This paper considers the problems associated with the human exploration of Mars, and also proposes solutions. First, several reasons for exploring Mars are given. Then, the problem of manned travel to Mars is taken up, with focus on the energy requirements imposed by the laws of celestial mechanics, and the limitations of present-day rocket technology. Next, two solutions are examined: chemical propulsion, facilitated by refueling on Mars, and electric propulsion. The paper concludes with a cost/benefit analysis of the human exploration of Mars.
Why should humans explore Mars?
One reason to explore Mars is scientific. We can increase the store of human knowledge through the exploration of Mars. Consider, for example, one very important scientific question: How did life originate on Earth? In order to shed more light on this question, scientists can ask a related question: What is the probability of life originating in a particular planetary environment? Exploring Mars will provide much data that may eventually allow scientists to reasonably estimate this probability.
Granted that there are valid scientific reasons for exploring Mars, the next question is: Why use humans? Why not rely on robots, which are much cheaper and safer? The answer is that robots have limits. Consider, for example, the task of searching for Martian fossils that may be four billion years old. The oldest fossils on Earth have been found by paleontologists in remote corners of the globe, after years of pain-staking effort. Had this task been left up to robots, it is unlikely that these fossils would have been found. Even the best of robots do not come close to matching the sophistication of human beings. This sophistication has been essential for making the most profound discoveries here on Earth.
There are other reasons to explore Mars. According to President Bush, "The desire to explore and understand is part of our character." [1] The European Space Agency is also planning to send humans to Mars. According to their first planning document, "The desire to explore is a fundamental heritage of the European people." [1] However, ESA’s director of human spaceflight, Daniel Sacotte, recently stated: "The search for territory is basic for animals and for mankind. …let’s go for having the territory." [1] So, eventual colonization is another reason for the manned exploration of Mars. Indeed, the very-long-term survival of the human species may depend upon having self-sustaining colonies on multiple worlds, as insurance against a planetary catastrophe such as a large asteroid impact.
Obstacles to the human exploration of Mars
Sending humans to Mars will not be easy. There is a minimum energy requirement for a trip to Mars, determined by the gravitational fields of Earth, the Sun and Mars. To escape the Earth’s gravity, a vehicle must attain a velocity of about 11.2 km/s. Once free of Earth’s gravity, the spacecraft needs additional velocity to travel to Mars, which is further away from the Sun and therefore in a higher energy orbit than the Earth. In order to minimize this additional velocity, the vehicle can enter an elliptical orbit known as a Hohmann transfer orbit, and the journey can be timed to arrive at Mars when it is closest to the Sun (perihelion). The additional velocity needed to reach Mars when it is at perihelion, 1.38 AU from the Sun, is 2.3 km/s. (1 AU, or astronomical unit, is the average distance from the Earth to the Sun.) However, if the vehicle leaves Earth at a velocity of about 11.4 km/s, or just 0.2 km/s above escape velocity, it will retain the necessary velocity of 2.3 km/s when it is far from Earth.
Once at Mars, the spaceship must slow down to enter orbit there, and a landing craft will have to decelerate to land. It may be possible to accomplish most of this velocity change through gravity assist and aerobraking maneuvers, so we will consider the velocity requirement for a trip to Mars to be 11.5 km/s. However, humans may very well prefer a plan that includes a return trip to Earth! Mars’ escape velocity is 5.0 km/s. The additional velocity needed to enter a Hohmann transfer orbit back to Earth is 2.6 km/s. (This time I assumed Mars to be at it’s average distance from the Sun, 1.52 AU.) If the spacecraft leaves the vicinity of Mars at about 5.6 km/s (relative to Mars), it can enter the minimum energy transfer orbit back to Earth. Finally, the spaceship must enter Earth orbit, and the astronauts must land on Earth. Again, I assume these maneuvers can be accomplished with gravity assist and aerobraking techniques.
From the above analysis, the total energy requirement for a round trip to Mars that must be supplied by reaction engines is 11.5 + 5.6 = 17.1 km/s. By way of comparison, a round trip to the Moon requires a total velocity of 11.1 + 2(2.4) = 15.9 km/s. For this calculation I used the lunar escape velocity of 2.4 km/s. Since the Moon has no atmosphere, a landing craft must use rocket engines to land as well as take off, which doubles the velocity requirement.
