Some years ago, I spotted a small green hardcover book at a library de-accession sale, a 1966 text on rocket science, which I snatched up for a quarter. Later, I found another copy offered on the Internet for about $400. Now, as we approach the 50th Anniversary of Apollo 11 and NASA begins to launch humans back to low Earth orbit, the facsimile reprint of this undeservedly forgotten book is a remarkable testament to the reach of visionary thinking in the early years toward a spacefaring future.
Thrust into Space offers an unusually insightful exposition of the physics of spaceflight, including an elementary but especially clear treatment of celestial mechanics, along with an always quantitative, if back-of-the-envelope, outline of the energetics, efficiency, and economics of advanced propulsion systems that could one day carry humans across the solar system. Measuring a nicely compact 8 × 5 in., the slender navy-yellow paperback is easily carried about for devoted study. In his Preface, Hunter optimistically remarks that the text “is written for the modern, technically oriented high school student. Only comparatively simple expressions are utilized. Much of the massive calculations performed today are used to refine the last ounce of performance out of very complicated systems.”
Did the man say ounces?! Yes, as common to 1960s engineering in America, this book uses “English” units, but this is not so bad as it sounds. Many of the plots are given in a non-dimensional form, with distances scaled in planetary radii or Astronomical Units and velocities relative to the relevant circular orbit speed. The text's 77 numbered equations make no explicit use of vectors or calculus and almost no trigonometry. Readers equipped with more advanced mathematical tools can take pleasure in deriving for themselves some results only stated.
Consider, for example, the challenge of reproducing Fig. 4–12 showing fast transfer times to the outer planets as a function of Earth launch velocities spanning both elliptical and hyperbolic (solar-escape) trajectories, hard to find in modern texts. Although I am not entirely satisfied with the inelegant patch of nested algebraic expressions I devised for this, I can confirm that the figure is (of course) correctly plotted. The payoff in the resulting display of these curves is the breath-taking reduction in flight times with only a modest increase in launch velocity over the (two-body) minimum-energy Hohmann transfer.
Fully 31 of the text's 56 numerical plots are given in the log-log or semi-log form extolled in this journal by Sanjoy Mahajan [Am. J. Phys. 86(11), 859], many sporting multiple curves, all of these along with the other 17 diagrams clearly labeled with readably sized lettering. There are only a very few typographical errors. The most serious in my reading of the original was in Eq. (3–10) on p. 57, where factor 2 should appear in the denominator instead of the numerator. Now, the 50th Anniversary Edition provides the correction.
Among the many illuminating nuggets: on pp. 62–63, Hunter notes that the attainment of Earth geosynchronous orbit requires an impulsive velocity six percent higher than the escape speed. On p. 66, “a jet transport circling the earth would utilize about the same energy as required for an earth satellite.” (Readers working through the quantitative discussion on this page will enjoy verifying that this amounts to about 3 J/kg or, as Hunter puts it, about 4 kW-h/lb.) Figure 4–4 displays the launch velocities required for Hohmann transfers to the other planets, along with the extra increments needed to establish either highly elliptical or low circular orbits at arrival. This shows that travel to Mercury is comparably difficult to flights to the outer planets. It also shows that with gravitational braking, highly elliptical orbits about the destination planets can be achieved with only relatively small additions to the launch velocities, except at Mercury and Pluto. Noting that flight to anywhere in the solar system can be achieved with a total velocity increment comparable to what is required to go to the moon and back, Hunter adds that “unfortunately, travel times throughout much of the system are excessive.” He apparently did not anticipate today's programmatic tolerance for even longer flights, as for NASA's Jupiter orbiters, six and five years for the Galileo and Juno spacecraft, as compared with the 2.7 year Hohmann transfer.
However, Hunter also provides a discussion of gravity-assisted trajectories for interplanetary flight, coyly noting that “the use of Jupiter is particularly effective” and that “if one had enough patience and good enough guidance systems, a probe could be deflected from Jupiter around the Sun in such a way as to travel to Saturn.” This was eight years before the execution of exactly this maneuver by Pioneer 11, and the likely inspiration for its fictional anticipation in Arthur Clarke's 1968 novel, 2001–A Space Odyssey. According to the new foreword in the 50th Anniversary Edition by J. D. Crouch, Hunter “was the first to recognize the strong effect of Jupiter's gravity on planetary probe vehicles and was instrumental in opening up the outer solar system by supplementing rocket performance with planetary gravitational impulse.” Hunter's first recorded claim to this idea was a 1963 white paper presented to the National Aeronautics and Space Council, also published the next year in Astronautics and Aeronautics,1 both oddly missing from the list of his publications in the reprint's new Addendum. In his paper, Hunter referenced the earlier (but then unpublished) work of Michael Minovitch, as recorded in a JPL Technical Report without consideration of Jupiter, who later claimed the “invention” as his own.2 This is not the place to settle competing claims as to the origin of the idea. But as Hunter notes on p. 98, the Russian Lunik III used an analogous lunar flyby to raise its perigee and adjust its flight path as early as 1958.
