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 or supervolcano eruption.  According to the renowned astrophysicist Stephen Hawking, "It is important for the human race to spread out into space for the survival of the species.  Life on Earth is at the ever-increasing risk of being wiped out by a disaster, such as sudden global warming, nuclear war, a genetically engineered virus or other dangers we have not yet thought of [11]."

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 the Earth, Sun, and Mars.  Let's estimate this minimum energy requirement.  To do this, we must first calculate the total velocity change a rocket must produce in order to reach Mars.  To escape the Earth’s gravity, a vehicle must attain a velocity of at least 11.2 km/s (kilometers per second) or 7 mi/s (miles per second).  Once free of Earth’s gravity, the spacecraft needs additional velocity to travel to Mars, which is farther away from the Sun and therefore "higher up" in the Sun's gravitational field.  In order to minimize this additional velocity, the vehicle can enter an elliptical orbit known as a Hohmann transfer orbit.  Also, the journey can be timed to arrive at Mars when it is closest to the Sun (this distance is called 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.)  It turns out that if the spacecraft takes off from Earth at 11.4 km/s, or just 0.2 km/s above Earth's escape velocity, it will retain the necessary velocity of 2.3 km/s once it is far away from Earth.

Once at Mars, the spaceship must slow down to enter orbit there, and a landing craft will have to slow down still more.  It should be possible to accomplish most of this velocity change through aerobraking maneuvers rather than with rocket engines.  In order to aerobrake, the vehicle must skim through the upper atmosphere of Mars, using frictional drag to slow it down.  NASA has used this maneuver successfully in the past [12].  So, let's consider the minimum velocity change that must be supplied by rocket engines to reach Mars to be 11.5 km/s.  However, humans may very well prefer a plan that includes a return trip back to Earth!  The escape velocity from Mars is 5.0 km/s.  Plus, the spaceship will need an additional 2.6 km/s in order to enter a Hohmann transfer orbit back to Earth (assuming Mars is at its average distance from the Sun, 1.52 AU).  It turns out that if the spacecraft takes off from Mars at 5.6 km/s, or just 0.6 km/s above Mars' escape velocity, it will retain the necessary velocity of 2.6 km/s once it is far away from Mars.  Finally, once the spaceship reaches Earth, it will need to slow down so that the astronauts can land safely.  Again, let's assume this can be accomplished through aerobraking, so that no additional rocket fuel will be needed.

From the above analysis, the total velocity change for a round trip to Mars that must be supplied by rocket engines is 11.5 + 5.6 = 17.1 km/s.  By way of comparison, a round trip to the Moon requires a total velocity change 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 change needed.

An additional velocity change of 1.2 km/s over what was accomplished by the Apollo missions back 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 mission time is about 2 years and 8 months, whereas the Apollo 17 mission lasted just 12 days.  This means the Mars journey 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.  Finally, extra protection from the hazardous radiation of deep space must be supplied to the astronauts for their long voyage.

Let's suppose that the Mars mission will be 15 times larger than an Apollo mission (which required one Saturn V rocket).  Also, the additional 1.2 km/s velocity needed compared to an Apollo mission increases the amount of fuel required by another 30%.  (From the rocket equation, which is exponential, a small percentage increase in velocity requires a much larger percentage increase in fuel.  This is the great problem of space travel, in a nutshell.)  Thus, the equivalent of about 20 Saturn V rockets will be required to send a human expedition to Mars.  In terms of the new Ares V cargo rocket that NASA is developing, this is equivalent to about 18 Ares V rockets.  (These rockets will put the Mars vehicle into Earth orbit, along with the necessary fuel and supplies for the trip 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 18 or 20 Ares V rockets, it is doubtful that any country or consortium of countries will foot the bill for such a massive undertaking.  Ways must be found to reduce the cost of a manned trip to Mars.  How can the cost 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.  A chemical process known as 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 decomposed to produce oxygen.  Thus, methane fuel, oxygen and water can be produced on Mars, avoiding the need to transport these supplies all the way from Earth.  Not having to haul the fuel needed for the return trip reduces the total mass of the mission by about an order of magnitude.  In this way, the total cost of the mission can be greatly reduced.

