Not by themselves. There's plenty of energy in fusion, but how do you contain it? On Earth, with huge tokomak rings generating enormous magnetic fields, we might be able to build a magnetic pinch-bottle to hold a controlled fusion reaction; but aboard a space ship? If you can build something light enough to go aboard a ship smaller than the Queen Mary and able to contain controlled fusion, you've got a device that will change far more than the asteroid Belters: it's obviously a defense against hydrogen bombs, to begin with. We'll discuss various properties of fusion powered ships some other time; for now, it's enough to point out that they aren't the panacea we wish they were.
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Figure 18
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Figure 19
(K. E. = T x Boltzmann Constant, which I won't explain = ½ m v2; table assumes monotomic hydrogen fuel, with mass of 1.6733 X 10-24 grams/particle.)
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Well, what can the Belters do? They can get around with NERVA engines, but what do they use for fuel? There isn't a lot of hydrogen out among the asteroids.
Oddly enough, there is a propulsion system that gets Isp (theoretical) in the region of 20,000 seconds, doesn't have excessive real temperatures, and can be built right now Even better, it's likely we can find fuels for it in the Belt.
This is the ion drive ship. Ion drives employ metal vapors as fuel, and the metal is accelerated by magnetic fields, not heat. If the asteroids turn out to be rich in metals, some kind of ion rocket may be just what the Belters need. It lets them get fuel from the rocks. But even with a 30,000 second Isp ion drive we won't have a torchship for driving around at one g. Torching uses too much energy, and the ion drive won't develop the needed thrust anyway. A mercury vapor ion engine, for example, although very efficient, only gives thrusts of about 10-4g. You get there efficiently, but it takes a long time.
No, the conclusion is obvious: with anything foreseeable in the way of rockets, the Belters aren't going to develop their civilization. They won't have ships good enough to let them reach each other—and if they do get such ships, it's as easy to reach Earth as the other asteroids. With real torchships, both the Belters and the Earth Navy will have no trouble getting anywhere. I'm afraid the Belter Independence Movement is a long way off.
What with science robbing SF writers of Mars, and Venus, and now the Belters, it's all rather sad, and I've been looking for something more cheerful. I may have found it.
The Jovian Moons offer a distinct possibility for a multi-world civilization. They're respectable in size, and may well have water ices, or methane, or some other source of hydrogen on them: fuel for a NERVA engine without sending out to Mars for it.
It takes a long time to get to Jupiter's moons, so there's an incentive to stay there once you've arrived; yet it takes less delta v to get to a Jovian moon than to land on Ceres. May be we should go there first?
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Figure 20
Data from C. W. Alien, Astrophysical Quantities, 2nd ed. 1963, University of London, Athion Press. Assumes density of 3.5 grams/cm3 when no value is known.
This is the usual mass for asteroids. J-XII, XI, VIII, and IX are retrograde and highly inclined, and no calculations of velocity changes required for trips to or from them were made; their characteristics are included here only for completeness and because the data were already calculated.
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The basic characteristics of the Jovian system are given in Figure 20. We've had to assume a lot of things to get these numbers, and by the time this appears some of the figures may be out of date: Pioneer will encounter Jupiter during the interval between now and when this is published. I'll be the first to cheer if Pioneer makes hash of my assumptions.
Presuming it won't, let's look at travel amongst the Jovian System. First, discard the outer satellites: they're retrograde, and take so much delta v to catch that if you can land on them, you can go nearly anywhere. The others are more reasonable, and the delta v's for travel among them are given in Figure 21. Except for Amalthea down there close to Jupiter, we can do it all with NERVA-style ships. Moreover, the travel times are very short, and you get favorable geometry for Hohmann transfer every couple of months or less. The four big Galilean Moons take about as much delta v to travel among as it took to get out there in the first place, but if they're hydrogen-rich, fueling your NERVA will be no problem.
The outer three rocks are very easy to travel among, and you could do it with a backyard rocket burning kerosene. Since those rocks are probably captured asteroids, they're as likely to be interesting as any of the others the Belters are concerned about.
So we can end on a cheerful note, saying Goodbye to the Belters, but also making ready to greet the Minister Plenipotentiary and Ambassador Extraordinary from the Jovian Moons.
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Figure 21
All values are in km/sec. Values below the diagonal are delta v's needed to go from orbit around one satellite to orbit around the other, landing on neither. Values above the diagonal are surface-to-surface velocity change requirements. Diagonal values are the circular orbital velocities of the moons.
Escape is velocity change required to leave the Jupiter system entirely.
Ships for Manned Spaceflight
I was recently caught in an argument between Rusty Schweikert, astronaut-scientist, and Gene Thorley, Chief of the NASA Earth Resources Survey. After a while I had a sense of déjà vu: the man-in-space people have been fighting with the black box boys at least since 1954 when I first got involved in the space business.