Hunter discusses the gravity assist conceptually, as an elastic collision between a space vehicle and a moving planet, and states that the maximum heliocentric speed post-encounter is twice the planet's orbital velocity, in the case of Jupiter 26 km s–1. (Pioneer 10 came close to this, with a heliocentric post-Jupiter speed of 22.4 km s–1.) The maximum post-flyby speed corresponds to a head-on collision, for which the “swing around angle” is 180°. Although the text omits the explicit expression for the deflection angle, Fig. 4–9 plots this as a function of the ratio of the hyperbolic excess velocity to the escape velocity. In practice, only a massive planet, for which , permits a large deflection. Further details can be found in the treatment by Müller3 and others in AJP.
As early as p. 77, Hunter remarks that “much of the rest of this book will be devoted to the question of what can be done other than simply to adapt ballistic missiles for space purposes,” and most of the last third of his text is devoted to nuclear rockets, including their configuration as single-stage spaceships. This is a reflection of the unimaginably different context of the book's political milieu. President Kennedy's 1961 address to Congress, urging America “to take longer strides,” was presented with four new proposals for space. “First… the goal, before this decade is out, of landing a man on the moon…” Little remembered, however, is Kennedy's second proposal for 23 million dollars to fund the development of a nuclear rocket, in his words promising even more exciting exploration, “perhaps to the very end of the solar system itself.” While his third and fourth proposals, for even larger sums for communication and weather satellites paved the way for their indispensable contribution to life today, the nuclear rocket soon fell out of favor among advisors to succeeding presidents. But when Thrust Into Space was first published, nuclear propulsion was the apparent coming future, with dramatically successful ground tests of the NERVA rocket (cf. p. 130) staged the same year, and Hunter helped push the idea while a member of the Space Council under Presidents Kennedy and Johnson. Today, James Hansen and other climate scientists are beginning to challenge the anti-nuclear sentiment, emphasizing the overwhelmingly superior safety record of nuclear energy as compared to fossil fuels, even accounting for the design failures of Chernobyl and Fukishima.4 NASA has recently begun to invest again in R&D for space nuclear propulsion.
Mindful of nuclear safety (cf. pp. 179–181), Hunter stresses that “although spaceships present only small problems in terms of general earth atmospheric contamination, we are extremely sensitive on the subject.” I have been unable to trace the computational source of Fig. 5–18, plotting the radioactive dose (in Rem = 0.01 Sv) to a ground observer in the event of a catastrophic failure of a gas core rocket, depending on its ignition altitude, but it is obviously based on some atmospheric diffusion model. The plotted curves allege that the explosion of a 120 GW rocket above 2 km would impose a dose to someone on the ground less than 0.01 mSv, roughly the same as the natural background exposure over one day. (A revision of this figure with a mesoscale dispersion model would make an interesting project for an atmospheric science student.)
On p. 140, Hunter invites the reader to “imagine a true spaceship. Such a vehicle should be fast enough to travel throughout the solar system in a few weeks time, and economical enough so that current cost barriers would become quaint primitive estimates.” As he blithely remarks on p. 186, “truly convenient solar transportation will require velocities as high as 500,000 feet per second” [152 km s–1] or about five times the Earth's heliocentric orbit velocity. At this speed, the traditional viewpoint that planetary gravity fields are the primary challenge to space travel would be almost irrelevant, and likewise gravity assisted flybys would be practically useless. Or as stated on p. 143, “The moral is: a rolling spaceship gathers little gravity.”
Of course the attainment of such speeds, for a useful payload fraction, presents other problems and Hunter emphasizes cooling as the essential limitation on the specific impulse (“the time for which one pound of propellant could produce one pound of thrust”). Higher specific impulse requires higher engine temperatures, and solid structures are limited by their melting points. Looking beyond the proven performance of the NERVA solid core reactor, Hunter mentions the possibility of a liquid core engine but then devotes several more pages to his clearly favorite concept of a nuclear gas core rocket operating with a uranium plasma at thousands of degrees and a specific impulse of 2500 s (as compared with ∼400 s for chemical propellants) or, with the help of large radiators, perhaps up to 10,000 s. A hypothetical gaseous fission transport and its calculated performance are described along with a diagram of its arrangement on pp. 182–184, which Hunter admits “looks more like a Buck Rogers spaceship than a conventional ballistic missile.” The ultimate gas core engine might achieve perfect containment of its uranium plasma within a transparent quartz bottle, flushed and cooled with a surrounding stream of propellant. (This idea, nicknamed the “nuclear light bulb,” was studied for some years at the United Aircraft Corporation, but the cancellation of its modest funding in the 1970s prevented a conclusive demonstration of its feasibility.)
