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Travelling to Mars

The diagram at the left illustrates the famous Hohmann transfer orbit, which, in the absence of opportunities for gravity assist trajectories, is the method most economical in fuel for travelling from one planet to another.

Two large black circles represent the orbits of the Earth and Mars. The blue curved line joining them, half of an ellipse with the Sun at one focus, is the path of a spaceship going from the Earth to Mars. Earth and Mars are shown in green in their positions when the spaceship is launched from Earth, and in red in their positions when the spaceship lands on Mars. Also visible in the diagram is the Sun, as a yellow circle in the center, and there is a small dot representing the other focus of the elliptical orbit of the spaceship above the Sun. The diagram is from a viewpoint to the north of the ecliptic, so the planets as well as the spaceship are moving counter-clockwise.

If the time taken by Earth to orbit the Sun is 1 year, the time taken by Mars to orbit the Sun is about 1.881 years, and the orbital period of the spaceship in its orbit is 1.4174 years. Since the spaceship makes half of an orbit to reach Mars, the voyage there takes about .7087 years. Of course, the orbit of Mars is noticeably different from a circle, so actual mission times would vary. (The orbit of the Earth, like those of Venus and Neptune, is very close to a circle, although it, too, is an ellipse rather than a perfect circle.)

For a voyage to Mars with people aboard, however, it is desirable to use something called a free-return trajectory; that is, an orbit which would bring the spaceship back to Earth if it could not land on Mars, without the need for a major additional rocket burn. One way to do this would be to launch the spaceship from Earth with a little extra energy, so that its orbit would go out slightly beyond Mars, with an orbital period of 1.5 years instead of 1.4174 years. This would mean that its orbit would intersect that of Mars earlier, and therefore also give the astronauts a shorter trip. But it would mean that the ship would have to make two full elliptical orbits, taking 3 years, before it met Earth on its second return to the Earth's orbit.

Thus, Dr. Robert Zubrin, whose innovative plan for reaching Mars was outlined in the book The Case for Mars, recommends using a bit more extra fuel, to place the spaceship headed for Mars in an orbit with a period of 2 years. His plan, called "Mars Direct", represents the most reasonable and economical plan for reaching Mars using largely existing technology. Its outstanding feature is the original idea of sending liquid hydrogen to Mars, where it can be used, in a fairly simple process, to produce both methane and oxygen from the carbon dioxide in the Martian atmosphere for use as rocket fuel for the return journey. Another important feature of his proposal is that, to allow a spaceship with sufficient mass to be useful to be sent to Mars orbit or the Martian surface, the spacecraft will not carry the rocket fuel required to match its velocity with that of Mars upon arrival, but will instead accomplish this by means of aerobraking. This, although possible, certainly appears to me to be one of the more difficult and risky aspects of such a mission.

The greatest single difficulty of a personelled mission to Mars is the fact that people need constant supplies of air, water, and food: while Dr. Zubrin notes that it would be impractical for the astronauts to bring with them all the supplies needed for such a lengthy mission, and also that it is not possible to readily achieve near-perfect recycling of these consumables, he claims that a Mars mission is feasible if reasonably efficient recycling of air and water is combined with the necessary supplies of food for the voyage and additional supplies of air and water to balance the limitations of the recycling used.

A somewhat modified version of his proposal is the current Mars Reference Mission at NASA.

In Mars Direct, two spacecraft are involved in each mission:

The Mars Reference Mission involves three spaceships:

The Mars Reference Mission can be criticized as inefficient, because it involves sending the fuel for the return to Earth to Mars, when this can be largely avoided. This is, of course, done intentionally, for purposes of safety, to avoid dependence on the ability to produce fuel on Mars. But some have countered that an orbital rendezvous is itself a risky manouvre.

On the other hand, I recently saw a criticism of Mars Direct, on the basis that the proposed Earth return vehicle would be too cramped for a long journey in space.