The arguments haven't changed, although you'd have thought Skylab might Have ended it; but no, the black box boys still say that anything a man can do in space, instrument probes can do better and cheaper—and two instrument missions cost less than one manned mission. Meanwhile, the astronauts say that you can't learn anything from a probe that you hadn't thought to ask it to tell you, and a trained astronaut-scientist will think of new experiments while he's in space and can do them.
I won't pretend neutrality, having started in the Human Factors laboratories and put several years into work on keeping men alive in the space environment; obviously I'm prejudiced in favor of the astronauts.
Unfortunately, the black box boys have a strong point. It's going to cost a lot to send manned missions to the planets, and with present spacecraft, manned interplanetary travel can never become routine. It's not just a question of refining what we've got, either; there's a definite theoretical limit to what we can do with chemical rockets, and manned interplanetary cruises—other than spectacular one-shots to say we've done it—are beyond those limits.
Let's see why and then look at ships that can take man to the planets.
First we'll need a couple of basic facts about propulsion. Jim Baen and I are agreed that this chapter won't become a substitute for a textbook, and I'll keep the lecture short.
Rockets are still the only means of interplanetary travel we have, and they work by throwing mass overboard. The more mass tossed, and the faster it goes, the more thrust:
Thrust (force) = (rate of mass loss) x (exhaust velocity)
or T = (M0-M1) x (Ve) / t (Equation1)
What this says is you take the weight of the ship when you get through burning fuel, subtract that from the weight you started with, divide by time of burn and multiply by the velocity the burned fuel went aftwards from the ship; and you get thrust. Now in the foot/pound measurement system, thrust is expressed in pounds and sounds like a weight. It's not, it's a force, but it does have one convenient property.
One pound of thrust will just support one pound of weight in the gravity of the Earth's surface. It will accelerate that same mass at one gravity if you started in orbit. In metric systems, thrust is expressed in newtons or dynes, and if you don't understand the difference between mass and weight, they aren't easy to interpret However, equation one makes it easy to see that if you don't want to throw much mass overboard, you'd better get it going aft a
t a fast clip—that is, you need high Ve.
Now Ve happens to be related to the temperature of the burn in the rocket engine, so naturally there's a limit to how high that can get; if it's hot enough, the engine melts, and your rocket won't work so good. It should be clear, though, that the theoretical Ve obtainable with any given combination of fuel and oxidizer is a good measure of how efficient that would be as a rocket fuel.
However, for reasons I won't go into, instead of Ve most engineers use another measure of fuel efficiency known as Specific Impulse, abbreviated Isp; and this is given in units called "seconds." That's not really a unit of time. Isp is the "pounds of thrust obtained per pound of fuel expended per second," obviously a measure of efficiency; and
Isp = Ve / g (Equation 2)
where g is the acceleration of gravity: 980 cm/sec/sec in the metric system and 32 ft./sec/sec in the English.
Now we have a measure of fuel efficiency, but we don't know "what we need for interplanetary travel. As I've shown before in these columns, one of the most convenient figures to look at is "delta vee," meaning the total change in velocity we can get from a ship if we burn all the fuel in it. Delta v is convenient because it doesn't matter if you burn all the fuel at once, or keep turning the motor on and off; and furthermore, we can calculate the delta v needed for various space missions without knowing anything about the ships at all. Big or little, it takes the same delta v to get into orbit, or to go from here to Mars.
We're almost done with the rocketry basics, but we need one more equation:
Delta v =Ve loge(M0/M1) (Equation 3)
What this says is that the total velocity change you can get from a rocketship can be found by knowing the exhaust velocity of the fuel burned, and the ratio of the mass when you started to the mass when you finished the mission. Log-base-e is the "Natural log" of that ratio, and if you don't understand logs, don't worry about it. It's tabled in handbooks or given by scientific pocket computers.*
Early chemical rockets used fuel/oxidizer combinations with Isp of under 200 seconds. That means that at a mass flow rate of 1 pound a second, the rocket could lift about 200 pounds against gravity. Recall, though, that this is the total weight lifted, including the fuel to be burned in the next seconds, etc., and you'll see it's not so good after all.
Incidentally, if you'll look at the three equations you'll see why liquid-fuel rockets start lifting slowly and get faster and faster as they rise. The mass-flow stays the same, but they're burning fuel and getting lighter all the time. Since the thrust hasn't changed, but the mass it has to lift is decreasing, the acceleration the motor can impart to the rocket is increasing all the time.
Rocket chemists worked very hard to get higher Isp (and thus higher exhaust velocities), and now the best solid-fuel rockets have Isp in the order of 250 seconds. Meanwhile, liquid-fuel rocket motors were developed to give even higher specific impulses, and by using liquid oxygen (LOX) and routing that around the motor to cool it before it was burned, higher burning temperatures were achieved. Eventually, LOX made Isp of 300 nearly routine. More exotic fuels were employed, including liquid hydrogen with LOX, and finally hydrogen and fluorine.
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* An easier way to calculate delta v is to send $3.00 to RAND CORPORATION, 1700 Main St., Santa Monica, Calif. 90406 and ask for a "Rocket Performance Computer." It's a circular slide rule developed by Ed Sharkey, and it comes with a book of instructions. You enter with Isp and mass ratio and it gives delta v directly.