Unlike chemical rockets, nuclear thermal rockets employ an unburned propellant such as hydrogen or water, not only for their reaction mass but also for regenerative cooling, separate from their fission (or fusion) fuel. The distinction is essential to both the physics and economics of Hunter's “Solar System Spaceships,” with fully 7 figures devoted to plots of estimated costs in $/lb. (When nuclear rocket science meets the “dismal science,” the prospects may not be so dismal after all.) During his early career at Douglas Aircraft, Hunter was in charge of calculations on airline performance and economics and was one of the few in the aerospace industry to combine this knowledge with his later experience in space vehicle design. He gives no source equations for this part of his treatment, except as they stand on the celestial mechanics, but here, are a few notes on my reconstruction of his figures. As an important preliminary, Fig. 5–7 plots the variation of the specific impulse with the “dilution” (the ratio D of the propellant flow rate to the fission/fusion rate). These log-log plotted curves are scaled as , where is the undiluted impulse, mnemonically given as c/22 g = 1.4 × 106 s for fission and c/8 g = 3.8 × 106 s for fusion. Although not derived, this schematic approximation is consistent with a linear proportionality between the dilution ratio and gas temperature, along with the square root dependence of Isp on the latter. This relationship, along with the fuel cost (Hunter assumes $5000/lb for uranium, actually more than the current price), then yields the fuel plus propellant cost per weight, also depending on the “separation” S for the ratio of the unburned fuel lost to the expelled propellant. (For the regimes of interest, D ≫ 1 and S ≪ 0.1.) While these details of nuclear rocket economy are impossible to find in any modern text, they are the essential basis for Hunter's amazing claim on p. 178 for “space-ship-transportation costs throughout the solar system which are not much greater than terrestrial transportation costs.” Further quantitative details on spaceship cost analysis are given in a 1960 paper by Hunter, Matheson, and Trapp.5
On pp. 196–201, Hunter considers still more advanced fusion rockets, reprising the cost vs. specific impulse for these in Fig. 6–7. He mentions the decreased shielding needed for the deuterium + helium-3 reaction, owing to its low yield of neutrons, but considers the price of this fuel to be as expensive as fission (this before the post-Apollo realization that He-3 may be refined from the lunar regolith). Finally, he mentions the possibility of photon and mass annihilation rockets, along with the relativistic counterpart to the rocket equation, amusingly very different looking than the classical physics version.
The appended Bibliography of only 17 references is unthinkably short by modern standards but includes Sutton's classic text on rocket propulsion, historical works by Goddard, Hohmann, and Tsiolkovsky, two classic books on extra-terrestrial intelligence, and Susanne Langer's Philosophy in a New Key. A complete list of symbols, along with a detailed glossary and index, adds further to the many little things that make this book so clear and readable.
A few warnings on conventions: While many celestial mechanics texts reference their zero potential energy level to an infinite altitude or radial distance, Hunter instead chooses his to coincide with the Earth's or other planetary surface (cf. pp. 29 and 55), for which the total energy is always positive, thereby matching the parlance of aviation and ballistic missiles. Some authors prefer to keep the semi-major axis a of a hyperbolic orbit positive, though this requires a change in the sign within the Vis-Viva equation. Hunter does not change his Vis-Viva but allows a to flip sign. Some authors use a fractional difference in place of an initial-to-final mass ratio in their rocket equation. So watch your gauges and beware of blindly comparing formulas between one book and another.
For all its wit and technical detail, this is a deeply humanistic work. In the final chapter, Hunter asserts that humanity's expansion across the solar system could bring “a new Renaissance” and foresees that “space is the one place where we can obtain natural resources without damaging either the Earth's ecological balance or its natural beauty.” Having previously noted that gas core rockets would routinely operate beyond solar escape speed, here he imagines that “the plunge of high performance spaceships deep into unknown territories, where even their tremendous control of energy may not always be adequate, should supply a new basis for drama, music and art.” If not for a long time yet, maybe a day brought sooner than otherwise by the new readers of this book.
References
Michael Allison worked for many years at the Goddard Institute for Space Studies in New York City and is now an Adjunct Professor of Astronomy at Columbia University. A member of the NASA/ESA study group for the Cassini/Huygens mission to Saturn and Titan, he also served on the science teams for several planetary flight projects, most recently Juno at Jupiter.
