Echoes from Space

Table of Contents

Chapter 1: Let’s get moving Page

Chapter 2: Beyond the Solar system

Chapter 3: The Rocket Equation

Chapter 4: An ambitious Endeavor

Chapter 5: What it takes

Chapter 6: The Fuselage

Chapter 7: The big, big Tanks

Chapter 8: The mightiest of all

Chapter 9: Where is the Math?

Chapter 10: Off the Launch Pad

Chapter 1 : Let's get moving!

Whether Neil Armstrong's "That's one small step for a man, one giant leap for mankind," was inspired by the moment's greatness or the work of a NASA speechwriter, is secondary. What mattered is that people around the world, riveted to their flickering black and white TV-sets, instinctively understood that they witnessed more than a landing on our moon: Humanity’s shedding of the shackles of gravity.

Yes, those few words from an astronaut on lunar ground heralded nothing less than that we, humans, were no longer inseparably bonded to planet Earth. That human mind had surmounted the barrier that, through the eons of history, towered between our world and the immensity of the cosmos.

Such was the overture to the "roaring sixties", those decades of scientific achievements which got us as close as one can get to a regular airline to the moon, and as fringe benefits, lead to the launch of space-station “Skylab”, robotic touchdowns on Venus and Mars, and close-up photographs by unmanned space probes out to the boundaries of the solar system.

But then, unseen at first, a shadow fell over the concept of tearing down the barriers banning us from the immensity of the worlds beyond Earth. All of a sudden, staggering breakthroughs did little to preserve the spirit of those who, a few years before, had crowded Cape Canaveral for a glimpse at the launch of the first lunar rockets, and the billions of people who ecstatically cheered Neil Armstrong's first steps on lunar ground.

As if a few short years had taught people to silently look the other way as Congress yielded to a few protesting welfare junkies while politics triumphed over science and money won out over the mind.

Had Armstrong’s gigantic step forward lead into an equally gigantic step backward, as if those in power had tolerated all space efforts for reasons no farther reaching than to make good on JFK’s ten years deadline for beating the Soviets to the moon? Or should we seek deeper causes for the death of a spirit that, like the once unstoppable wave of settlers’ westwards, had propelled Americans into space? Something stronger than congressional bickering, a feeling of disappointment, deep enough to uproot all former enthusiasm for human achievements? A broken promise, a wish ignored?

Or hadn’t it been those grandiose schemes what galvanized peoples minds while the conquest of space was within reach. Something far less ambitious, maybe, and yet closer to the heart. Could it have been the dread of being alone in the universe?

Backstage of the history of humanity, but never consciously admitted, such fears had been omnipresent in the human mind since antiquity, where the search for “brothers from another world” lead to peoples’ belief in mythical figures. At the turn of the nineteenth century, similar believes might have fueled the sightings of rectilinear streaks on planet Mars, first reported by the Italian astronomer's G.V. Sciaparelli. Promptly interpreted as waterways constructed by a hypothetical Martian population, they proved helpful to Percival Lowell’s 1894 fundraising for an Observatory in Flagstaff, AZ, equipped with one of the most perfect telescopes of those times and dedicated exclusively to the study of Martian canals. Sure enough, Lowell supported Sciaparelli's interpretation of his sightings as the imprints of intelligent life on the planet, since, as he put it, “water must be so scarce on Mars that the inhabitants economize to the utmost whatever stock there may be.”

Life on Mars was then taken for granted, so much so that in 1901, the French “Guzman prize” for communication with extraterrestrials summarily disqualified signals from Mars as “too easy to obtain.” (Attention, electronic hobbyists! This prize remains as yet unclaimed).

Later, when astro-photographs relegated the canals as optical illusions, many researchers hung on to their old beliefs and blamed the pictures’ low resolution for the missing vestiges of waterways, until the Mariner 6 and 7 spacecraft revealed the true and, yes, disheartening picture.

And yet, visions of Martians continued into the 20th century, at least as occasional cartoon characters, such as the drawings of an astronaut in the act of gratuitously offering glass beads to a gathering of “little green Mars-people, while his peers in the background hoist an American flag with an “Off Limits—US property—keep out” sign on its pole.

Such cartoons, insignificant by themselves, could still be interpreted as something more then an expression of most peoples’ wishe to become the masters of the universe. Here again, those little green beings on our planetary neighbor would have been living proof that we, mankind, are not the only ones in the cosmos. And our yearning for that bit of reassurance might have been what ultimately triggered all that excitement about reaching other worlds.

Who knows how far American space efforts could have advanced, had our spacecraft encountered some – any – equivalent of those green cartoon people from planet Mars. Or still, the discovery of life of any kind, even bacterial, might have been proof enough that living beings are not confined to Earth, and would have quenched the dreaded notion of being sole in a world too vast for human understanding. The kind of dread that, a few decades ago, still fomented Americans’ mythical belief in flying saucers.

Hopes flared, once again, when the worlds’ mightiest radio telescopes started their research into intelligent signals from space. If civilized beings strove somewhere in our galaxy – so the reasoning went – some of them would, in all probability, have mastered the technology of generating and receiving electromagnetic signals. And if they were as eager as we humans to get in touch with other civilizations, they might as well beam their beeps into space right now for us to receive.

At the turn of the nineteenth century, Nicola Tesla, father of today’s polyphase alternating current technology, claimed with absolute certainty that he captured in his Colorado laboratory signals from another planet. Later, in the 1970s, the idea caught on and the big Arecibo radio telescope in Puerto Rico began scanning the cacophony of random radio noise from space for something that made sense, or at least distinguished itself by repetitive sequences.

