of relevance, and cash cows in the computer industry have a far shorter lifetime than they do in other industries as the computer industry moves far more swiftly.

True, MS's cash cows probably still have a few more decades of life in them yet, but Microsoft is at least smart enough not to rest on their laurels and make an effort at getting into the mobile sector, however pathetic their current attempts at doing so are.

By the way, I looked up United Technologies, and well, I don't know why you bring them up. They're a technology company all right, but they don't look a computer company to me. They look more like Boeing than Microsoft or IBM, and well, the aerospace industry is rather different from the computer industry, and doesn't have anywhere near the same rate of change that the computer industry does.

A solid rocket is propellant in a tube. However the way you mix and cast the propellant is much more complex and error prone than fueling a liquid rocket. Small manufacturing errors can lead to cracks in the solid fuel which can cause the whole thing to explode. The oxidizer (e.g. ammonium perchlorate) is mixed together with the fuel (e.g. some kind of rubber). If you make one mistake during the mixing process, the whole thing can explode. Solid propellant is much more expensive per kg than liquid propellant such as LOX/Kerosene.

In a liquid fuel rocket most of the expense is in the engine, rather than the fuel. If you reuse the engine N times, you are reducing engine cost by a similar proportion.

SSME is expensive, but if you consider the fact that the engine is reused, it costs about the same as other engines in the same engine thrust class. SSME has had several revisions. The latest revision is able to do 10 or more flights between overhauls. As time went by and the SSME was upgraded, its costs kept decreasing while solid rocket costs kept increasing. You can read about that here in the Shuttle Operations funding requirement in page 23, here. The cost of External Tank+SSME is lower than Reusable Solid Rocket Motor+Solid Rocket Booster. In fact even manufacturing the expendable external tanks costs more than SSME.

Those are large and very high speed pumps that operate at the limit of what materials science can provide

The fuel pump puts out 69,000 horsepower at 37,000 rpm while being roughly the size of a car engine.

I thought this was interesting. http://utc.com/press/releases/2008-03-02.htm

I'll suggest UTRC, though I don't really know about the work environment (which seems to matter to you). Considering the projects of UTC proper though (high performance turbine engines, scramjets, rotorcraft etc.), I think it'd be exciting research for a MechE major.

Actually, the changes aren't that hard to make. The problem with the current engine design is that the hybrid rocket`s isp isn't high enough. Simply changing to another type of rocket doesn't help much though, the spacecraft needs to be an egg-shell filled with fuel in order to get to orbit, if there is no staging.

The problem is that the exhaust gases from a rocket are moving at the speed of sound. You can get much more thrust from the same fuel if only that exhaust were moving faster. It turns out that Rutan has been working on a new type of engine (pulse jets) which does just this, see http://www.pw.utc.com/shock-system/flightsoffancy. html
for more details. Now if you work out the isp from these new power plants, they are just amazing. It cuts the mass fraction for fuel from 90% down to something like 50%, or even lower. (Remember, the rocket equation has an exponential term in it, so even small changes in thrust per unit fuel mass make a huge difference.)

Burt Rutan said in a recent conference that it requires three breakthroughs for orbital craft to be viable, and that he already has made one of them. It wouldn't surprise me at all if this is that one. (With the others being related to reentry.)

Voyagers 1 and 2 were deliberately built simple and rugged, and were tightly constrained by the power available from their RTGs. Modern spacecraft are more complex and often consume more energy. Spectrum Astro's DS1 factsheet gives the bus orbit average power as 500 W. Admittedly, that probably isn't with all systems "idled" (whatever that means), but there is a limit to how much you can switch off on a spacecraft in mid-flight.

I can run a graphing calculator for a day on a couple double a batteries that has 10 times the processing power of these craft

A graphing calculator is not an internally redundant rad-hard flight computer (30+ W), with its associated I/O interfaces. It does not have a comm system (which will draw power even when not transmitting - you always want to be able to receive). It does not have attitude sensors. It does not have attitude actuators (which can be large power consumers on a 3-axis stabilized spacecraft, as you would want to be with a low-thrust system since spin-axis precession is probably infeasible). These things all take power. 500 W? Not necessarily. Several hundred W. Quite probably.

That the cost of the plutonium is completely dwarfed by the cost of launching the fuel?

The cost is not just the cost of plutonium itself, but the additional cost and complexity that results from flying a radioactive (and toxic) substance. Cassini cost $1.2 billion just to develop - the launch cost is a small fraction of the development cost, let alone the total mission cost. Admittedly, not all of Cassini's cost was driven by the RTGs, but they definitely contribute to a higher cost than you would otherwise see.

Hall effect thrusters, while having ISPs of "only" around 2,500 (compared to ~450 for a good LOX/LH engine) give power/thrust ratios of near .65-.70 newton per kwH in the case of the T-220 (assumedly the T-40 performs similarly). A 200W T-40 HET, therefore, would well outperform DS1's engine operating at full power, and yet use a tiny fraction of the propellant of a chemical engine.

Unfortunately, electric propulsion system performance doesn't tend to scale linearly. There are economies of scale that come with larger systems. Quoting from the Pratt & Whitney website:

The T-40 operates at 0.1 to 0.4 kW and produces 5 to 20 mN of thrust, with specific impulse values varying between 1,000 and 1,600 seconds, depending on operational conditions.

a single Cassini RTG could power a T-40 HET with power to spare (you can bring more RTGs as you want for insturments) and produce over 100 millinewtons of continuous thrust. Over a year, it could impart, to a 1000 kg spacecraft, over 3000 m/s delta-V**. Seing as it took Gallileo 5 years to get to Jupiter, that's 15k m/s delta-V** - I.e., you could get to Saturn using *no* gravity assists as fast as Gallileo did *using* gravity assists.

Since you have overestimated HET performance you are getting numbers that are unrealistic (which is exacerbated by the exponential dependence of propellant mass on Isp). Using your numbers (which are optimistic) we get:

Isp 3800 s
dv 15 km/s
mdry 1000 kg
thrust 0.1 N

mprop 496 kg
TOF 5.8 years

However, if we use realistic (but still optimistic - I'm assuming the upper end of the quoted T-40 performance range, which requires closer to 400 W) numbers for low-power HET performance, we get**

Isp 1600 s
dv 18.84 km/s
mdry 1000 kg
thrust 0.02 N

mprop 2325 kg
TOF 57.8 years

Both the newest Boeing Delta and Lock-Mart Atlas use license-built Russian engines with nary a design change.

Partially correct. While the Lockheed Martin Atlas 3 and Atlas 5 use the Russian RD-180 engine, the Boeing Delta 4 uses the RS-68 engine in its first stage, designed and built by Boeing's Rocketdyne subsidiary. Both vehicles use variants of the RL10 upper stage engine from Pratt & Whitney, another US company.

Hamilton Sundstrand, a United Technologies company.

Pick the right employer, and they'll pay for grad school. Sounds like a pain in the butt, but you can (1) save big bucks, and (2) earn some cash and (3) gain some industry experience.

I once worked for United Technologies. I'm not going to advocate them as an employer, but they have a kick-ass deal for those who want to go to school: Work full time, they give you some time off for classes, they pay for 100% of all course fees and books up-front even if those classes (or your major) aren't job-related. And for each degree you earn (Bach., Master, or Doctor), they give you 200 shares of company stock (at $60+/share, that's $12000+.)

Of course, the tough part is part-time grad school... it'll take longer, and to be honest, I doubt that a part-time academic experience is as good as a full-time experience.

But hey, after the $12k, quit and go back to school full-time. You'll loose some time, but you'll gain some industry experience and $.

Sorry, didn't answer your question.