Thus, as the Mars Reference Mission has been dubbed "Mars Semi-Direct", I have reacted to this by coming up with "Mars Three-Quarters Direct". This scheme may involve from three to four spacecraft per mission. If four are used, they would be as follows:

Since coming up with this modification of Dr. Zubrin's scheme, I have realized that there is further room for improvement in the concept given above. Or, at least, room for further decrease in fuel requirements for the mission.

The ship launched from Earth, carrying supplies for the return journey from Mars orbit to Earth, could be launched on a free-return trajectory to Earth, for example, one with a period of 1.5 years. Such a ship would, in three years, cross the orbit of Mars four times. Let it be launched in advance of sending the astronauts to Mars, at such a time as would lead to it encountering Mars on the fourth of those crossings.

Then, this ship would not require to be accelerated by a significant amount (of course, course corrections would be needed to ensure it did encounter both Earth and Mars) to go from Mars to Earth. Now, the astronauts would simply need to produce enough fuel on Mars to rendezvous with it.

Since it wouldn't enter Mars orbit, they would be producing more fuel on Mars than in the Mars Reference Mission; they would lift off from Mars in a small craft, providing life support sufficient only for a short journey, but the delta-V that craft would undergo, in order to match velocities with the return ship, would be sufficient to take it to Earth.

But because that craft would not have what the astronauts need to support them on the journey to Earth, it is smaller than the return craft in Mars Direct, and so the required amount of fuel to be produced on Mars is lower than in that mission profile.

If my previous mission plan were intermediate between "Mars Direct" and "Mars Semi-Direct", as this plan comes even closer to the Mars Reference Mission, I suppose it could be dubbed "Mars Five-Eighths Direct".

It has a potentially serious limitation, however. In this scheme, the safe return of the astronauts to Earth is dependent on a rendezvous with a ship that was launched from Earth over two years previously, and on that ship being sound and functional enough to bring them home safely. This kind of element of risk was something that Dr. Zubrin was very careful to avoid in his Mars Direct proposal. The risk could be reduced by making the return craft into something on the order of an O'Neill colony, with other astronauts from Earth tending it during its entire three-year journey. If we move in that direction, however, then we are starting to move in the direction of a cycler station, and this is a different concept (although there is a strong resemblance of sorts between the return craft in this scenario and the "Semi-Cycler" recently proposed by one of the Apollo 11 astronauts). Another way to reduce the risk is simply to make that return craft nothing more than a tin can containing tin cans, and include in the ship to lift off from Mars the quarters and life-support machinery for the return journey. This increases its mass somewhat, but not as much as providing within it the supplies as well as the equipment required for that journey.

The ship bringing the astronauts from Earth could, as in the previous scenarios, descend to Mars, and serve as their habitat there, or it could remain in orbit and serve as the Earth return vehicle, thus taking on two of the four roles identified here.

The latter case makes particular sense, considering that this ship needs to contain enough food for the astronauts to survive a journey of 2 or 3 years, in the event of a failure requiring the use of the free-return feature of the trajectory. The Hohmann orbit, and the 1.5 year orbit, have an advantage over the 2-year free-return trajectory in that the change in velocity required is smaller at the Mars end of the trip, as well as being smaller at the Earth end and therefore requiring less fuel for the launch. On the other hand, if the 2-year trajectory is attainable, it does make sense to return the astronauts to Earth more quickly in the case of a mission failure, since such a failure may be associated with other emergency conditions.

This mission profile has the advantage of Mars Semi-Direct in that only a small ship is launched from the surface of Mars; but it is still a larger one than in that plan, because it also carries the fuel needed for the return journey to Earth up from the Martian surface. Thus, that fuel is still produced on Mars without having to launch the entire Earth return vehicle from the Martian surface. Splitting the mission up into four launches presumably allows the maximum size of any one ship to be reduced: the first ship doesn't need to carry the scientific instruments to be used on Mars, the Earth return vehicle doesn't need to carry fuel; thus, the requirement for heavy-lift capability is still further reduced.