Like all previous efforts in search for our alien brothers and sisters, this one too set out with high hopes. After all, the sky holds 41,253 square-degrees for us to check out, and every one of them may buzz signals in one out of a wide band of frequencies, from megahertz to gigahertz and beyond. And we have still a third variable: Time. Signals of a certain frequency from a certain domain of the sky may not be present twenty-four hours a day, but materialize in bursts of relatively short duration, depending on the endurance and patience of their hypothetical senders.

This research program, fittingly code-named “Serendip”, consistently searches the sky in 168 million channels of radio frequencies. Lately, more ambitious and farther reaching programs have gotten under way, such as the “One Hectare Telescope,” or “1hT,” at UC Berkeley's Hat Creek Observatory, an array of no less than one thousand interconnected eight foot radio telescopes, the electronic equivalent of a single dish two acres and a half in size.

Moreover, the analysis of signals from space has been entrusted to thousands of privately owned personal computers, which in toto offer far higher computing capacity than the traditional workstations could come up with. Every single one of their owners, we may assume, hopes deep in his or her heart to become the one to stand up and, arms extended, scream, for all of humanity to hear, the redeeming words:

“We are not alone!”

Four little words, but enough to upset our age-old perception of the world that surrounds us. Fantastic, overwhelming, breathtaking, as such a discovery would be, it should make us think twice before we act. Should we really lean back with a sigh of relief, and expect our newly found brothers to work shoulder on shoulder with us humans toward the solution of the new, extended world problems, or should we rather recall Darwin’s famous thesis of the “survival of the fittest?”

If we come up as the “fittest” among galactic HAMs, then the aliens wouldn’t have much to offer. But with anything less than the superlative on our side, beware. The best we could hope for would be that the lightyears of interstellar space, which kept them at bay so far, would continue to do so. The reward for our wireless efforts would come as one more factor of “angst,” as if there wasn’t enough to fear in the world as it is: Fear of incurable plagues from mutant bacteria and virus, fear that the Earth’s capacity for producing foodstuff could be strained to the point of worldwide famines. Fear of an asteroid impacting our planet and triggering a monstrous “tsunami” around the globe, followed by a long winter that, for those that survived that far, would never end. And, more remotely, fear that we would die away powerless, once the Sun’s surface temperature starts to rise, or ultimately on the day when the Sun turns into a “red giant star”.

Though we use to file away those threats to our existence as “calculated risks,” angst remains as deep, even atavistic feelings our conscious mind cannot control. It may have invaded the human thinking process long ago, when we won the Darwinistic race for supremacy, yet instead of savoring our victory, wondered: “Why us and nobody else?” Ever since, humans yearn for an understanding of what bridges they had crossed and burned behind them with the development of conscious thought, and more important, awareness of that ability.

Here starts our search for the “the missing link,” not a set of bones but, in this case, an equivalent of the human mind in other creatures. Times again, those efforts lead nowhere but into the unbridgeable rift between human and animal brainpower, as decades of research into communication with primates, such as chimpanzees, produced trained animals rather than conversation partners. And many of the successes from earlier efforts, including the accomplishments of the famous horse “Der kluge Max (the smart Max),” who reportedly counted to twenty, have been unmasked as fakes, as if mankind’s expulsion from paradise symbolized our break with the community of living beings around us.

Grecian mythology still overflows with images of strange creatures commanding magical powers, some of them forbidding, others even comic, such as the Pygmy, reported as thirteen inches tall, riding rams and goats, and fighting in springtime the cranes from nesting in their territory. Others, less benign, include the satyrs, predecessors of the Roman Fauns, whose prime entertainment consisted in terrifying Grecian shepherds. They are described as furred boys with blunt pug noses and curly hair, budding horns protruding their scalp, while their legs, feet and tails resemble those of goats.

Ancient Greece’s remote and forbidding woods became the homes of Centaurs, horse-like animals with human torsos. By modern standards, we would pin signs, such as “Do not feed the Centaurs,” on tree trunks, but as it was, those wild and lawless forest dwellers were left to trap, and occasionally trample unsuspecting passers by. If such behavior disqualified them as chaperons for travelling maidens – there were exceptions. One unusual Centaur, Chiron, presided over a forested school for the children of gods and kings, and equally for newborns found abandoned in the hills while doomed too weak to grow into worthy warriors. Chiron taught music and dance, and also such useful trades as medicine, surgery, and the ways of the stars.

Chiron’s life came to a tragic and premature end on a peacekeeping mission in a conflict between his former pupil and later hero of Greek mythology, Heracles, and a pack of wild Centaurs. A stray arrow from the proper Heracles’ bow hits Chiron in his knee. The wound could have been treated, hadn’t it been for Heracles’ slaughter of Hydra, the nine-headed swamp monster, and his subsequent soaking of his arrows’ tips in the monster’s blood.

Infected forever by the magic of this poison, Chiron was headed for eternal suffering, hadn’t the gods granted him euthanasia and, in a somewhat belated recognition of Chiron’s merits as educator and humanitarian, placed his image amongst the stars of the Southern celestial hemisphere. There it houses the bright Alpha Centauri, the star closest to the Sun. If we ever attempted to travel between fixed stars, Alpha Centauri would, in all probability, be our first destination.