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TABLE ONE
Best Delta v for chemical rockets.
Isp = 400 Vp = 3.9 km/sec
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However, with the best chemical fuels, the theoretical maximum Isp is no more than 400. Actually, no one has got that yet; and it's certain that no chemical rocket will do better.
Isp of 400 is an exhaust velocity, at best, of 3.9 kilometers/second. Let's plug that into equation three for various mass ratios and see what happens. (Table One.)
It takes about 8 km/second to get into Earth orbit, which means the best chemical rockets have to be almost 90% fuel simply to get to orbit in a single stage; but let's assume we start in Earth orbit.
To get to Mars requires about 5.5 km/sec velocity if you start in Earth orbit—and it takes that much again to get back. Clearly, if we're to carry any payloads to Mars, we need refueling out there.
Equally clearly, we've got a problem, because how do we ferry enough equipment to set up a fueling station on Mars? About 80% of our payload put into Earth orbit gets burned before we reach Mars.
To make a round trip, which means carrying the fuel to come home with, we have to put 20 pounds into Earth orbit for each pound making the trip from Earth to Mars and back again. Even one way takes a factor of 4 to 1, not impossible, but expensive enough. Still, we could imagine commerce in which 4 tons of fuel were burned for each ton of payload delivered.
Unfortunately, minimum energy transfers (and those are the only kind possible with chemical rockets; anything else required delta v in the tens to hundreds of km/sec) takes time: 260 days to Mars.
People eat, drink, and breathe. With the best recycling we're going to have consumables aboard the ships—and the recycling systems are massive, too. Let's be generous and say we hold things to 5 pounds a day per passenger, and start with people who weigh 200 pounds each. That's 1500 pounds of passenger and consumables—and 6000 pounds of fuel for his one-way trip.
If we can't refuel at Mars and have to carry our return LOX and hydrogen out with us, it's far worse. You need 150,000 pounds of fuel in Earth orbit for each round trip passenger. Clearly, that's not a commercial proposition. Chemical rockets can give us commerce with Mars only if we can build a Mars orbiter and fueling station, and even then it's marginal: and remember, we've given chemical rockets the best possible performance. It's not good enough.
What are the alternatives, then? We have several, one of which could have been developed by the end of this decade.
How would you like to have had a 10 person scientific mission leave Earth orbit in June, 1979, to arrive at Mars 227 days later; orbit Mars for 48 days, then head for Venus; on the way to Venus, encounter the asteroid Eros and stay near it for a day or so; then go on to orbit Venus for 55 days, and finally, 710 days after it departed, return to Earth orbit?
It could have been built. I have a model of the spacecraft that could have carried that mission. It employs a stabilized main section, and a counterbalanced rotating crew-quarters section to give about 10% gravity; it carries plenty of scientific instruments, and a small nuclear electric power plant; and by making rendezvous in Mars orbit with an expendable fuel pod, PILGRIM could have sent down a manned Mars lander.
The model was built by MODEL PRODUCTS of Mount Clemens, Michigan, and sold for about 5 dollars under the name PILGRIM OBSERVER The engineering and celestial mechanics of the model and its mission were very well worked out—and we "really could have built it for a 1979 flight. The engine employed was an atomic rocket called NERVA
Unfortunately, neither the model nor the engine are available any longer, and for the same reason: no public interest. MPC took PILGRIM out of production at about the same time as Congress cancelled the budget of Project NERVA This was just after Apollo 15, when people lost interest in space, and I was involved in trying to save NERVA: involved to the extent of writing some columns in daily papers, and furnishing the House Science Committee with data. But despite my efforts, which weren't important, and those of Congressman Barry Goldwater, Jr., which were very important, NERVA died.
Ironically it died a great success. It had been ground tested and found to work fine.
NERVA works like the "atomic rockets" of the better science fiction writers of the 40's and 50's. Basically, it's a nuclear reactor with a rocket nozzle at the end: you squirt fuel, say hydrogen, through the reactor; it gets hot; and out it comes, fast, to propel the ship.
Now NERVA didn't burn any hotter than the best che
mical rockets; in fact, some chemical rockets operate at nearly 3000°, which is better than NERVA's design specs called for. However, Ve, which is what you want to maximize, depends not only on the temperature of the reaction, but also on the molecular weight of what you're throwing overboard.
Hydrogen burning in oxygen produces water, with molecular weight of 18. Even hydrogen and fluorine give off HF with a weight of 10. (It's also rather corrosive, since the least moisture converts it to hydrofluoric acid.) But NERVA squirted out molecular hydrogen, and that has a weight of only two.
The best tested Isp for NERVA was 650. The designers of PILGRIM assumed they'd get 850 by 1978, and that was reasonable. Most engineers now think NERVA-type craft can get Isp of 1200. Let's plug those into equation three and see what we come up with.
A Step Farther Out Page 20