Zubrin envisions sending an unmanned ship to Mars first, before the manned expedition departs [3].  This cargo 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 (kilowatt) 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 Martian ground cars.  This plan reduces by a factor of 16 the amount of fuel and oxidizer that would have to be sent to Mars for the return journey.  Instead of 18 to 20 Ares Vs, with this on-site refueling plan the Martian mission could be accomplished with just two to four Ares Vs.

It is clear now (June, 2008) that NASA is taking this idea of refueling on Mars seriously.  In their originally announced plans to return to the Moon, NASA proposed using methane fuel for the service module of the Orion crew exploration vehicle and also for the ascent stage of the Altair lunar lander [4].  NASA has since backed off from this ambitious plan in order to accelerate development of the Orion.  However, NASA is still funding work on methane propulsion, and may include it in later versions of Orion/Altair.  NASA considers methane to be a key part of their developing strategy to send humans to Mars.  Early indications are that methane will prove to be an excellent rocket fuel, with several advantages over existing fuels.  Methane is a high-performance, non-toxic, storable rocket fuel that is readily available throughout the solar system [10].
 

Another approach to reducing the cost of a manned Mars mission is to make use of electric propulsion rather than chemical propulsion for the deep space portion of the trip.  The rocket equation tells us that the fuel efficiency of a rocket depends on its exhaust velocity.  To achieve a given velocity change for a given amount of payload, less fuel or propellant is needed if the exhaust velocity of the rocket 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 speed.  (Ions are charged atoms that can be manipulated by electric fields.  Typically, atoms of the inert gas xenon are used.  These atoms are turned into ions by stripping them of their outer electrons, which leaves them with a positive charge.)  Ion rockets have been flown on deep space missions with an exhaust velocity of 30 km/s, more than six times greater than the best chemical rockets.

The Dawn deep space probe, launched in late 2007, is powered by ion engines [9].  Dawn is scheduled to enter into orbit around the asteroid Vesta in 2011.  After several months, Dawn will leave Vesta and journey on to the dwarf planet Ceres, which it will orbit in 2015.  In order to accomplish this unprecedented journey to two worlds, Dawn's ion engines must achieve a total velocity change of more than 10 km/s, greater than the velocity change required to reach Earth orbit.  Dawn would have to carry more than a hundred tons of chemical fuel to accomplish this mission.  Instead, Dawn carries less than half a ton of xenon propellant.

Ion rockets have proven to be very reliable, and the technology is relatively simple and safe.  One disadvantage of the ion drive is that it produces very low thrust, and cannot be used to lift off from the surface of a planet.  Once in space, however, the ion rocket is a very practical and thrifty way to travel from Earth orbit to Mars orbit and back again.

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 fuel efficiency and thrust.  For a given power level, fuel efficiency and thrust are inversely related.  The formula, derived in appendix 2 of this paper, is:  power = ½ thrust ´ exhaust velocity.  (Higher exhaust velocity is equivalent to greater fuel efficiency, as explained in appendix 2.)  Rockets normally operate at maximum power.  Therefore, at a fixed (maximum) power level, greater exhaust velocity (fuel efficiency) means lower thrust.  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 (megawatt) nuclear reactor and effectively utilizes 80% of this power.  Applying the above formula, the thrust is just 480 newtons, or 108 pounds.  (See appendix 2 for the details of this calculation.)  If this thrust is applied to a spaceship weighing 100 metric tons, then by Newton's second law (a = F/m) the acceleration is only 0.0048 m/s/s (meters per second per second), or about 0.00049 g.  (1 g, read "one gee," is the acceleration due to gravity on the surface of the Earth, about 9.8 m/s/s.)  That's less than 0.05% of the thrust a rocket needs to lift off from the Earth's surface!  This is why ion drives cannot be used on planetary surfaces.  (This also applies to advanced rockets of the far future, such as fusion or antimatter rockets - see appendix 1 for details.)  Once in orbit, however, the ion engine can run continuously for months or years, eventually 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 panels is only 1/40 that of lightweight nuclear reactors [6].  This means that a solar-electric rocket with the same mass as a nuclear-electric rocket will be much less powerful, and therefore will take much longer to reach its destination.  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].  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 chemical 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.
 
 

Appendix 1:  The problem with fusion rockets (and science fiction stories!)