Science fiction aside, could a trip to another star ever become reality? In a scale model with the sun the size of a grain of sand (1 mm in diameter), Alpha Centauri would locate at thirty-seven miles away. That leaves us to ponder how far technology would have to advance for such a task, and what specific preliminaries would have to be achieved. A committee could be assembled to discuss the problem into oblivion. Or, on the other hand, we could listen to Dr. Stephen Hawking, Lucasian Professor of Mathematics at the University of Cambridge, when he predicts in his address “The Universe in a Nutshell” that progressive heating of the earth will preclude humanity’s survival through one more millenium, and that we should start thinking about resettling a contingent of the human race somewhere else in the cosmos.

Yes, we should not lose our time in discussions of what can and what cannot be done, but solve the riddle in ways Alexander the Great untied the Gordian knot: Pulling the sword from its sheathe and with a mighty swing, cutting right through that maze of entangled rope. And those devoid of a sword could roll up their sleeves and plunge into the design of an interstellar space vehicle, compute its dimensions, and specify the materials it would be crafted from. Working on paper our way through such a project would invariably show what portions are doable with present day’s technology, and where future technological advances would have to step in. Paraphrasing the jargon of good old Captain Kirk from the starship Enterprise: “Boldly designing where others fear to tread.”

An unconventional approach indeed to an engineering project of that scope, but the one and only with the potential of sparing us from never-ending “preparations.” True to the Chinese adage: “The longest voyage starts with one single step,” let’s take that step now and here.

Chapter 2 : Beyond the Solar System.

Fascinating and successful as research into the solar system has been, it revealed our planetary surroundings as nothing more than an assembly of lifeless rocky, icy, and gaseous bodies. Our stellar neighbors are the one and only hope for satisfying humanity’s collective desire, and – yes – our own, of reassuring ourselves that somewhere, maybe far, far out in the cosmos, life is waiting to be discovered.

If the sheer size of the void between Earth and even the nearest fixed stars makes the concept of interstellar space travel somewhat less than realistic, past decades of uncounted technological breakthroughs taught us that most anything that we really want to achieve can be achieved. So let’s rephrase the question of whether we could travel into the neighborhood of another fixed star, into how far present day’s technology would have to advance for making such a trip possible.

Energy for planetary probes like the Pioneers and Voyagers came from chemical reactions in rocket engines. Extra gains in cruising velocity were obtained by the gravitational "slingshot effect", a surge of acceleration obtainable in a close flyby at a massive planet. Gravitational force F is proportional to the inverse square of the distance R from the planet’s center, Abbildung in dieser Leseprobe nicht enthalten which makes the slingshot effect the stronger the closer we pass by to the planet without skimming its atmosphere or crash-landing on its surface. Such “close encounters” would simply swing the probe around the planet in a quasi-parabolic orbit, and on the way out, the probe would lose the speed previously gained. For a net gain, a booster rocket is fired at the point of closest approach, hurling the craft into a kind of “shortcut” out of the planet’s gravitational field. Hereby, cruising speed increases far more than commensurate with the booster rocket’s thrust.

This technique, first demonstrated with NASA's Mariner 10 Venus/Mercury mission in 1973-74, reduced the time for the probe’s subsequent flight to Neptune from thirty years to twelve.

Likewise, the space probe Voyager I, launched on August 20, 1977, started out with 14.4 km/sec of initial velocity and, through a swing around Jupiter, gained 16 km/sec for its way to Saturn. The same technique helped to place the Ulysses solar observer into its out-of-ecliptic trajectory over the poles of the Sun.

Voyager II, following Voyager I, reached the margins of the solar system in 1989. It could stay in contact with Earth for some 15 or 20 more years, yet it will take at least 25,000 years to reach the neighborhood of other fixed stars.

In any case, the slingshot effect falls far short of boosting the speed of chemical rockets to the levels afforded for interstellar trips. A paragraph titled "A Rocket to the Stars", by Arfken, Griffing, Kelly, and Priest in their book “University Physics” highlights that with the following quiz:

"What would be the ratio of initial mass (m o ) and final mass (m) – that is before and after burning off all the combustible available for propulsion – for a rocket supposed to travel at one tenth of the velocity of light Abbildung in dieser Leseprobe nicht enthalten, assuming that the rocket-engine ejects the escape gases at Abbildung in dieser Leseprobe nicht enthalten (typical for present day's rocket motors)?” The authors then use the Rocket equation Abbildung in dieser Leseprobe nicht enthalten to deduce the ratio of the weight of the rocket with full versus with empty with tanks from

Abbildung in dieser Leseprobe nicht enthalten as Abbildung in dieser Leseprobe nicht enthalten

“A ratio so large (expressed by a one followed by 2600 zeros)”, they conclude, “would leave not even one single atom from whatever there was when the engines got started. Thus, rockets driven by chemical reactions do not develop sufficiently high exhaust velocities for interstellar travel."

As if such news weren’t bad enough, we still have to admit that one tenth of the velocity of light 30,000 km/sec or 18,641 miles/sec) would still be far too slow for our purpose. At that speed, even such relatively short trips as the one to our closest neighbor among fixed stars, the 4.34 light-years distant Alpha Centauri, would take over forty-three years. And reaching Barnard's Star, somewhat farther out but still in the Sun’s neighborhood, takes fifty-nine.