By using a small ship containing the astronauts to land on Mars, there is also one "backwards" step that can be taken. The habitat and the Earth return vehicle can both use aerobraking in order to either land on Mars or enter Mars orbit. But if the Mars landing vehicle is sufficiently small, fuel requirements for using rockets to enter Mars orbit and then land could be minimized. This would address the concern that aerobraking might be either too risky, or produce too bumpy a ride, for a vehicle with astronauts on board.

In "The Case For Mars", Dr. Zubrin notes the costs of launching two existing rockets of different sizes, the Delta II and the Titan IV. Their capabilities are noted on the Internet sites of their respective manufacturerers, Boeing and Lockheed-Martin.

vehicle    pounds to LEO   pounds to         pounds to    cost per launch
                           geosynchronous    Mars
Delta II          12,820            4,500*       2,200        $55 million
Titan IV          47,800           12,700        9,500**     $400 million
Saturn V         308,000           82,000**     63,000         $2 billion

* to geosynchronous transfer orbit. Presumably, the ratio between
the two columns should be the same for all sizes of rocket, and so
the figure to actual geosynchronous orbit should be about 3,500 pounds.

** my estimate

A Titan IV has about one-sixth the payload capacity of a heavy-lift vehicle in the Saturn V class. Note that a Delta II is more economical per unit of mass than a Titan IV; the cost figure for a Saturn V-class launch may be optimistic (it does not include development costs), as this trend is likely to continue.

Could one do a mini-Mars Direct with one astronaut, using existing Titan IV boosters, instead of developing a heavy-lift capability? For one thing, the Saturn V-class vehicle was proposed to carry four astronauts, not six, to Mars. For another, I tend to believe in being cautious; hence, I proposed my notion of splitting the mission up into even more launches because I despaired of it actually being possible to support even one astronaut on the journey to Mars even in a large vehicle carried aloft by a Saturn V.

Pessimistic about other things, though, I admit to fearing that we won't send anyone to Mars unless we figure out a way to send some poor sap there in a rocket of the Delta II class. If nanotechnology enables us to live forever by transferring our minds to silicon artificial brains which take over the functions of our neurons one by one, this is not impossible. We may even wind up being able to do that before we develop some form of suspended animation for astronauts, or before we get around to developing another heavy-lift rocket booster; there is no overwhelmingly compelling motive for human exploration of Mars comparable to the Cold War issues which prompted the Apollo program. However, current NASA exploration of Mars is of a type suitable for preparing for manned exploration, the possibility of life on Mars is a reasonably strong motivation, and the expenditures involved in a mission such as Mars Direct or the Mars Reference Mission are significantly below those required for the Apollo missions, as they make use of the lessons learned in that program. It is possible, therefore, that we might see an effort begun by the United States to send people to Mars, perhaps a decade from now, resulting in a personelled Mars landing in about the year 2020.

Since these words were written, of course, the U.S. government has announced plans to develop a new family of rockets and space exploration vehicles, to be used first to send astronauts once again to the Moon, and then to continue onwards to Mars. The timeline of this program, even for the return to the Moon, is significantly longer than that of the Apollo program.

The following diagram illustrates the principle of an almost androgynous docking frame. This door frame will not connect to another one exactly like itself in another orientation,

but it will connect to its own mirror reflection. The middle part (vertically) of the door is androgynous, but the need for a reasonably good seal at the top and bottom leads to the asymmetry. The main problem with a design like this, however, is probably avoiding vacuum welding between two docking frames before they are slid together fully, rather than leakage, which can be dealt with by covering the perimiter of the door opening with duct tape.

A Space Shuttle can deliver a 65,000 pound (23,500 kilogram) payload to low earth orbit.

If it takes a 63,000 pound vehicle to carry four astronauts to Mars, supporting them on the way there, then the Space Shuttle is sufficient to place this in low Earth orbit.

This assumes a two-year free-return orbit, which involves a delta-V of about 5 km/sec; the three-year free-return orbit only requires 3.5 km/sec. Since the limiting factor is the size of rocket booster we can get into space in one piece, for this type of mission, the easier orbit will be needed.

