neil burns' physics thesis
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In his self-published book Haunted by Neil Armstrong, author Andrew Neil Burns reproduces (pp. 11-13) what he recalls having written for a physics thesis at St. Andrews College in 1963. The professor's direction was to list, in two hours, 20 challenges the United States would face in putting a man on the Moon according to John F. Kennedy's challenge.
Burns maintains he got a high score (17 points out of 20) and earned his degree based on this essay. (However he opted for a career in chartered accountancy.) He alludes to this essay several times as proof that a Moon landing before the end of the decade was out of NASA's grasp. Instead we show that Neil Burns' understanding in 1963 was either abysmally wrong, or later fails to take into account advancements made between 1963 and 1969, or both.
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At NASA the highest-level great minds such as Wernher von Braun, Max Faget, Bob Gilruth, and so forth numbered very few. The driving principles of Apollo came from this comparatively small group of well-experienced, well-organized people.
Then in the relevant industries, well-known figures such as Tom Kelly and Harrison Storms took on the major subtasks assigned to them, parceling them out among their own hierarchical organizations. Kelly even wrote a book describing how he organized his part of the Apollo project.
When Burns wrote in 1963, nearly all the high-level planning for Apollo had been completed. The debates that had been part of that process were a matter of record in the aeronautical engineering literature. In other words, the galvanizing had already occurred by 1963, but Burns was unaware of it.[1]
SCI-FI TRUMPS KEPLER AND NEWTON?
NASA has data for the speed and direction of the craft they wish to place into orbit, but the calculations are highly complex.
Here is the first of several attempts to convince the reader that productive manned space flight is just too mathematically complicated to have succeeded before the decade deadline.
Nowhere does Neil Burns give any examples of the "highly complex" calculations he says are required, nor explain exactly why they're intractable. Keep in mind Burns says he's writing as a senior physics student. Physics relies on complex models stated most often in mathematical terms, therefore not for the mathematically incompetent or faint of heart. Compared to the mathematical models Burns would have grappled with during his degree studies in physics in the 1960s, orbital mechanics is fairly straightforward.
Below we'll discover that Burns doesn't understand orbits very well. That helps explain why he can't do much more than say "the math is too hard." To someone who doesn't understand orbital mechanics the derivations would seem hopelessly abstract and inexplicable, whereas a qualified practitioner would not be dissuaded.
The mathematics behind basic orbital mechanics can be comprehended using only rudimentary algebra and trigonometry, something a 21-year-old physics student should consider old hat. And while the derivations of some of the equations comprise several pages of formal mathematics (necessarily so in a textbook), and in a few cases require advanced techniques such as calculus, the Q.E.D. equations themselves — the ones that would have to be worked in the course of a space flight — invariably comprise only a few terms and require only basic arithmetic skills to work.[2]
The formulas and equations were first announced by Arthur C. Clarke, who is credited with working out the theory relating to orbiting craft.
Arthur C. Clarke is not the progenitor of orbital mechanics, and it's preposterous of purported physics student to suggest he was.
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The quantitative foundation of orbits (Fig. 2) was laid by Johannes Kepler.[3] They were rendered in their modern form by Sir Isaac Newton, who confirmed Kepler's findings according to his own formulation of mechanics.[4] All that happened centuries ago. We have built extensively upon their work in subsequent years, but Apollo used Keplerian/Newtonian orbits as does most of commercial spacefaring today.
In fact, in his seminal "Extra-Terrestrial Relays" article in Wireless World, October 1945, Clarke presents the geostationary orbit graphically (Fig. 3, not via equations. In fact, the only equations he employs in the paper are the classic rocket equation (Tsiolkovsky) and a brief computation of mass ratios for the hypothetical launch vehicle. Neither of these equations have anything to do with orbits, nor did Clarke invent them.
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Celestial mechanics was already a highly developed science by the early 1900s. Synchronous orbits were no mystery prior to Clarke. Naturally-occurring synchronous orbits, such as that of the planet Mercury, were studied by Einstein. Arthur C. Clarke is credited with combining the idea of a geosynchronous satellite orbit and a radio relay, and for laying down the basic requirements of achieving it. That innovation, not any general revelation about orbital mechanics, is what Clarke did. He made no other significant contribution to the study of orbits.