That much for “star-to-star hopping at moderate speeds”. Clearly, we must learn to move considerably faster than Abbildung in dieser Leseprobe nicht enthalten unless we are willing to resign ourselves to boarding a spaceship as teens with no other aim than to spend our retirement years at the expedition’s stellar destination. Science fiction concepts, such as a hibernating crew aside, interstellar cruising speeds has to be far higher. The amount of energy, Abbildung in dieser Leseprobe nicht enthalten afforded for accelerating a spacecraft of the mass m to its terminal velocity v , grows with the square of v , which makes fuel consumption for reaching the desired velocities enormous (Fig.2.1, lower curve). Moreover, operating at velocities within the realm of the speed of light takes us into relativistic mechanics, where the phenomenon of mass enhancement, predicted by the special theory of relativity, begins to show (Fig.2.1, upper curve).

We lack direct experience with the relativistic mass enhancement in our daily life because the velocities we deal with here on Earth are too slow for it to be measurable. Even out in the solar system, mass enhancement effects are minimal. For instance, the orbiting velocity of Earth around the Sun, Abbildung in dieser Leseprobe nicht enthalten or Abbildung in dieser Leseprobe nicht enthalten causes a mass increase of merely Abbildung in dieser Leseprobe nicht enthalten

On the other hand, experimental proof for the reality of mass enhancement abounds in the microcosm of nuclear physics. Actually, in the design and operation of particle accelerators (a.k.a. atom-smashers or superconducting colliders) mass enhancement is the paramount design parameter. At low driving energies, the lighter particles dash ahead of their heavier counterparts, while at highest energy levels, all particles, heavy and light, tend to assume almost equal velocities as they get close to the speed of light. This because lighter particles gain mass as they speed up and tend to become nearly as massive as their heavier atomic brothers.

For example, at 1 MeV driving energy, electrons travel already at 94.1% of the speed of light (c), while the 1836 times heavier protons idle at twenty times lower speed, of 4.62% of c. By contrast, at 1000 MeV (1 GeV), electrons and protons travel at respectively 0.9999c and 0.8760c. And at 10 GeV, these figures, 0.9999c vs. 0.9963c, are all but identical, as the gap has narrowed to 0.0036c. Finally, at 100 GeV, both types of particles move at virtually the same speed. But never have particles of any kind exceeded the velocity of light, regardless of the amount of giga-electron-volts that went into speeding them up.

The reason for such a “glass ceiling” is that the mass m o of an object at rest (which we mortals experience as weight) changes when the object travels at velocities comparable with c , the speed of light. With the restmass m o for the object in repose, the mass m of the object in motion at the velocity v is given by the formula:

Abbildung in dieser Leseprobe nicht enthalten Eq. 2.1)

At “moderate” speeds, such as Abbildung in dieser Leseprobe nicht enthalten this yields

Abbildung in dieser Leseprobe nicht enthalten

a still negligible 0.05% of relativistic mass enhancement:

Even at speeds as high as c/2 (93,000 miles/sec), mass increases by a factor of only Abbildung in dieser Leseprobe nicht enthalten or by 15.5%. But from here on, it “takes off”:

51% gain at ¾ c, and Abbildung in dieser Leseprobe nicht enthalten a term which confirms that the speed of light cannot be surpassed. In Fig.2.1, this makes the Abbildung in dieser Leseprobe nicht enthalten line an asymptote of the relativistic energy curve.

The combined effects of the square law of kinetic energy and mass enhancement jack up the demand for fuel as if the laws of nature had united against human conquest of deep space. But rather then giving up, let's survey once again how dire predictions on space travel in the past have yielded to advanced technology.

A leading encyclopedia from the epoch between the two World Wars still states that rockets will never transcend into space, because the energy from exploding one kilogram of black powder wouldn’t suffice to lift the explosive’s proper weight beyond the Earth’s atmosphere. And in a 1948 article in the American Journal of Physics, titled Can We Fly to the Moon? the authors extrapolate data from the German Second World War V-2 rocket to the building of larger rockets, and reach the conclusion that a payload of 10 kg was the utmost we could some day send to the moon, but by no ways a human being.

So much for the nay-sayers. The day will come when we succeed, but as one of the preconditions for success we should recall the words of the Austrian commander, Count Raimondo Montecuccoli, coined in the 1674 campaign against Louis XIV of France: “To wage war, you need first of all money; second, you need money, and third, you also need money”, and paraphrase them into: For interstellar space travel you need first of all energy, second, energy, and third, you also need energy.

Energy in quantities that pale the paraphernalia of conventional and alternative ways for powering spacecraft, from chemical rockets to ionic propulsors, solar sails, and hitch hiking on laser beams. What’s left is one option only: The unfathomable pool of nuclear energy.

Much like the chemical reaction: 2H + O = H2O , a.k.a. combustion of hydrogen with oxygen, happens with the release of (heat) energy, the nuclear reaction Abbildung in dieser Leseprobe nicht enthalten, namely the fusion of four hydrogen nuclei into one helium nucleus, releases energy, yet on a much higher scale. In the first case, we fuse two elements, hydrogen and oxygen, into a molecular compound, commonly known as water. In the second case, we fuse several atoms of one element, hydrogen, into a new element, helium. But while a properly proportioned hydrogen/oxygen mixture ignites at a mere 580 oC (1076 oF), the bond of hydrogen nuclei with each other starts no sooner than at the stunning temperature of 10 to 15 million oC .

Those who back in 1776 marveled at the functioning of James Watt’s twin action steam engine witnessed one of the first practical demonstrations of the conversion of thermal energy into kinetic energy. But it took another 131 years and the development of the special theory of relativity to reveal the energy of nuclear reactions. It happened when Albert Einstein used the relativistic formulations for time, length, and mass, in rewriting the equations of physics in relativistic terms. In the process, the conventional formula for the kinetic energy of a mass m moving at the velocity v : Abbildung in dieser Leseprobe nicht enthalten became: Abbildung in dieser Leseprobe nicht enthalten where here again, c stands for the velocity of light.