Two astronauts, and a vehicle for travelling to Mars similar to the Spacelab, with a total weight of around 63,000 pounds, can be placed in orbit by the Shuttle. And, if necessary, any number of 12,800 pound capsules, containing food, water, and other supplies for the journey to Mars, previously launched by Delta II rockets, can be attached to it at that time, so if life-support proves a more difficult problem than thought, a larger ship could be constructed simply.

Supplies and equipment for use on Mars can be launched there by Delta II rockets as well, 2,000 pounds per launch, and anything that needs to be sent in a somewhat larger piece could be sent by Titan IV.

However, while our astronauts have supplies waiting for them on Mars, and now have all the consumables they need for their journey there in a large spaceship, that spaceship is in low earth orbit. How do we get them to Mars?

A Titan IV can deliver 47,800 pounds to LEO, and 9,500 pounds to Mars. Assuming no configuration penalties are involved, this means that it essentially delivers to LEO a 9,500 pound Mars payload, and a 38,300 pound booster for delivering 9,500 pounds to Mars from LEO. So, if it were to deliver the booster only to LEO, with no payload, that booster would be large enough to deliver 11,850 pounds from LEO to Mars.

Even if everything else could be delivered to orbit in small pieces, if you have many small rockets, instead of one big rocket, you have more chances of one of them blowing up instead of firing properly at the time of ignition.

Two astronauts instead of four, but three years of supplies instead of two, mean we need to send to Mars about 48,000 pounds, if the goals for efficiency of life-support set by Dr. Zubrin in "The Case for Mars" can be achieved.

Thus, what would be needed to send the astronauts on their way would be:

One Space Shuttle launch; 65,000 pounds; two astronauts, their ship for the journey, and supplies.

Four or five Titan IV launches, sending up the boosters to be used to deliver all of this to Mars.

The risks involved in starting five rocket engines at once may be tolerable. However, another problem still has not been addressed: returning the astronauts to Earth.

While the supplies the astronauts will use on Mars can be delivered by innumerable Delta II launches, the Earth Return Vehicle envisaged in Mars Direct needed to be sent to Mars by a Saturn V-class vehicle.

The ship the astronauts used to go to Mars is assumed to have been left in Mars orbit, along with the food and supplies they would have had to use in the case of an emergency free-return trip back to Earth. Their journey to Mars itself would be made in a tiny ship. So it isn't necessary to launch the food they need for the journey back to Earth from the Martian surface.

If a vehicle weighing 9,500 pounds without fuel would be adequate to carry to Mars orbit the fuel produced on Mars to bring the astronauts back to Earth, then the hydrogen used to make fuel on Mars, and the equipment to do so, could be sent by separate launches. But this involves the astronauts having to fuel the return vessel on the Martian surface, and it and the fuel plants would need to be brought within a "hose length" of each other by surface transport. And if such a vehicle is not adequate, one again needs to deal with firing multiple rocket engines. While the linking of vehicles together in Earth orbit may be feasible, expecting a small group of astronauts to do it in Mars orbit involves more risk.

This seems to prove that a heavy-lift capability is needed for a trip to Mars. However, there is one more thing to consider.

The Earth Return Vehicle, and the booster that will send the astronauts to Mars, are both things that it is highly desirable to launch in one piece. Both vehicles have to be safe enough to use with astronauts themselves. But neither need have astronauts on them when launched.

A heavy-lift vehicle that does not have to be man-rated can be formed with minimal development costs. Its first stage can be composed of seven Titan IV first stages, lashed together. The second stage, instead of being seven Titan IV second stages, would be built from something larger if possible. So an Earth orbital rendezvous of the rocket that powers the voyage from low Earth orbit to Mars with the ship containing the crew eliminates the need to spend several years designing a new heavy-lift vehicle based on the Shuttle engine, or rebuilding the Saturn V.

