1. Orbital Mechanics

The planets in our solar system are bound to the sun by gravity in elliptical orbits, a discovery that ranks among the most revolutionary in the history of science and instantly rendered the study of calculus useful for all time. However, it is sufficient to this discussion to understand that the Earth and Mars follow orbits that place them in the same relative positions every 26 months and that the absolute distances between the two planets follow a 15-year cycle. At their closest points during the 26-month cycle Mars appears bright red-orange in the night sky; at the closest oppositions during the 15-year cycle, Mars appears twice as large from Earth as it does when it is farthest. Optimum launch opportunities are defined by the lowest possible mass of the spacecraft that must be propelled, because the greater the mass the more fuel is needed, which further increases the mass and cost of the expedition. The mass/energy requirements follow the 26-month cycles within the 15-year cycles; energy requirements within the 26-month cycle vary by 60 percent and within the 15-year cycle by a factor of ten. The differences are huge and, essentially, define when spacecraft can be launched to intercept Mars.

The physics, math, and engineering necessary to identify the "optimum" scenario for an expedition to Mars were understood by Werner von Braun who included the calculations in an appendix to a science fiction story he wrote to counter boredom while serving the nascent U.S. rocket program in 1947-48; the austere life among the German scientists interned at White Sands, New Mexico, was similar in some ways to what might be expected on a planetary expedition. The manuscript was apparently unremarkable, but von Braun used the technical appendix as the basis of a lecture he gave at the First Symposium on Spaceflight held at the Hayden Planetarium in New York City in 1951. The appendix was published in a special edition of the German journal Weltraumfahrt in 1952 and later that year as a book, titled Das Marsprojekt. It was translated into English and published in the United States in 1953.

Von Braun's plan involved 70 crewmembers and ten 4,000-ton ships that would be assembled in low-Earth orbit from parts launched by three-stage winged ferry rockets; a staggering 950 launches would be required to lift the components, supplies, and fuel out of Earth's gravity well and to support assembly of the fleet in orbit. Seven of the ten interplanetary ships would resemble tinker toys made of girders and spheres and lack the streamlining necessary for a planetary landing, but three would have bullet-shaped fuselages equipped with wings to glide through the thin atmosphere of Mars. Rocket engines would propel the fleet on a minimum-energy Earth-to-Mars trajectory with crews discarding the empty fuel tanks during the eight-month weightless cruise phase. Rockets would be fired again to slow the fleet for insertion into Mars orbit. After surveying the planet for suitable sites, one of the winged ships would be dispatched to land on skids at the polar ice cap that is seasonally visible through telescopes from Earth. The crew would then make an arduous 4,000-mile mechanized traverse to build a landing strip near the equator for the two remaining winged spacecraft to land on wheels. The wings would be removed and the fuselages elevated to a vertical position in preparation for launch, rendezvous, and return to Earth with the ships remaining in orbit, many months in the future. Von Braun's plan, which is called a conjunction class mission due to the relative positions of the planets at launch, required the least energy (mass and cost) of all launch options, but would subject the crews and equipment to eight-month transits and 16 months on the surface, for a mission duration of nearly three years. Von Braun believed the journey would be possible by the mid-point of the 21st Century.

The Mars Project attracted the attention of author, Cornelius Ryan, who served on the editorial staff of Collier's, a weekly magazine with nearly three-million subscribers and a tradition of shaping public opinion and government policy. Ryan commissioned von Braun and other leading space scientists, writers, and astronomical artists of the period to prepare a series of articles based on The Mars Project. The series, titled "Man Will Conquer Space Soon!" was published in eight, beautifully-illustrated installments between March 1952 and April 1954. The primary difference between von Braun's original plan and the one described in the magazine series was the addition of a toroidal space station in Earth orbit to facilitate assembly of the interplanetary ships. The donut-shaped structure became the archetypal space station form in popular culture and the articles propelled von Braun to national prominence and fueled the collective imagination of post-war America. Von Braun and Willy Ley promptly produced four books that expanded on the topics covered in the Collier's series and included a revised plan for an expedition to Mars that involved 12 crew members, two ships, and "only" 400 launches of fuel, supplies, and components for assembly in orbit. Walt Disney and producer Ward Kimball were among those inspired by von Braun's plans and hired him and others to help develop three episodes for the wildly popular Disneyland television program. "Man in Space" was broadcast in March 1955 to an audience of more than 40 million viewers, including President Dwight Eisenhower who called Walt Disney the next day to request a copy of the program that could be shown to key Pentagon officials (Smith, 1978). "Man and the Moon" aired in December 1955 and, like the previous episode, used documentary footage, on-screen appearances by von Braun and others, and narrated animation to provide remarkably accurate predictions of future events; the programs described the likely effects of weightlessness on humans and introduced the public to a new field of study, called Space Medicine. The third episode in the series, "Mars and Beyond," featured ships with solar-powered ion engines suggested by another German scientist, Ernst Stuhlinger, rather than von Braun's chemical rockets; the program was broadcast on 4 December 1957, two months after the Soviet Union shocked the world with the launch of Sputnik, the first artificial satellite.