With Abbildung in dieser Leseprobe nicht enthalten the new term, Abbildung in dieser Leseprobe nicht enthalten resembled the work of a genie, set to reveal a new, inexhaustible source of energy. If the math was correct, an unfathomable treasure was there, waiting for humanity to dig it out. Einstein rightly suspected the energy Abbildung in dieser Leseprobe nicht enthaltentrapped in the atom, a far shot at a time when the structure of the atom was yet to be discovered. Moreover, the theory of relativity had been deduced with relation to the macrocosms, and hadn’t been expected to reveal anything within the atomic domain, lest of all such mind bogging figures as Abbildung in dieser Leseprobe nicht enthalten, which with Abbildung in dieser Leseprobe nicht enthaltenbecomes Abbildung in dieser Leseprobe nicht enthalten several orders of magnitude above the energy output of chemical reactions.

For instance, the heat of combustion of one kilogram of gasoline is 11,700 kcal. With 4186 joule per kilocalorie, that equals Abbildung in dieser Leseprobe nicht enthaltenThus, the atomic energy in the same quantity of gasoline, Abbildung in dieser Leseprobe nicht enthalten amounts to Abbildung in dieser Leseprobe nicht enthalten almost two billion times the combustible’s thermal energy. If our family car had an “atomic engine”, one tank full of fuel would take us . . All right, you got the idea.

However, only a hypothetical matter/antimatter reaction would release the full amount of energy the Abbildung in dieser Leseprobe nicht enthalten formula predicts, and even if we were to succeed in the unlikely task of producing antimatter in greater quantities than one nucleus at a time, storing such a substance would be like safekeeping a stick of dynamite in a pool of molten iron. Actually, Einstein himself was less than optimistic about the ways of tapping the vast resource of energy he had discovered.

The concept of atoms as the ultimate and indivisible building blocks of matter goes back to the 5th century BC Grecian philosophers Democritus and Leucippus, but their ideas lacked experimental proof. The roots of a fact-based atomic theory appear in John Dalton’s 1808 publication on chemical reactions, where atoms are shown to unite into molecular compounds in ratios expressed by whole numbers. In 1911, Ernest Rutherford came up with the perception of the atom as a positively charged nucleus with elementary negative charges (electrons) orbiting around it. But it remained an open question how electrons, known as the carriers of electric current, could circulate without losing their kinetic energy to the generation of electromagnetic waves. Mind you, the electrons passing through the windings of a radio transmitter’s coil radiate such waves to our hearts’ content. But they consume power in the process.

To this end, Niels Bohr (1885-1962) deduced in 1913 from the quantum theory the existence of a number of discreet orbits for electrons to use without radiating. Herewith, the concept of the atom with a positively charged nucleus, surrounded by orbiting electrons, became a realistic possibility. It also became obvious that the bulk of an atom’s inherent energy had to be housed in the nucleus, because the electrical energy of the electron cloud, or total ionization energy, of 13.6 electron volt for hydrogen, fell far short of Einstein’s Abbildung in dieser Leseprobe nicht enthaltenpredictions. Hence the name-change from atomic energy to nuclear energy.

The hydrogen atom consists of a single nucleus, the positively charged proton, and one orbiting electron, wherein the mass of the proton is 1836 times that of the electron. This presence of one negative and one positive elementary electric charge makes the atom electrically neutral, which is the state of matter as we know it. However, under special circumstances, such as in the presence of electric fields, atoms may lose or gain one or more electrons and become ions – charged atoms. This happens for instance in fluorescent lamps and in galvanic solutions for metal plating.

Helium, the second lightest chemical element, has a nucleus of two protons, each carrying a positive electric charge of Abbildung in dieser Leseprobe nicht enthalten Since equal electrical charges repeal each other, such a nucleus would spontaneously disintegrate if it weren’t for the “strong force”, a force of nature present exclusively within the domain of atomic nuclei, yet conspicuously absent in the surrounding electron cloud and in macrocosmic mechanics. The range of the strong force, of Abbildung in dieser Leseprobe nicht enthalten determines how big a stable atomic nucleus can be. Thus we may speculate (in an admittedly simplistic manner) that, if the reach of the strong force were twice of what it actually is, the number of chemical elements would increase by a factor of Abbildung in dieser Leseprobe nicht enthalten to approximately 800.

As it is, bismuth 209, with 83 protons and 126 neutrons, is the heaviest stable element. The remaining elements with atomic numbers from 84 (Polonium) to 105 (Hahnium) decay with half-lives ranging from several times the age of the universe down to microseconds.

Since the “strong force” is meant to overcome the mutual repulsion of protons, we can get an idea of its magnitude by figuring how strongly two identical elementary electric charges would repel each other if spaced by the diameter of a proton, or Abbildung in dieser Leseprobe nicht enthalten center to center, so that they just touch. With the proton’s charge of Abbildung in dieser Leseprobe nicht enthalten Coulomb’s Law gives the repulsive force F as:

Abbildung in dieser Leseprobe nicht enthalten or for the case in point:

Abbildung in dieser Leseprobe nicht enthalten

the equivalent of about nine pounds of force. If that figure seems less than overwhelming, remember that it refers to one single pair of protons. From the diameter of the proton, of Abbildung in dieser Leseprobe nicht enthalten we can deduce that (in purely geometric terms) the area of one square centimeter (10-4 square meter) could house Abbildung in dieser Leseprobe nicht enthaltenprotons, whose summed up repulsive forces amount to: Abbildung in dieser Leseprobe nicht enthalten

In reality, atomic nuclei with more than one proton exist only in the presence of neutrons, chargeless particles of circa the same size and mass as protons. If we imagine our two protons separated by a pair of closely spaced neutrons, the center distance from proton to proton becomes Abbildung in dieser Leseprobe nicht enthalten what we had before, and since electrostatic forces decrease with the square of distance, only one third of the former value, that is Abbildung in dieser Leseprobe nicht enthaltenremains.