An additional velocity requirement of 1.2 km/s over what was accomplished by the Apollo missions in 1969 doesn’t sound too bad. However, a trip to the Moon takes 3 days, whereas a trip to Mars takes about 8 months. Also, humans on Mars will have to wait about 15 months before they can return to Earth, because the two planets must be in the correct alignment before the return journey can begin. (The Hohmann transfer orbit intersects the Earth’s orbit at only one point, and the Earth and the returning spaceship must both be at that place at the same time.) The total journey time is about 2 years and 8 months, whereas the Apollo 17 mission lasted just 12 days. This means the Mars trip will require about 50 times more supplies – food, air and water – than a trip to the Moon. Also, we cannot expect humans to live 17 months in a capsule the size of Apollo. The astronauts will need much larger living quarters, including exercise facilities to maintain their health in the weightless environment of space. We may also expect a larger crew to be sent to Mars, with sufficient equipment to make their 15 month stay on Mars productive.
Let us suppose that the Mars mission will be 15 times larger than an Apollo mission. Also, the additional 1.2 km/s velocity requirement increases the total mass of fuel required over the lunar mission by about 30%. (From the rocket equation, with an exhaust velocity of 4.4 km/s, the ratio of initial mass to final mass is exp(1.2/4.4) = 1.3.) Thus, the equivalent of about 20 Saturn V rockets will be required to send a human expedition to Mars.
Solutions – technology to support the human exploration of Mars
While it is conceivable that a manned mission to Mars could be mounted using the equivalent of 20 Saturn V rockets, it is unlikely that any country or consortium of countries will attempt such a feat. Ways must be found to reduce the cost of a manned trip to Mars. How can the energy requirements be reduced?
Aerospace engineer Robert Zubrin has proposed that a manned trip to Mars make use of the resources of the Martian atmosphere to reduce the fuel and supplies that must be sent to the Red Planet. He proposes that the expedition bring hydrogen and a small nuclear reactor to Mars. The atmosphere of Mars is 95% carbon dioxide. The Sabatier reaction can be used to produce methane and water from hydrogen and Martian carbon dioxide. [2] Also, the atmospheric carbon dioxide can be dissociated to produce oxygen. Thus, methane fuel, oxygen and water can be produced on Mars, avoiding the need to transport these supplies from Earth. Not having to haul the fuel needed for the return trip all the way to Mars reduces the total mass of the mission by about an order of magnitude, and the total cost of the mission can be greatly reduced.
Zubrin envisions sending an unmanned ship to Mars first, before the manned expedition. [3] This vehicle would land on Mars and get to work, producing methane, oxygen and water. The manned expedition would not leave Earth until the necessary supplies were manufactured on Mars and ready for use. Zubrin gives an example of the unmanned ship bringing 6 tons of liquid hydrogen cargo, a 100-kW nuclear reactor and other supplies to be used by the human expedition. Using a chemical processing unit, 108 tons of methane and oxygen could be produced. 96 tons would be used to fuel the Earth return vehicle, and 12 tons would be used for long-range ground cars. This plan reduces by a factor of 16 to 1 the amount of fuel and oxidizer that would have to be sent to Mars for the return journey. Thus, instead of the equivalent of 20 Saturn Vs, the Martian mission could be accomplished with the equivalent of perhaps two or three Saturn Vs.
There is evidence that NASA is taking this idea of refueling on Mars seriously. In their recently announced plans to return to the Moon, NASA has proposed using methane fuel for the service module of the Crew Exploration Vehicle and also for the ascent stage of the lunar lander. [4] It appears that NASA wants to gain experience with methane rockets prior to a manned trip to Mars.