Thus, the mission profile is:

During one launch opportunity:

During a subsequent launch opportunity:

During the launch opportunity on Mars for the return to Earth:

This variation of "Mars Three-Quarters Direct" which involves an extra orbital assembly step to avoid the need to develop a new heavy-lift booster (the Mars booster and the Earth Return Vehicle still would need to be developed) can be given the catchy name of "Mars Next Tuesday".

The following diagrams may make the sequence of events clearer:

The events that take place on or around Earth:

First, the supplies the astronauts will need on Mars are sent there. A variety of existing launchers can be used for this. But the Refuelling Rendezvous Vehicle is large enough that a heavy-lift vehicle is required to send it to Mars.

Another heavy-lift vehicle sends a booster into orbit that will be used to power the trip of the astronauts to Mars.

While this proposal is intended to prove that a trip to Mars is possible, even with severe constraints on the available technology, it is expected that a real mission to Mars would be simpler, because more capable vehicles would be available. However, it is interesting to note that NASA's current plan for returning to manned exploration of the Moon and continuing to Mars involves launching the astronauts into space on the smaller Ares I rocket, while using a larger vehicle, the Ares V, comparable in capability to the Saturn V, to launch the heavier components of the mission unaccompanied by the astronauts. Thus, the approach of avoiding the overhead of man-rating the heavy-lift vehicle is being taken in real life.

Then the astronauts themselves go into orbit with the Shuttle, in a Spacelab-like crew module carrying the supplies they will need to go to Mars and back. This module is joined to the booster, which then takes the crew module out of Earth orbit, and sends it on its journey to Mars.

The events that take place on or around Mars:

The Refuelling Rendezvous Vehicle produces, from the Martian atmosphere's carbon dioxide and hydrogen sent with it, the fuel needed for the journey back to Earth. Thus, despite all the changes, this is really only a minor variant of Dr. Zubrin's Mars Direct.

The crew module enters Mars orbit by aerobraking, and then the astronauts head to the surface of Mars in a small capsule. To land gently enough on Mars, the capsule will perhaps combine a giant parachute with descent powered by rocket engines.

For the return to Earth, the second stage of the RRV, carrying a capsule containing the astronauts similar to the one in which they landed, docks with the crew module in Mars orbit, and then powers the combined vehicle on its way to Earth.

This is somewhat more elaborate than the original Mars Direct proposal, as it contains two rendezvous manouvers. These were added separately, for different reasons: the one in Mars orbit was added first, so that the food and supplies for the return journey to Earth would not have to be needlessly landed on Mars, and then launched from there again, and the one in Earth orbit was added to make it easier to design a heavy-lift vehicle.

Is it reasonable to think that a heavy-lift vehicle would be a major problem to design, however? The two designs noted in Dr. Zubrin's book, the Shuttle Z and the Ares, are basically reconfigurations of the Space Shuttle; the main change is the replacement of the Shuttle by a second stage.

The first stage of the Saturn V, the type of rocket whose performance it is desired to match, used five F-1 rocket engines, each with a thrust of 1,522,000 pounds (fueled by kerosene and oxygen). The three rocket engines of the Space Shuttle each have a thrust of 375,000 pounds. However, the two solid rocket boosters have thrusts of 2,900,000 pounds each.

The momentum a rocket engine provides to a space ship, of course, is also determined by the amount of time that engine provides a given level of thrust. Solid rocket boosters only provide thrust for a short amount of time; but for any given product of thrust and time, a high thrust for a short time is more efficient, because it reduces the losses due to gravity by causing the spaceship to attain higher speeds at an earlier time.

For comparison, the two solid rockets on a Titan IV each have a thrust of 1,700,000 pounds, and the first stage, which appears to have a single engine, a thrust of 551,200 pounds.

If the F-1 rocket engine were to be made available once again, using it in a new rocket design which also included solid rocket boosters could produce an impressive heavy-lift capability exceeding that of the Saturn V. But this would likely be an expensive project. Five F-1 engines provide seven and a half times the thrust of the three Shuttle engines, so one could imagine scaling up the thrust provided by solid rocket boosters similarly. (Incidentally, the J-2 hydrogen/oxygen engines, used on the second and third stage, had a thrust of 230,000 pounds each.)