To generate this kind of pressure in a (super-strong) air cylinder of, say, 9 mm (0.90 cm) internal diameter and therefore Abbildung in dieser Leseprobe nicht enthaltencross sectional area, we would have to load it with Abbildung in dieser Leseprobe nicht enthaltenThat’s approximately the mutual gravitational attraction of a pair of globes, each the size and the mass of Earth, placed next to each other. Newton’s law gives for that case: Abbildung in dieser Leseprobe nicht enthalten We may find the nine millimeter air cylinder on e-bay, but will surely miss out on a second Earth to weigh down the piston. Clearly, mechanical compression is not the way to go, but this exercise helps to visualize the mind bogging magnitude of the forces involved in the fusion process.

The alternative is inertial forces, usually defined as the reluctance of mass to change its state of motion. The acceleration a of a mass m, speeding up from its initial velocity v 1 to its final velocity v 2 in the time interval Abbildung in dieser Leseprobe nicht enthalten is given by: Abbildung in dieser Leseprobe nicht enthalten The force for obtaining that acceleration follows from Newton’s second law Abbildung in dieser Leseprobe nicht enthalten For instance, if a car weighing 1500 kg is specified as accelerating in ten seconds from zero to 100 km/h , that is by Abbildung in dieser Leseprobe nicht enthalten the vehicle’s engine has to generate the force of Abbildung in dieser Leseprobe nicht enthalten Likewise, your brakes have to act with that same force of 425 kgf in order to bring the car to a ten seconds stop.

However, if a car hits a solid wall, the time for coming to a stop drops to near zero. For that case of Abbildung in dieser Leseprobe nicht enthalten Newton’s law would read Abbildung in dieser Leseprobe nicht enthalten which shows why the forces developed in accidental impacts bring about such catastrophic results.

Conversely, the potential of inertial forces for reaching extremely high values helps in the task of edging protons into the range of the strong nuclear force. To that end, protons must impact each other at velocities commensurate with temperatures as high as ten to fifteen million degrees Kelvin (degrees Kelvin = degrees C + 273). This kind of heat is present at the core of the Sun, where the consistent fusion of hydrogen nuclei into helium nuclei generates the energy the Sun radiates into space and on picturesque beaches here on Earth.

For the hydrogen bomb, high pressure and high temperatures are achieved in an envelope of fissionable uranium 235, involving a measure of lithium hydride. At the onset of the envelope’s explosion, the lithium hydride decays into the hydrogen isotopes deuterium and tritium, which then fuse into helium nuclei.

Fissionable materials, such as the envelope of the H-bomb, are the classic way to obtain nuclear energy. In both cases, fission and fusion, merely a minute part of the nuclear masses converts into energy at the rate given by Einstein's mass/energy formula, Abbildung in dieser Leseprobe nicht enthalten But even the small fractions of nuclear energy, released in the conversion of one element into another of the periodic table exceed the energy obtained from chemical reactions by several orders of magnitude. Just compare a nuclear mushroom with the explosion of a conventional bomb or missile.

Nuclear fission occurs spontaneously in heavy atoms, and was first observed as radioactivity. All isotopes of heavy elements with mass numbers greater than 206 and atomic numbers greater than 83 are radioactive, insofar as they emit energetic radiation and particle beams. The degree of radioactivity of a substance is given by its half-life, the time afforded for 50% of the parent material to decay into lighter elements. The half-life of natural Uranium, U-238, a weakly radiating material, is 4.468 billion years, roughly the age of the Earth. U235, the classic atomic bomb material, ranks second with its half-life of 0.704 billion years, approximately the time since the birth of life on our planet.

Bombardment with slow neutrons of uranium-235, uranium-233, and plutonium-239 may cause a runaway fission in those materials, which therefore have been classified as fissile material. In a typical fission reaction, initial capture of a neutron changes U-235 into U-236, an uranium isotope that splits unevenly into two lighter elements, strontium-90 and the rare gas xenon-144, according to:

Abbildung in dieser Leseprobe nicht enthalten

This and similar Uranium fission reactions thus yield in the average about 200 million electron-volt (200 MeV) of energy per atom of parent material, compared to 26.7 million electron-volt produced in a hydrogen to fusion reaction. However, this apparent advantage of the fission process changes if we consider – instead of the reactions' integral energy output – the energy released per atomic mass unit u .

This unit of nuclear mass has been standardized as Abbildung in dieser Leseprobe nicht enthalten of the mass of the neutral carbon atom, which nucleus consists of six protons and six neutrons, and closely matches the mass of an atom of the lightest element, hydrogen, of the atomic mass 1.0080 u .