Even in 1963 no legitimate course of study in physics would teach a student that a contemporary science fiction writer had only recently announced the underpinnings of analytical astronomy, nor allow any such belief to persist for long. Nor would any professor of physics tolerate such popular bunkum in a degree thesis.
Depending on its speed, there will be a centrifugal force driving it away from the planet, proportional to its speed.
The proper term is centripetal force. "Centrifugal" force is a layman's misnomer. The proper quantity is velocity, not speed. Finally, centripetal force is proportional to the square of the velocity.
These are not trivial errors.
Speed and velocity are different concepts in physics. A bona fide physics student is very unlikely to use one when he meant the other. Force is a vector quantity, hence the vector quantity velocity is called for. Degree students quickly eschew incorrect popular terminology such as "centrifugal." Proper terminology is one of the ways we distinguish experts from novices.
Finally, the order of magnitude dependance between two quantities in physics is the most essential part of that dependance. Physics experts do not misstate or gloss over them.
Clarke worked out that at a speed of 15,000 mph the force would balance gravity at an altitude of 150 miles.
Incorrect. At a mean altitude of 150 nautical miles (a standard measure of orbital altitude) the required mean speed for a minimally-eccentric orbit is 17,694 miles per hour. Far from being "highly complex," this value can be computed from the simple equation
v = SQRT ( μ ( (2 / r) - (1 / a) ) ) (1)where
μ is the standard gravitational parameter, r is the radius of the orbit for which the velocity is desired, and a is the semi-major axis of the relevant orbit.
Unless these forces balance the craft will carry on towards outer space. But when they do balance the craft will go into a near circular orbit around Earth.
No, that's not how orbits work. There are infinite orbits around Earth, or any other primary body, of all (conic-section) shapes and sizes (e.g., Fig. 4). A spacecraft will, in all cases, go into one of those orbits the moment it ceases accelerated flight — i.e., the moment the engine stops firing. The orbit in each case is uniquely determined by the state vector of the satellite at engine cut-off.
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If the orbit happens to intersect the atmosphere to a suitable depth, or the planet's surface, the satellite will crash. This is the orbit (i.e., ballistic trajectory) taken by ICBM warheads. They're put into orbits that "crash" them precisely onto the target on the planet's surface.
Given sufficient momentum, the satellite will pursue one of the open orbits — parabolic or hyperbolic — and by so doing leave the local system along a curved path.
But if it pursues a closed orbit, that orbit may have any eccentricity. Some of the early Earth-orbiting satellites had considerably eccentric orbits, as do comets.
Burns' concept of an orbit seems to be some single delicate condition whose parameters have to be precisely achieved or else the satellite will either crash or fly away uselessly into space to be lost forever. If so, it's very much at odds with how celestial mechanics has been formulated, understood, taught, and practiced for more than a hundred years. It's not the sort of thing he would have been taught as a physics student, and it's certainly not how orbits behave in real life.
The calculations require computing power, and is only possible if all the basic information is known. Any craft would require a computer on board to provide the next calculation.
This is misleading. The Moon has no computer, and it has pursued a stable orbit around Earth for some billions of years. The Mercury spacecraft had no computer, nor did Explorer, Sputnik, or any of the early Soviet manned spacecraft. It requires no computing power whatsoever simply to be in an orbit. And that's what spacecraft spend the vast majority of their time doing: following an orbital trajectory.
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A calculation is required only if you want to change that orbit, and then only once per change — i.e., infrequently. There is no need to perform constant computation in order to remain in some desired orbit.[5]
Burns doesn't explain what he means by "basic information." But the terms in any equation must naturally be given values if they are to be solved for some real-world problem. . In Equation (1) for determining orbital speed, three terms are needed. The first, μ, is a constant value. Term a is an unchanging property of a particular orbit, computed once by a simple equation upon entering that orbit and then left alone. Term r is derived from apogee, perigee and the desired time. As with a, apogee and perigee are unchanged for a particular orbit and can be computed once and set aside.