Another approach to reducing the cost of a manned Mars mission is to make use of electric propulsion rather than chemical propulsion for the transfer from Earth orbit to Mars orbit and back. The rocket equation tells us that the fuel efficiency of a rocket depends on it’s exhaust velocity. To achieve a given velocity change (delta-vee) for a given amount of payload, less propellant is needed if the exhaust velocity is greater. Unfortunately, chemical rockets are limited to about 4.5 km/s exhaust velocity. This limitation can be avoided through the use of electric rockets. Currently, the most practical version of the electric rocket is the ion rocket. (Plasma rockets are also under development, but they are not ready for deployment. [5])
With the ion drive, electric fields are used to accelerate ions to very high speeds. Ion rockets have been flown on deep space missions with an exhaust velocity of 30 km/s, more than six times faster than the best chemical rockets. Ion rockets have proven to be very reliable, and the technology is relatively simple and safe. One disadvantage of ion drive is that it produces very low thrust, and cannot be used to lift off from the surface of a planet. Once in orbit, however, the ion rocket is very practical.
Why is the thrust of the electric rocket so low? Newton’s laws of motion tell us that there is an inescapable trade-off between propellant efficiency and thrust. For a given power level, efficiency and thrust are inversely related. The formula is: power = ½ thrust ´ exhaust velocity. (Higher exhaust velocity means greater efficiency, as the rocket needs less propellant to reach the desired velocity.) Rockets normally operate at maximum power. To illustrate this trade-off, let’s consider an example. Suppose an ion engine has an exhaust velocity of 50 km/s (as seems possible in the near future). Further suppose that this engine (or bank of engines) is powered by a 15 MW nuclear reactor and effectively utilizes 80% of this power. Applying the above formula, the thrust is just 480 newtons, or 120 pounds. If this thrust is applied to a spaceship weighing 100 metric tons, the acceleration is only 0.0048 m/s/s, or about 0.00049 g. This is why ion drives cannot be used on planetary surfaces. Once in orbit, however, the ion engine can run continuously for months or years, producing very large velocity changes. For example, applying a constant thrust of 0.00049 g for 5 months will produce the fantastic velocity change of 63 km/s! Coupled with nuclear power, the electric rocket can make manned interplanetary travel practical.
The ESA is planning to use ion propulsion in their manned Mars program. However, Europe is not willing to consider nuclear power. Instead, they plan to use solar power. Unfortunately, the power-to-weight ratio of solar cells is only 1/40 that of lightweight nuclear reactors. [6] Using a 10,000 square foot array of solar cells, European physicist Jose Antonio Gonzales del Amo estimates that the ion engines will produce 10.5 newtons of thrust, and will take five years to deliver an 11-ton cargo payload to Mars. [7] Therefore, the European plan is to use ion propulsion for an unmanned cargo ship, and to send humans in a faster chemical-powered spaceship once the cargo ship has reached Mars. Gonzales estimates that the use of ion propulsion will double the cargo that can be sent to Mars affordably.
Because of their continuous, low thrust acceleration, spacecraft driven by electric rockets do not follow elliptical transfer orbits. Instead, they follow spiral orbits. An electric rocket spirals around a planet in ever-larger orbits until escape velocity is reached. At that point, the ion-powered vehicle follows a spiral trajectory away from the Sun. At about the halfway point of its journey, the spaceship must turn around and begin decelerating, so that it has time to slow down enough to be captured by the gravity of the destination planet.
Currently, ion engines use the heavy inert gas xenon as their propellant. However, if an ion-propelled spaceship is to make the return journey from Mars back to Earth, it could be refueled with the lighter inert gas argon, which is present in the air of Mars. Although argon is not quite as efficient a propellant as xenon, the savings due to not having to cart it all the way from Earth to Mars makes this a worthwhile trade-off. The argon would have to be transported from the surface of Mars to orbit by a chemically powered rocket, presumably using methane fuel also obtained from the Martian atmosphere.
Conclusion
Do the benefits of a trip to Mars justify the cost of such a journey? First, let’s consider the cost. According to Robert Zubrin, in 1989, prior to considering his Mars Direct plan, NASA estimated the cost of a manned trip to Mars at $400 billion. After adopting Zubrin’s concept of utilizing the Martian atmosphere, NASA revised its estimate down to $50 billion in the late 1990s. [8] Utilizing ion propulsion could further reduce this cost by a factor of two.
The benefits of the human exploration of Mars are harder to quantify.
We cannot put a dollar figure on the human desire to explore, our thirst
for knowledge, or the benefit of eventually becoming a multi-planet, spacefaring
civilization. However, these benefits are real and substantial.
Some day, humans will set foot on Mars.
References
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