For conversion, one kilogram (2.20 lb) of mass equals Abbildung in dieser Leseprobe nicht enthaltenor inversely, the mass u, expressed in kilogram, is:

Abbildung in dieser Leseprobe nicht enthalten

Herein, the negative exponentAbbildung in dieser Leseprobe nicht enthaltenstands for the reciprocal ofAbbildung in dieser Leseprobe nicht enthalten

The 26.7 MeV of energy from a fusion reaction stem from the fusion of two hydrogen atoms into one helium atom, while fission derives its 200 MeV from the 235 unit masses of the nucleus of the isotope Uranium 235. Therefore, the energy outputs per atomic mass unit from these processes are:

Fission: Abbildung in dieser Leseprobe nicht enthalten

Fusion: Abbildung in dieser Leseprobe nicht enthalten

For equal amounts (by mass or weight) of nuclear fuel, fusion thus yields:

Abbildung in dieser Leseprobe nicht enthaltentimes the energy of fission.

Fusion powered nuclear engines must thus be expected to develop nearly eight times the energy of fission engines.

Furthermore, fissionable material cannot be stored in quantities exceeding its particular critical mass. A solid sphere of uranium enriched to more than 90% of U-235 will spontaneously chain react if its weight exceeds 114.5 pounds (about seven inches diameter). The Hiroshima bomb weighed in total circa 64 kg. Fissionable uranium isotopes would thus have to be stored in carefully separated, small pieces - and beware – should an interstellar speed-bump shake some of them together.

By contrast, liquefied hydrogen as rocket fuel would be free of such storage problems, but an engine capable of triggering, upholding and controlling fusion reactions has yet to be developed. Hydrogen to helium fusion happens consistently in the Sun’s interior and is triggered in the course of star formation by heat generated by gravitational compression of the gas at the star’s center. The weight of the star’s outer layers, responsible for initiating the chain reaction, also takes care of keeping it confined.

But the reenactment of this natural process in an earthly environment is far more complex than one would have expected. So far, nuclear fusion as a self-sustaining chain-reaction has been achieved in explosions only, and present-day controlled fusion reactors, typified by the tokamak design, like the TFTR at Princeton, still use up more energy than they manage to generate.

Undeniably, the monetary investment into that kind technology will be mind bogging, and if it were to no other objective than nuclear propulsion for future starships, such moneys would never become available. What works in our favor is the world’s ever-growing need for electricity.

Herein, nuclear fission powerplants have lost the popular appeal they once enjoyed as people’s proverbial “source of inexpensive energy”. First, because their “cheap” energy turned out the most expensive, and second for a series of accidents, most notably the meltdown in Russia’s Chernobyl, which killed thirty thousand people, and sent radioactive rain as far as central Europe. Even if future plants could be built to considerably higher safety standards, a secure strategy for disposing of the ever growing number of burned out reactor cores, containing radioactive material with half lives of thousands of years, has yet to be found.

By contrast, radioactivity in fusion reactions stems from neutron radiation and decays rapidly. Unless we wish for the return of the “coal-age”, nuclear fusion is left as e only viable source of energy on the day when oil wells run dry. As we approach this benchmark, research into nuclear fusion power is bound to increase. That’s good news for us spacecraft builders, and should embolden us to take present-days nuclear fusion devices as the stepping stones in mankind’s foray into the vastness of interstellar space.

Among several applicable nuclear fusion reactions, the highest energy output comes from the fusion of four hydrogen nuclei into a helium nucleus in a process known as the Carbon Cycle. It got this name because carbon is part of the reaction chain, but, like a catalyst in chemical reactions, reemerges upon completion of the process without being bound by the end product – helium. In nuclear lingo, this interesting fusion reaction reads as follows:

Abbildung in dieser Leseprobe nicht enthalten

Herein, the superscripts stand for the atomic mass of the element in point, and the subscripts for its atomic number, the number of positive electric unit charges in the nucleus. Further, Abbildung in dieser Leseprobe nicht enthalten symbolizes the positron, a positive elementary electrical charge, and thus the counterpart to the electron, Abbildung in dieser Leseprobe nicht enthalten the negative elementary electric charge. Note that the carbon atom, Abbildung in dieser Leseprobe nicht enthalten, which initiates the reaction, is being regenerated in the last step of the process, ready to be used all over again.

Essentially, these formulas stipulate that four hydrogen nuclei are being used up to generate one helium nucleus. The energy released in the process stems from the difference of 0.02879 mass units (u) between the total of the mass of four hydrogen nuclei and the mass of one helium nucleus. Since mass cannot simply vanish, it gets converted into energy at the rate predicted by Einstein’s relativistic formula Abbildung in dieser Leseprobe nicht enthalten With mass expressed in atomic mass units (u), and energy in electron-volt, this formula can also be expressed as:

1 atomic unity mass = 931 mega-electron-volt,

or: Abbildung in dieser Leseprobe nicht enthalten

Thus, the energy from the conversion of hydrogen into helium results as:

Abbildung in dieser Leseprobe nicht enthalten

and as far as energy output is concerned, we can express the entire Carbon Cycle reaction by:

Abbildung in dieser Leseprobe nicht enthalten

With 1.0080 u for the atomic mass of hydrogen, we figure the energy released per mass unit of hydrogen as:

Abbildung in dieser Leseprobe nicht enthalten

Herein, energy is still expressed in electron-volt, a unit tailored for the microcosm of nuclear physics, where the familiar joule would be too bulky for convenience and introduce conversion constants in most equations.

In the present application however, we have to get back to units compatible with the formulas of traditional physics and engineering. Energy – often thought of as an abstract concept of physics – actually is what we pay for with our monthly utility bills. Electric utilities could as well charge us for mega-electron-volts, but for practical reasons, they rely on kilowatt-hours (kWh) instead (Here, the prefix kilo stands for the multiplier of 1000, e.g. 1 kilowatt = 1000 watt, and the watt-hour equals Abbildung in dieser Leseprobe nicht enthaltenor 3600 joules). In principle, our electricity meters could just as well be made to display joules, or even electron-volts, although some among us consumers could find that less than convenient.