The computations are by no means intractable by hand. Buzz Aldrin successfully computed an orbital rendezvous during his Gemini mission using only a sextant and a slide rule. The sextant provides the "basic information." The slide rule is the "computer.""
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To be sure, the Gemini spacecraft delivered in 1963 included a digital computer supplied by IBM (Fig. 5). A descendant of this computer would go on to guide the Saturn V launch vehicle.
An onboard computer eases the burden on the crew, and a sophisticated computer expands the kinds of missions a spacecraft can do, But it is not strictly required to have one. The computations and the "basic information" that pertains to them can be held easily on a single sheet of paper and computed with a 1960s slide rule in only a few minutes.
The current size and weight of computers is very large. An onboard computer could be provided only if the craft was very big.
A common layman's misconception. We discuss the computer issue in depth here. See also Fig. 6.
The speed must be very precise or the craft will crash to the ground. NASA has no experience achieving this.
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This is a fundamental misunderstanding of orbital mechanics.
The dynamic state (velocity and position) at engine cutoff determine which orbit it will enter (Fig. 7). It won't simply "fall to the ground" necessarily if some precisely defined velocity state is not met. Most orbital insertions occur at perigee, whereafter the spacecraft rises to its apogee. Only in the most catastrophic of launch failures will a satellite's velocity be so slow, and its altitude so low, that it cannot reach some orbit. It may not be the desired orbit, but Burns insinuates there is only one orbit, and you either reach that one orbit by achieving precise velocity, or you crash.
By 1963 NASA had successfully flown all its Mercury missions and was preparing to begin the Gemini missions. It had orbited a number of unmanned satellites. To say NASA had "no experience" achieving practically useful orbits is ignorant in the extreme. By 1969 NASA had mastered advanced orbital concepts such as rendezvous and docking.
In a more sinister example, the United States Air Force in 1963 was preparing to deploy its second-generation ICBMs, which work according to the same principles as orbital insertion. The notion that precision orbital maneuvers were impossible in 1963 is in direct denial of the facts.
Once the craft is in orbit, it will be given a boost of the right amount in the right direction so that it heads precisely toward the Moon. The complexity of the calculations make the chances of doing that extremely low.
Burns continues his vague naysaying but provides no justification or example of these supposedly intractable problems. First, one doesn't "head precisely for the Moon." One embarks upon an orbit designed to place the spacecraft at a point near where the Moon will be when the spacecraft arrives. That's not a "direction," it's simply a more elongated orbit whose apogee is within the Moon's sphere of influence.
Those who have studied orbital mechanics formally, and comprehend it correctly, are quickly introduced to transfer orbits (Fig. 8). They are concurrently instilled with the maxim that every path in space is an orbit — that is, it can be described using the mathematical models of orbits. The alteration of an orbit by a posigrade maneuver so as to raise its apogee is in principle very simple.
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Consider again Equation (1) and see what could be made of it. The new desired orbit has new semi-major axis a′ which lets us compute, at the coincident point having radius r, the quantity v′, which is the velocity that the spacecraft would need to have at that point if it were in the new orbit. The quantity (v′ - v) is the delta-v required for the maneuver, to be executed about the point r.
The rest is straightforward process-control engineering. One simply fires the engine in a posigrade direction until an integrating accelerometer confirms that the required change in velocity has been achieved. This wasn't even exotic technology in 1963.
The possibility that the new orbit will orient its semi-major axis differently complicates the computation only slightly.
WE HAVE CLEARED THE TOWER
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NASA's Saturn rocket stands 13 stories and is almost entirely full of fuel. The problems they have experienced relate to the force they have to exert to absorb the massive weight of the fuel so that the whole craft can rise from the launch pad.
The 13-story height estimate suggests Burns refers to the Saturn 1 or 1B (Fig. 9), which was never intended to do more than deliver payloads to Earth orbit. The Saturn V was the launch vehicle for the lunar landing missions, but Burns does not discuss it.