Another thing to note: since I assume a mission failure is unlikely, and that making the amount of propulsion needed to send large vehicles to Mars as small as possible is important, I am inclined to favor a 1.5 year orbit for the trip to Mars instead of a 2 year orbit.

Thus, since the ship has supplies on it for 3 years, and it spends .75 year getting to Mars, it will still have 2.25 years worth of supplies on it for the return journey.

And that journey will also only take .75 years.

This means that if it could take four astronauts to Mars, it could take twelve astronauts back. Assuming rations for an emergency free-return trajectory would be Spartan, however, taking eight astronauts back would still not be a problem.

Also, if drinking water were not recycled, but losses from there were folded into wash water, which I suspect could be recycled with rather more than the 90% efficiency that Dr. Zubrin conservatively proposes (any that doesn't get recycled will make the ship rather soggy, unless it is leaky), the increase in the weight required to support each astronaut would be modest.

Thus, if one sends two ships to Mars, each with two astronauts aboard, one has a greater margin of safety, and, in addition, all four astronauts can return using one of the two crew modules, joining it by means of one RRV.

This offers another opportunity. I have tried to keep the use of heavy-lift vehicles to an absolute minimum, proposing to send as much of the supplies the astronauts will use on Mars on Delta II rockets if possible, or Titan IV rockets if necessary. Thus, I've assumed that the habitation module the astronauts will use on Mars can be built from several small packages, but around a nucleus sent by Titan IV. If, however, only one crew module is needed in Mars orbit, one could be landed on Mars to serve as a habitat there, although for reasons of reliability it might be desired to avoid this initially.

Using a crew module of the same shape as Spacelab is a loss, however, compared to the shorter, but larger-diameter shape possible with a personelled heavy-lift rocket.

Of course, the risk associated with firing multiple rockets at once can be reduced by a configuration such as the one shown below:

Here, eight rockets, spaced apart by lightweight trusses, are tethered to a ninth rocket and a crew module. The rockets are therefore spaced apart, and separated from the crew. Even this could be assembled without overly elaborate facilities in space, and it might be noted that the ISS already does exist. The RRV could be sent to Mars the same way. The rockets would have to be launched into LEO by something comparable to the Titan IV, and even then they would be small enough that many would be needed.

With a heavy-lift capability, a configuration like this would allow sending four or more interconnected crew modules to Mars at one time, which would have an advantage from the standpoint of reliability on the long journey there and back, and a larger RRV could be sent to Mars to push them all back to Earth together as well. Of course, constructing in space a very large ship to go to Mars would seem to be taking a step back to the overly ambitious and expensive past proposals.

But the problem of a sufficiently reliable and compact life-support system for several years of separation from Earth is a more difficult one to solve than the problem of acquiring a heavy-lift capability.

The Sojourner rover went to Mars in a tetrahedral package. The four triangles that make a tetrahedron can also form a larger triangle, and twenty triangles form an icosahedron. Thus, with suitable design, the packaging for the small-sized supply modules sent to Mars in advance can be made suitable for constructing a larger pressurized volume, to be covered with Martian soil. Of course, permafrost is rather difficult stuff to work with, but if that is encountered, it will be mined for water. A Titan IV launch would be used to send to Mars a habitat that would be at least somewhat larger than the capsule the astronauts landed on Mars with, and, as noted, two sets of astronauts could be sent to Mars simultaneously, and one crew module could be landed on Mars to serve as a larger habitat.

Another proposal for making it easier to travel to Mars is through the use of what is called a cycler.

This would not change the delta-V required for a trip to Mars; what it would do is simplify the life-support problem. If an asteroid with a permanent base on it, or a habitat of the type described on the previous page, were permanently left in an orbit linking the orbits of Earth and Mars, then one could go to the cycler from Earth in a small spaceship with only limited life-support capabilities, and then go to Mars from the cycler in a similar spaceship. This would remove one of the major additional things required for a Mars journey that was not needed in order to go to the Moon.