The relationship between the units of electron-volt and joule is:

Abbildung in dieser Leseprobe nicht enthalten

Thus, the above figure of 6.622 MeV converts into:

Abbildung in dieser Leseprobe nicht enthalten

On the other hand, we have the relation of

Abbildung in dieser Leseprobe nicht enthalten

which gives us for the mass of the hydrogen nucleus, of 1.0080 u :

Abbildung in dieser Leseprobe nicht enthalten

Therefore, the energy E o , generated by nuclear fusion of hydrogen into helium is:

Abbildung in dieser Leseprobe nicht enthalten

Neglecting the minute mass of the electron that circles the nucleus in a hydrogen atom, we see that every single kilogram of hydrogen, fed into a hypothetical fusion engine, would yield 634.2 trillion joules of energy. Such figures dwarf even federal budget forecasts, but would they suffice for powering a trip between stars?

There is one way only to find out. Let’s take it!

Chapter 3 : The Rocket Equation

Achilles, the superman in Hellenistic folklore, couldn't win a race with the turtle, to which he allowed – say – a 100 yards headstart. Although Achilles runs ten times as fast as his opponent, he reaches the place from were the turtle took off no sooner than the latter has crawled 10 yards ahead, to 110 yards from Achilles’ start-line. When Achilles makes it to 110, he finds the turtle at 111. At 111, the turtle is still ahead of him, at 111.1. Since such reasoning can be carried on indefinitely, one might be tempted to conclude that Achilles, had he survived into our days, would still be racing the turtle.

Now, take a rocket, which proper weight we consider negligible in comparison to the weight of the fuel in its tanks. Suppose that, under these conditions, such a 1000 lb “all fuel” rocket travels its first mile by burning up half, that is 500 lbs of its propellant. With the total of its weight thus reduced to Abbildung in dieser Leseprobe nicht enthalten the rocket needs only 250 pounds of fuel for the second mile of the trip, while its weight drops to 250 lbs. The third mile takes Abbildung in dieser Leseprobe nicht enthalten 62.5 lbs go for the forth mile, 31.25 for the fifth, and so on, as if the fuel in the tanks would last forever.

In short: As the rocket is losing weight by burning away its fuel reserves, it needs less and less fuel per mile, the farther it gets. Where will it end? In theory, never. In quantum theory, until only one atom of fuel is left, with nothing to react with.

Both those problems sound like phony logic, but only for the “Sophisma of Zeno of Elea,” the Achilles/turtle race, is that actually the case: He who cannot reach the turtle is not Achilles, but our train of thoughts that, in consecutively decreasing steps, stops short of the critical 111.11111. . . yard point where, in real life, Achilles would be bound to catch up with his competitor.

By contrast, the conclusion of the rocket problem is not the result of flawed logic. Rather it is indicative for the potential of multi-stage rocket propulsion in general. That the outcome seems unreal comes from the precondition of a zero-mass rocket-structure, unconceivable in the real world.

Rocket propulsion can be understood as the action of unidirectional pressure from exploding gases. In Fig.3.1) a tank or vessel has been internally pressurized to p atmospheres (atm) by the ignition of an explosive charge within. As long as the exhaust port (of cross sectional area Abbildung in dieser Leseprobe nicht enthalten) remains sealed (Fig.3.1 left), pressure on any of the walls of the tank is compensated for by equal pressure against the opposite wall, and the vessel remains at rest.

However, with the opening of the nozzle (Fig.3.1, right), the area of the left wall of the vessel is being reduced by the nozzle’s cross sectional area A . Gas pressure p throughout the vessel remains unchanged, but the areas subjected to that pressure are no longer of identical size. They differ by the area A, and the resulting force, Abbildung in dieser Leseprobe nicht enthalten tends to move the vessel, which in the process metamorphosed into a rocket, to the right.

Gas springs, like the ones that hold the trunk of a car open, are a good example of that very same principle in everyday life. They too derive their force from uniform gas pressure acting on areas of different size, given by the full cross-sectional area of the piston on one side, and this same area , minus the cross-sectional area of the piston rod, on the other.

Rockets operate best in the vacuum of space, where p is being used to its full potential. On earth, the 1 atm atmospheric outside pressure reduces the effective exhaust pressure to Abbildung in dieser Leseprobe nicht enthalten

The working of an arrangement like Fig.3.1) can be demonstrated by releasing a blown up toy balloon with its neck still open. It readily moves contrary to the flow of the escaping air as long as some degree of internal pressure is left. In a rocket motor, this pressure is consistently refurbished through the combustion of fuel, such as hydrogen and oxygen.

Rockets have a long history. In the 12th and 13th centuries, the Chinese used black powder driven rockets in fireworks, and tipped them with incendiary devices for use in warfare. The Mongols and Arabs readily adopted these “Fire Arrows” in their raids on towns and fortresses.

In Europe, rockets were tried in warfare, but lost out to firearms early in the 14th century, following the invention of black gunpowder by the English monk Roger Bacon and the German alchemist Berthold Schwarz. Guns were used soon after (in 1334) for the defense of the Episcopal See of Meersburg, Germany, while rockets lived on in fireworks. Handwritings from 1529 by Conrad Haas even mention multistage rockets.

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