Every Earth launch vehicle is "almost entirely full of fuel." A mass ratio of 20:1 is common even today, and is considered relatively indicative of all liquid-fueled launch vehicles.
In fact, the Saturn 1B was straightforward and unremarkable. It used the highly reliable Rocketdyne H-1 engines, quite capable of "absorbing the massive weight" (more non-physics terminology) of the fuel, vehicle, and payload. It was medium-sized compared to its peers and presented no special difficulties in design, development, or test. It had a perfect operational record.
Burns here simply states the requirements a successful rocket must meet. That doesn't prove that any given rocket won't able to meet them.
To date NASA has flown only one-man spacecraft. Larger crews require larger spacecraft, which exacerbate the initial boost problem. It is unlikely that NASA will solve this problem.
Burns doesn't explain why he thinks it is unlikely. He just announces without evidence or argument that it will be.
RADIATION BOOGEY MAN
Little is known of the environment the crew would encounter, but space radiation is likely and would be hazardous in the extreme. Heavy protective clothing would be required to shield them from what they cannot know.
Burns repeats a typical layman's belief regarding space radiation and the shielding it would require. We cover that question here.
Before 1969 NASA sent manned and unmanned vehicles far into the Van Allen belts and into cislunar space and, along with data from many sounding rockets, built a suitably accurate picture of the cislunar radiation environment.
"AND RETURN HIM SAFELY TO THE EARTH..."
The speed required to obtain orbit around the Moon is 15,000 mph.
Ludicrously incorrect. If the reader wanted the strongest confirmation that Neil Burns doesn't understand space flight, this is it. We suspect Burns just naively believed the single figure he cites for Earth would also apply to the Moon.
The first question to answer is which orbit? As mentioned above, there are an infinite number of orbits around the Moon, just as around the Earth, each with its own geometric shape and size and speed requirements. Because of the Moon's lesser gravity, much slower orbital speeds are appropriate for orbits around it, compared to Earth. 15,000 miles per hour is far too fast for any useful closed lunar orbit.
The Apollo LM ascent module aimed for a near-perilune insertion point just 9 nautical miles above the surface. For the desired orbit, the spacecraft velocity at insertion should be just under 3,800 miles per hour (1,700 meters per second).
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The force required to do this is beyond comprehension and the resulting G forces would probably be fatal to the astronauts.
No inertial force is "beyond comprehension" if there are reasonable estimates or boundaries for the change in velocity and the time interval. The whole point of physics is to comprehend such things, not to wave one's hands about in alarmist hyperbole when confronted with a physics problem.
We struggle to understand why Burns accepts that going from the Earth's surface to orbit at 15,000 mph is perfectly reasonable, but doing the same thing from the lunar surface is somehow invariably fatal. The change in velocity is equivalent. The "G forces" would be dramatically greater than an Earth launch only if the accelerated flight time from the lunar surface were dramatically shorter. Since Burns doesn't list his assumptions or provide any further information or calculations, so we cannot determine where this absurd fatalistic prediction comes from.
Of course the ascending lunar module did not have to reach those speeds (Fig. 10). The correct analysis of the lunar module ascent is presented here in our response to author Der Voron.
The ascending ship has to rendezvous with the mother ship, which is traveling at a huge speed. The chances of them doing this are minimal.
This belief smacks of the layman's characterization of orbital rendezvous as "trying to hit a bullet with another bullet," specifically a straight shot aimed at the spacecraft as it passes overhead. It fundamentally misinterprets the strict correspondence that nature maintains between an orbiting spacecraft's altitude and its velocity. The absolute magnitude of that velocity is inconsequential since it is simply the velocity required for that particular orbit.
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Any other object in a similar orbit, and also in the vicinity, must necessarily also have similar velocity. Hence the relative velocity between nearby orbiting spacecraft must necessarily be small. It is necessary only to launch the second spacecraft within a narrow time window as the launch site passes through the target spacecraft's orbital plane. After that, a series of stepped phasing orbits (Fig. 11) converges its position and velocity with its target. Far from being a breakneck, do-or-die exercise, orbital phasing is tedious and time-consuming, with long periods between maneuvers.