A Hohmann orbit used for a specific journey from the Earth to Mars has, as noted above, a period of 1.4174 years. A body in such an orbit, however, while it would link the orbits of Earth and Mars, would only actually closely approach either Earth or Mars at infrequent intervals. Of course, if something were placed in an orbit with a period of 1.5 years, going from Earth's orbit to somewhere just beyond the orbit of Mars, it would encounter Earth regularly. Similarly, something placed in an orbit with a period of about 1.4107 years, would have an orbit extending from the orbit of Mars to just inside Earth's orbit, and, having a period of 3/4ths of a Martian year, would encounter Mars regularly.

Since the orbits of Earth and Mars are incommensurable, it would seem that the cycler idea is doomed from the start. However, what is intended is that the orbit of the cycler would be subjected to gentle adjustments leading to a continuing change in its major axis. Thus, the average time from one aphelion to the next, although not the average time to circle the Sun, would be harmonized exactly (over the long run, since adjustments at any given time would also take the eccentricities of Mars' and the Earth's orbits) to the period between oppositions of Mars as seen from Earth.

The synodic period of Mars is 2.1353 Earth years, or 1.1353 Mars years. Thus, two such synodic periods are 4.2706 Earth years, or 2.2706 Mars years. An orbiting body whose period was about 1.306 years would have this span of time as 3.2706 of its years. Thus, if such a body were in a circular orbit between Earth and Mars, it could appear near Mars, and also in opposition, at every second opposition of Mars. In an elliptical orbit, to serve as a cycler, the location of perihelion in the orbit would have to be shifted by 97.416 degrees in the span of time between two oppositions of Mars, so that it could, in a suitable position, link the two planets; this would be a change of 22.8 degrees a year. This would appear to require the use of a significant amoung of consumables for propellant. However, this, so far, ignores no doubt the key idea behind cycler orbits; since there are frequent, regular, encounters with the two planets to be linked, doubtless adroit use will be made of gravity assists at each encounter.

I had considered an alternative method of minimizing consumable requirements, by using a pair of cyclers in fixed orbits, each one harmonized to only one planet, with the idea that the two bodies would have orbits that were close to each others' over an extended distance, but which travelled at somewhat different speeds in that area, so that the incommensurability in the orbits of the two planets could be accounted for by the variation in the location needed to transfer from one cycler to the other.

Earth orbits the Sun once a year, and the Martian year is 1.881 Earth years. Earth orbits the Sun at 1 AU, and Mars orbits the Sun at 1.52 AU; this follows Kepler's laws,

     2       3
1.881  = 1.52  = 3.52

The Hohmann orbit was worked out for an ellipse with a semi-major axis halfway in size between the orbital radii of Earth and Mars, 1.26 AU. This is why it has an orbital period of 1.4174 years. One could approximate that orbit with an Earth cycler with an orbital period of 1.5 years, or with a Mars cycler with an orbital period of 1.41075 years, 3/4 of a Martian year. This would reduce delta-V requirements, but because the two orbits are nearly the same, the two cyclers would have a synodic period with respect to each other of 23.71 years. This, clearly, is the wrong way to go about setting up cyclers; we don't want two cyclers in nearly identical orbits, we want two cyclers in very different orbits, so that they encounter each other frequently.

What if we had an Earth cycler with an orbital period of 2 years, then, and thus an orbit with a semi-major axis of 1.59 AU, and a Mars cycler with an orbital period of 2/3 of a Martian year, or 1.254 years, and thus an orbit with a semi-major axis of 1.16 AU? (Note that the Mars cycler gets as close as 9/10ths of an astronomical unit to the Sun, but this should not be too terribly unreasonable.) This increases the frequency with which both cyclers encounter their respective planets, and also changes the periods of these two orbits in opposite directions.