I stated above that advanced rockets of the far future, such as fusion rockets, will not be able to lift off from planetary surfaces.  I better defend this statement, so contrary to so many science fiction stories!  It all goes back to this simple formula, derived in appendix 2:  power = ½ thrust ´ exhaust velocity.  Suppose we have a 100 metric ton fusion rocket, with a fusion engine capable of producing 100 GW (gigawatt) of power.  This enormous power output is equivalent to all of the commercial nuclear power plants in the U.S. - combined!  Still, this is the far future, so let's suppose this is possible.  The maximum possible exhaust velocity of a fusion engine is 30,000 km/s (one-tenth the speed of light).  This enormous exhaust velocity means the fusion engine will be fantastically fuel efficient, capable of powering interstellar missions.  Using the above formula, however, we can calculate the thrust of this fusion rocket to be only 6700 newtons, or 1500 pounds - less that one hundredth of the thrust needed for our 100 ton rocket to be able to lift off from the Earth's surface!

So how could a giant Saturn V rocket ever lift off from Earth?  The key is the exhaust velocity - by reducing the exhaust velocity, one can increase the thrust (at the cost of fuel efficiency).  To illustrate, the first stage of the Saturn V rocket put 48 GW of power into its rocket exhaust - equal to the power produced by 48 commercial nuclear power plants!  The exhaust velocity of this rocket was 2.8 km/s.  Using the above formula, the thrust works out to 34 million newtons, or 7.7 million pounds - enough to send Neil Armstrong to the moon!

In order for the advanced fusion rocket of the far future to generate enough thrust to lift off from a planetary surface (or to escape from space pirates), the rocket will have to carry a large amount of propellant (hundreds of tons), which the fusion engine could heat up and vent out the rocket nozzles at a modest exhaust velocity, say 10 km/s.  The propellant could be obtained from a planet's atmosphere or seas.  As for "torch ships" that can accelerate at 10 g's for days or weeks on end - one can show that this is not possible under any reasonable set of assumptions.
 

Appendix 2:  Derivation of the formula  power = ½ thrust ´ exhaust velocity  [13]

Thrust is another word for force.  By Newton's second law,

    F = ma

In this case, F is the thrust of the rocket exhaust, m is the mass of the exhaust gas (or consumed fuel) and a is the acceleration of the exhaust gas.  We can rewrite this formula as

    T = ma = m(v/t) = (m/t)v

where T is the thrust, m/t is the rate of fuel consumption (mass consumed per unit time), and v is the exhaust velocity.  In this form, we see that the thrust is equal to the rate of fuel consumption times the exhaust velocity.  For a given thrust, increasing the exhaust velocity decreases the rate of fuel consumption, which means greater fuel efficiency.  Now the power P of the rocket exhaust is equal to the kinetic energy of the exhaust per unit time, or

    P = ½(mv²)/t = ½[(m/t)v]v = ½ Tv

or power = ½ thrust ´ exhaust velocity.  For a fixed amount of power put into the rocket exhaust, increasing the exhaust velocity (and therefore the fuel efficiency) decreases the thrust.  This simple formula is the key to understanding the future of space travel, which will be dominated by low-thrust propulsion.

In the example given in the paper, we first solve our formula for thrust T.  Then

    T = 2P/v = 2 ´ (0.80 ´ 15,000,000) / 50,000 = 480 newtons

Since there are 4.45 newtons per pound, this is equivalent to 108 pounds of thrust.
 
 

References

1. Fred Guterl, The Race to Mars, Discover magazine, November, 2005, p. 63.
2. Robert Zubrin, Entering Space: Creating a Spacefaring Civilization, Tarcher/Putnam, 1999, p. 153.
3. Ibid., p. 102.
4. http://www.nasa.gov/mission_pages/constellation/main/index.html.
5. Franklin R. Chang Diaz, The VASIMR Rocket, Scientific American, November, 2000, p. 90.
6. Ibid., p. 97.
7. Fred Guterl, The Race to Mars, Discover magazine, November, 2005, p. 65.
8. Robert Zubrin, Entering Space: Creating a Spacefaring Civilization, Tarcher/Putnam, 1999, p. 104.
9. http://www.nasa.gov/mission_pages/dawn/main/index.html.
10. http://science.nasa.gov/headlines/y2007/04may_methaneblast.htm.
11. http://www.msnbc.msn.com/id/13293390/.
12. http://mars.jpl.nasa.gov/msp98/orbiter/aerobrake.html.
13. Arthur C. Clarke, Interplanetary Flight, Berkley, 1960, p. 157.

 
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