Trials have been conducted between two moving cars. It is nearly impossible to pass objects between them.
Leaving aside that Burns doesn't give any indication by whom, when, or where these alleged trials took place, two cars trying to pace each other is not an equivalent problem. Unaccelerated spacecraft flight is dictated entirely by the relatively simple physics of ballistic motion. No one has to constantly finesse a steering wheel or accelerator pedal in order to make contact.
Disorientation would be a problem. The astronauts would require a major amount of training to become adept under these circumstances, and it is impossible to recreate those circumstances on Earth.
Test pilots in high-performance aircraft had already experienced that kind of disorientation. This is why test pilots were selected to be the first astronauts. Pilot comfort and orientation had already been studied extensively during Project Mercury. For Gemini and Apollo no additional studies were needed. General disorientation can be induced on Earth using a multi-axis training fixture, and simulated fully for the space environment by aircraft flying parabolic climb-dive cycles.
DISASTROUSLY JOINED AT THE HIP
One assumes the craft will be in constant communication with the base.
Apollo was explicitly designed not to require this. The original Apollo system specification called for the potential of several Apollo spacecraft being simultaneously aloft, therefore requiring them to operate semi-autonomously while Mission Control concentrated on one of them at a time. Burns could have discovered this himself, but prefers to offer up the straw man that constant communications would be necessary for Apollo operations and therefore any interruption would be disastrous.
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Far better it was to engineer the system to be operated either locally or remotely, then to use a hybrid method in practice to provide redundancy. The Apollo spacecraft could operate entirely autonomously, without any radio link to Earth. The onboard computers contained enough information to operate the spacecraft safely for a considerable period, even through the basic maneuvers such as lunar orbit insertion or midcourse corrections to establish a free return.
So could the 1963 Gemini spacecraft, as a matter of fact, but its missions were simpler and required less automation. Paradoxically the autonomy requirement was more acute for the early programs because, unlike a Moon-bound mission that would be visible for an extended period to a single ground station, Gemini missions orbited in and out of radio coverage continuously. By 1963, American spacecraft had to operate autonomously.
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Conversely, flight controllers on the ground had the ability to "poke" commands through the telemetry link (Fig. 13) into the computer's memory, cleverly mimicking what a human pilot would enter at the DSKY. The unmanned test missions often used this feature. Most often the remote-update feature was used during manned missions to read up a refreshed state vector, integrating information received from the ground-based tracking network. This was very helpful, but not strictly necessary. It enhanced mission success, but was not required for it.
It will take a significant amount of time for a radio signal or command to be sent and returned.
A matter of less than three seconds for a round trip. Burns does not specify what actual operations would be necessary but impossible under those circumstances. Certainly closed-loop control would be problematic, but no such control was contemplated for Apollo. Nor is it necessary.
Sometimes the craft will be on the far side of the Moon and out of radio contact.
Just as the Mercury and Gemini spacecraft were regularly out of radio contact, yet accomplished their missions with a degree of autonomy appropriate to the sophistication of the onboard automation. The automation only got better between 1963 and 1969.
Unless all the calculations are performed in advance and go flawlessly there will be disastrous consequences. There are bound to be some calculations that cannot be performed.
Burns appears unable to name or describe any actual "impossible" calculations or fit them into an overall framework of mission planning. He simply assures us he's "bound to be" right about this. The basis for his assumption that space missions could never be adaptive is similarly unclear. It seems to stem from his assertion that practical orbital mechanics for spacecraft guidance and control is a nearly intractable problem due to "highly complex calculations."
The Apollo Guidance Computer (Fig. 12) had provisions for managing both accelerated and unaccelerated flight. Accelerated flight is the simplest to manage, and had been mastered in automation since the late 1940s even without the use of a computer. A digital computer solution to integrated acceleration and state-vector management was perfected in the 1950s. Burns is simply unaware of the state of the art.
For unaccelerated flight the AGC had suitable gravity models for Earth-fixed, space-fixed, and Moon-fixed orbital flight. That's all that's needed to maintain the state vector and get where you need to go.