The technical appendix to von Braun's unsuccessful attempt at creative writing and the subsequent lectures, magazine articles, books, television episodes, and of course Sputnik, led directly to the creation of NASA in 1958. The agency's initial focus was on matching the Soviet's accomplishments and then shifted to landing humans on the Moon in response to President Kennedy's famous directive. However, Mars remained the ultimate goal of the German-born scientists, and others who they influenced, despite their immediate concerns. For example, Stuhlinger, who had worked with von Braun during the war and served as director of the space science lab at the Marshall Space Flight Center, proposed a new approach to Mars in 1962 (Portree, 2001). The plan involved five ships, each with a crew of three astronauts, and paid greater attention to reliability and human factors issues than previous mission plans. In particular, the spacecraft were designed to spin to provide acceleration equal to one-tenth of Earth's gravity to mitigate the negative effects of weightlessness on the crew; three of the ships would each carry a 70-ton Mars lander, which provided the triple redundancy that became NASA's standard for ensuring reliability; and all 15 members of the expedition could return to Earth in a single ship if necessary. The most notable consideration in this regard was Stuhlinger's selection of an "opposition class" trajectory, which requires more energy and longer transits to and from Mars than von Braun's conjunction class plan, but a much shorter surface stay and overall mission duration. In other words, an opposition class plan might cost more to implement than a conjunction class mission, but would subject equipment and humans to less risk due to substantially shorter exposures. Stuhlinger argued that it was better to use more fuel, which would incur greater cost, in order to minimize the risk (i.e., increase the probability of a successful outcome). The debate continues to this day.

2. Estimating Risk

Risk is generally understood to be the quantifiable likelihood of loss or less-than-expected results. The concept is something with which we all are familiar. Every decision we make from the most trivial to the most important is attended by some sort of evaluation and consideration of the costs, benefits, likelihood of a successful outcome, and possible negative consequences. Humans are not particularly good at estimating risk, despite our extensive personal experience with the task. Research shows that we have a tendency to underestimate risk in circumstances where we have some control, and to overrate risk when we have little or no control. This is why we tend to be more fearful of flying in a commercial airliner than driving an automobile, even though the odds of dying on the road are 16 times greater than dying in a plane. Riding a motorcycle, which carries a risk of fatality 17 times that of driving a car, more clearly illustrates the influence of perceived control and other subjective factors when making decisions concerning acceptable risk.

Deciding whether or how to send a human expedition to Mars is more complicated than deciding if one should drive, ride, or fly on vacation, but the process is essentially the same: estimate costs, benefits, and probabilities of various outcomes, and then compare the benefits that would result from success to the consequences of failure while simultaneously comparing the probabilities of the outcomes. This approach produces objective recommendations, but requires quantification of all variables. When considering the risks of an expedition to Mars it is possible to calculate the probability of mission-threatening solar activity from historical records and to identify the failure rates of all mechanical components through testing. Even the expected incidences of medical and behavioral problems can be inferred from space analog experience, as illustrated by the following tables, which are derived from a spreadsheet that was configured by the current author to calculate some of the risks and incidence rates that might be expected on Mars expeditions, based on data from Antarctic research stations.

The tables compare conjunction and opposition class expedition plans with the durations of mission segments listed on the row labeled Days. The values in the row labeled Behavioral Problem assume a 3.3% per year incidence rate of serious behavioral problems throughout the durations of the two mission options (i.e., Conjunction Class/Long Stay, 905 days total; and Opposition Class/Short Stay, 661 days total). The row labeled Differential assumes a 3.3% incidence rate during the interplanetary transit phases and a 2% rate while on the surface of Mars, when confinement would probably be less of a factor and other stressors might be offset by the novelty of task performance. A serious behavioral problem was defined as symptoms that normally would require hospitalization and the assumptions were based on incidence rates of behavioral problems reported from Antarctic experience (Matusov, 1968; Gunderson, 1968; Lugg, 1977; Rivolier and Bachelard, 1988).