Burns isn't clear what he means by "disastrous consequences," but we go into some detail below about relevant mission goals, priorities, and failure modes.
PSEUDO-STATISTICAL HANDWAVING
It is possible to calculate the chance of success for any one occurrence, and statistical formulas for calculating overall chances for mission success. The chances here would not be 100% on any one occurrence and would be closer to 90%.
Burns alludes to some of the correct statistical principles of reliability estimation, which are a well-developed and very important part of engineering. But rather than display any expertise in the methods by working a problem, he just plucks an arbitrary figure out of thin air.
If there are more than a few critical points, and they are all at 90%, then the percentage drops by 90% each time: 81%, 73%.
This is too simplistic. First, Burns' 90-percent guess from the previous point is now taken as gospel. It's not a real-world component reliability figure in aerospace. In aerospace we talk about how many "nines" of reliability we achieve. Hence "two nines" of reliability (a suitable non-critical standard) is a probability of success p > 0.99 or 99%. Three to four nines is more commonplace for a critical component.
Second and most important, Burns describes only one of many ways in which individual probabilities combine to estimate overall system reliability. There are disjunctive combinations and conditional combinations that improve overall reliably greatly, but which Burns does not consider.
There must be dozens of critical points in a mission, and not all of those have a high chance of success.
Pure supposition.
Some degree of criticality is inevitable in any system. But a significant part of any design engineering exercise is reducing criticality by well-known means. Let's examine how this was done for Apollo.
The lunar module employed two completely separate guidance systems. They did not depend on each other, so they can be considered independent for the purpose of statistical reliability estimations. The primary guidance system (PGNS, pronounced "pings") contained all the programs needed to land on the Moon and return again to lunar orbit. The stand-by guidance system (AGS, pronounced "aggs") was much simpler and provided only the ability to return to orbit after an aborted landing attempt.
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If we hypothetically set the reliability of PGNS to two nines (p > 0.99) and the reliability of AGS to three nines (p > 0.999, owing to its simpler design), then that probability of failure, pf, is 1-p in each case. Only PGNS can land on the Moon, so the probability of an aborted landing due to guidance failure is trivially pf < 0.01 — one chance in a hundred.
But we consider different modes of failure. The Apollo program accepted from the very start that not every mission would be successful, hence the mission classifications G, H, J, and so forth. A higher priority than mission success is the safety of the crew, which is why AGS backs up PGNS, but only in the task of getting the LM back to a stable lunar orbit. If you define failure as the disastrous loss of the LM and crew due to total guidance failure, then both AGS and PGNS have to fail. The probability of that is the combined probability of failure,
pfPGNS × pfAGS = 0.01 × 0.001 = 0.00001. (2)
Systemic redundancy is not the only way to reduce or eliminate criticality. Note that AGS serves only to get the LM to lunar orbit. Why that goal? Because the LM in a stable orbit around the Moon places the astronauts in a safe position indefinitely, until one of the flight plan contingencies can be invoked.
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Criticality not only discusses how important it is for a component to work, but how important it is for it to work at that time. In Burns' conceptualization of systemic reliability, all the critical points have to function in the blind, from one end to the other. In reality, the missions were broken up into distinct steps (Fig. 15). At each step, there was either a fail-safe (e.g., the free-return trajectory) or an evaluation step that would determine the likelihood of success in the subsequent steps. By doing this, component criticality was limited only to the step currently being executed.
Thus the first step was to get to Earth orbit. At that point the further reliability of most of the launch vehicle became moot, as did the reliability of all the launch-escape contingencies. And then an evaluation step occurs to determine whether to continue. Hence when Apollo 12 was struck by lightning and engineers feared the parachute deployment charges would fail at re-entry, the decision was made to fly the landing mission anyway because the parachutes applied only to the very last step and did not affect the crew's ability to accomplish at least some mission objectives.
For a complex mission the overall chances of success would be negligible.
Burns makes a quantitative argument with no computation. After vaguely alluding to a few concepts in statistical probability, he just declares that success must necessarily be remote. The irony in this claim is palpable because the whole point of statistical analysis is to supplant just such intuitive guesswork with computed figures, which Burns cannot provide.
A high chance of success for each mission was not required, if by "success" is meant the completion of all the mission objectives. Apollo 13 was a "successful failure" in that it failed its mission objectives, but succeeded in preserving the life of the crew. In high-risk ventures, success is rewritten to include the successful execution of a contingency plan in order to deal with some incident failure.
The chance of success is so low it might be impossible to persuade any astronauts to undertake it.
What an absurd claim! Even in 1963 Burns should have known it to be factually false. Droves of test pilots competed fiercely to be astronauts for Mercury, Gemini, and Apollo. Unlike Burns, most of these men held engineering degrees and were quite familiar with the actual probabilities in aerospace. As test pilots they were also accustomed to translating those abstract probabilities into accepted personal risks.
SUMMARY
Neil Burns makes too many mistakes and displays too little correct knowledge for us to accept that he was an adept student of physics. His conceptual understanding of orbital flight is severely deficient, and he displays no useful knowledge of the state of engineering art or its established technique.
Burns does little more than offer up denial after denial. Argument from incredulity is common enough when one is pretending to be an expert. But Burns insists on denialist predictions from an arbitrarily chosen year early in the 1960s. He thoroughly ignores everything that happened between 1963 and 1969. It's one thing to say, "I don't believe NASA will be able to solve this problem by 1969." It's another thing entirely not even to care whether NASA did solve it in the interim. Why didn't Burns, writing in 2013, revise his 1963 paper to eliminate the predictions that didn't come true? Did he think the evidence would just go away?
The author makes a classic mistake by assuming that because he estimates the pertinent science is difficult, it must therefore exceed some objective threshold of feasibility. It can't be done because he can't figure out how to do it. Too often Burns just identifies a hurdle and then begs the question of NASA being unlikely to succeed. And often that's because he overstates the problem.
Physics is largely a theoretical pursuit. It relies on lengthy derivations and esoteric discussions written in terse prose using a plethora of equations. In contrast engineering is a practical pursuit. It accomplishes great things by adopting surprisingly simple, effective practical solutions that aren't necessarily derived verbatim from theory.
Authors who argue from a pure physics standpoint, whether as experts or novices, often miss the straightforward solution because they're trying to imagine what would embody all the properties of the underlying theory. So they imagine machines that must constantly work through all the equations that pertain to rocket flight and spacecraft motion.
A great deal of rocket science derives from simple process control theory, where a simple digital integrator (1950s technology) and a few mechanical accelerometers can get you to orbit — or to Moscow. This doesn't defy Newton or ignore his equations. It only solves them in the simplest, most reliable way. Very simply control laws such as "Fire this set of thrusters if the rotation rate is greater than this desired value" could be expressed in 1960s technology with a single small circuit board. The equations that describe that motion involve moments of inertia, angular momentum, and moment arm lengths. And the engineers who build the system sized the components and calibrated the sensors using those equations. But the circuit doesn't have to know anything about those derivations.
Burns' 1963 predictions have no more a toehold in fact than the rest of his book.
NOTES
- It's worth emphasizing that Burns claims he was a 21-year-old physics student when he wrote his thesis. However, the lion's share of the thesis actually addresses engineering, not physics. Burns had no qualification as an engineer and no experience in the U.S. aerospace industry, undermining the foundation of his knowledge on most of the points that follow.
- The derivation of Kepler's Second Law, for example, involves formulating a derivative by means of calculus. But the single equation at the end that expresses Kepler's 2nd Law can be worked using only elementary multiplication.
- Epitome astronomia Copernicanae, 1617-1621. Copernicus formulated the essential geometry of the solar system. Kepler refined it and quantified it.
- Philosophiae naturalis principia mathematica, 1687.
- It is however advisable to perform periodic computation to maintain the state vector, but these computations are trivial and do not even require a computer. Mechanical integrators were included on the German V-2 during World War 2, and the same type were used in Charles S. Draper's first inertial guidance system shortly after the war. Early rockets and spacecraft first used analog tube-based integrators, then special-purpose digital integrators when the technology became commonplace.