Table 1.

More recent incidence rates (Otto, personal communication 2008) suggest that the initial estimates might be low. Substituting 6% for the 3.3% incidence rate during transits causes the expected occurrence of a behavioral problem in a crew of six to increase from .374 to .534 for the long stay option and from .350 to .626 for the short stay option. That is, if the incidence rate of behavioral problems while on the surface were to be one-third to one-half of the rate during transit, the probability of a serious problem occurring becomes greater for the short stay option, due to the substantially longer time that must be spent by the crew confined to the spacecraft than in the long stay option. However, the long stay option generates a higher probability if the incidence rate were to remain constant throughout the mission. A uniform .06 incidence rate would increase the probability of a serious behavioral problem to nearly 90 percent for the Conjunction Class, long stay option.

Table 2.

Similar calculations were made to predict the incidence of physical injury, again based on Antarctic experience, but reduced by half to accommodate likely differences in tasks and protective equipment during a Mars expedition. The table shows that a crew of six should expect four injuries that prevent task performance at least temporarily during the long stay option and one during the short stay. Injuries are more likely to occur while working on the surface of the planet than in transit and probably will involve trauma to the hands, based on analog experience.

Table 3.

It is reasonable to question whether incidence rates for behavioral problems and physical injuries from Antarctic research stations should be used to estimate what might occur during a Mars expedition. Astronauts are subjected to more rigorous selection procedures than Antarctic personnel. On the other hand, Antarctic personnel spend a maximum of 12 months "on the ice," while members of an opposition or conjunction class expedition to Mars, such as those described here, would experience greater isolation and confinement for durations that are nearly two to three times as long.

The risks and likely incidence rates reported here would be recalculated by mission planners to ensure that the most appropriate data are used and that all issues that might influence differential rates are considered. Other risks would, of course, be calculated using relevant data. Although preliminary, the exercise shows that risks can be estimated mathematically. However, the possible benefits of an expedition are more difficult to predict, because the subject, by definition, involves the unknown.

3. Estimating Benefits

The decision process requires an estimate of the benefits that would derive from a successful expedition outcome. Estimating benefits and defining success in the context of the unknown are fundamentally subjective tasks, the products of which are determined by the explicit and implicit purposes of the expedition. This raises the question, why do nations and individuals explore? A partial list of historical reasons includes, searching for trade routes; surveying to facilitate commercial and/or military navigation; prospecting for new resources; enhancing national or individual prestige; and, contributing to science, which is the most recent addition to the reasons for exploration.

Calculating the likely benefits of exploration is made difficult because some benefits are subjective, intangible, and/or devoid of practical application. For example, Roald Amundsen was the first to reach the South Pole and the first to navigate the Northwest Passage, which contributed to notoriety for Amundsen and national pride for Norway, but neither accomplishment produced tangible benefits. Further, many of the discoveries made by explorers of the past were completely unexpected. The most notable example is Columbus, who was searching for Asia when he landed in the New World.

The polar explorers, whose expeditions usually were funded privately through subscription and the proceeds from book sales and lecture fees, were criticized for risking human lives. The primary criticism of space exploration, which is sponsored by governments, is the belief that there are more pressing social and economic issues that deserve government attention and resources. However, it is important to note that the relatively meager budgets of the world's space agencies contribute substantively to medical, technological, and economic development in addition to achieving explicit scientific objectives. Space exploration also inspires and enriches us subjectively.

It is impossible to predict all likely benefits of an expedition to Mars, but one of the most practical will be an effective countermeasure to bone demineralization, which must be discovered on Earth before any humans depart on a long voyage to the Red Planet. Muscles atrophy and bones become porous from disuse in the absence of gravity's normal influences. Two or more hours of strenuous exercise each day will prevent space explorers from being as weak as kittens when they arrive at their destination and specific resistive exercise appears to mitigate bone demineralization. However, exercise alone will not save interplanetary explorers from developing fragile bones. Something else is needed or there will be no expedition to Mars and, for this reason, scores of scientists are working on possible solutions. One or more of the treatments eventually will become available to the general public, which will remove the fear of premature death from a broken bone from the aging process. The cost to North American society resulting from broken hips alone each year is approximately equal to NASA's annual budget.

The potential benefits that will result from developing a countermeasure to bone demineralization are conveniently quantifiable, but most benefits of Mars exploration, other than creating jobs and fostering innovation and the development of technical and scientific skills, will be intangible. In particular, what metric can be used to calculate the value of knowing more about another planet in our solar system, or that life did or did not exist during an earlier epoch on Mars? Identifying all of the likely benefits in order to obtain support or otherwise justify expeditions can be so problematic that some polar explorers gave up in exasperation. For example, Fridtjof Nansen wrote,

Roald Amundsen responded more bluntly to his critics: "Little minds have room only for thoughts of bread and butter."

4. Minimizing Risk

Muscle atrophy, bone demineralization, and radiation loading require development of countermeasures to preserve health and performance of crew during long-duration space exploration; the risk of over-exposure to harmful radiation is the least understood of these factors and the one that presents the greatest technical challenges. In contrast, there are four basic design strategies for reducing the risk of component or system failure:

5. Implications

The primary implication of this discussion concerns the effects of time on human behavior, because time is a factor that can transform almost any issue into a serious problem. As shown by the preceding exercise, attempts to minimize risk by reducing the overall mission duration might actually increase the incidence of behavioral problems if the plan requires longer periods of confinement during transit. Further, the estimates of risk based on Antarctic experience identified tradeoffs between behavioral problems and physical injuries when comparing conjunction and opposition-class expeditions. The optimum solution would be to greatly reduce the time spent in transit by replacing chemical rockets with a faster method of propulsion.

Werner von Braun looked to the Antarctic experiences of his era for guidance when identifying the possible sources of risk for his Mars project, as we have done here. Von Braun concluded,

Such a grim outcome is unlikely based on space analog and previous space exploration experience. However, several expeditions during the heroic and modern periods were jeopardized by the deteriorating mental states of one or more participants. Only these long expeditions of the past come close to the durations currently projected for opposition and conjunction class Mars missions. More experience with planetary-type operations is needed to ensure the reliability of spacecraft and human crew during three years of continuous operation.

Mars has beckoned since the first humans gazed at the night sky and observed its distinctive color and movement. It is our nearest planetary neighbor and has been assumed, since before we reached the Moon, to be our next destination. Mars is a worthy objective for explorers, even if the benefits that might accrue were to be limited to intangible additions to scientific knowledge. But the question must be asked: Are the risks worth the likely benefits at this time? The answer is yes, but there are other options with lower risks and potentially greater benefits.

6. Recommendation

The Earth and Mars will remain locked in their 15-year cyclical dance until the Sun expands and consumes the inner planets, an event predicted to occur in about five billion years. In other words, Mars does not threaten our existence and will remain available to us for exploration for a very long time. However, there are many known astronomical bodies in our solar system that pose enormous risk to our planet and countless others that have yet to be discovered. The likelihood and potential consequences of an asteroid or comet impacting the Earth were not fully appreciated during the era of initial Mars mission planning, which influenced our expectations, but the many large craters still evident on Earth suggest an on-going threat and recent research has linked such events in the distant past to mass extinctions. At the time of this writing more than 1,000 objects are categorized as Potentially Hazardous Asteroids and astronomers add frequently to the list, with some discoveries made only days before they pass within a lunar distance of Earth.

Six-month expeditions by three-person crews on space ships composed of at least two Orion-like vehicles could explore asteroids in nearby orbits within a few years of deciding to do so, compared to decades to send humans to Mars. The expeditions would gather information about the objects that pose collision threats with the intention of developing methods to protect Earth. The missions also could lead to mining and other exploitation of the asteroids, while at the same time helping to prepare for the human exploration of Mars. Most important, expeditions to asteroids would expose the crews and equipment to risk for durations similar to current tours of duty onboard the International Space Station and the benefits would be practical and possibly Earth-saving information and experience. We should continue making plans to explore Mars and eventually establish a permanent presence; our species is vulnerable and will be less so when no longer limited to one world. We have a subjective attachment to Mars and exploring asteroids should be part of the plan to get there. The destinations are not mutually exclusive, but Mars attracts our attention while the asteroids demand it.

Pittsburgh at L-2 by Chesley Bonestell, 1976.