Now, their mutual synodic period is a reasonable 3.36 years. Can the perihelia of the two orbits be chosen so that the two cyclers are actually likely to be close to each other for a large proportion of the encounters? The idea is that the curves of the two orbits need to remain close to each other, although when each cycler is travelling in that area, it is travelling at a speed considerably different from that the other cycler would use in its orbit passing nearby.

Since a craft going from Earth to Mars would need to speed up to join the Earth cycler, slow down to transfer to the Mars cycler, and speed up again to land on Mars, this scheme significantly increases the total delta-V of the journey, however. To avoid this, one could use a Mars cycler with a longer period than that of the Earth cycler. This could be done by not having the Mars cycler go all the way to Earth orbit, and not having the Earth cycler go all the way to Mars orbit. Note, though, that doubling the required delta-V is not necessarily a disaster, from a system that greatly decreases the size and mass of the required spacecraft. This, though, raises another point: cyclers are useful because they decrease the need for travellers to another planet to carry life support with them. This means that the full benefits are only derived if there is also a base on the target planet that can provide life-support to the astronauts during their stay there.

So, let the Martian cycler have a period of 4/5ths of a Martian year? The encounters with Mars are now rather infrequent, once every 5 Martian years, but let us suppose we can live with that. The period would be 1.5048 Earth years. This suggests that such a cycler could, with gravity assists, be made to cycle with both worlds, but for now, let us explore the possibilities that do not involve the need to constantly alter the orbits of the cyclers. In any event, its semi-major axis is 1.31 AU, so its perhelion is at about 1.05 AU. This suggests an Earth cycler with a semi-major axis of just over 1.025 AU, but such a cycler would visit Earth too infrequently, having far too long a synodic period with respect to Earth: for example, one with an orbital period of 1 1/26 years. One with an orbital period of 1.5 years, on the other hand, would have far too long a synodic period with respect to the other cycler.

But there are other possibilities to choose from, such as an Earth cycler with a period of 1.333 years. That would encounter Earth and the other cycler at reasonable intervals, and the delta-V would now be monotonic: from Earth (1 year) to the Earth cycler (1.333 years) to the Mars cycler (1.5048 years) to Mars (1.881 years), so that the use of cyclers would not add too much to the total delta-V requirements of the journey.

Note, incidentally, when the major axes of the orbits of the two cyclers are at an angle to each other, one would have two choices of configuration, one where the intersection point would be convenient for a short outbound journey to Mars, and one where it would be convenient for a short inbound journey to Earth. This would be dealt with by allotting one of the planets two cyclers, and, presumably, that planet should be Mars so as to shorten the time required to return to Earth.

Once on Mars, how might permanent habitats be built? The Martian atmosphere is much thinner than that of Earth; while its greater extent is said to make it a better shield against meteorite impacts than Earth's atmosphere, it is true that ultraviolet light can reach the Martian surface. Thus, it has also been claimed that the Martian atmosphere is not an effective shield against cosmic rays.

Bringing sunlight to an underground Martian colony might be accomplished through an arrangement like the one drawn schematically below:

however, this design has serious problems.

The axis of revolution of the parabolic reflector is polar-aligned so as to simplify the motions of the heliostat mirrors, and allow more efficient collection of light. The heliostat mirrors would be laid out in an elongated hexagonal array.

Sunlight is directed to a large parabolic mirror by moving flat heliostats, the primary parabolic mirror then reflects the light to a convex parabolic secondary to collimate the light, forming an afocal Cassegrain system, and then a relay mirror sends the light straight down through a narrow shaft leading to the underground Martian base. Due to the intensity of the concentrated light beam, nothing is placed in the deep hole leading downwards, and thus the barrier between the atmosphere of the underground colony and the thin air of Mars is a glass cylinder within the colony itself, through which the sunlight is reflected to reflectors which spread the light evenly to the ground of the base.

The problem is that since sunlight upon Mars is less intense than sunlight upon Earth, the parabolic mirror must be larger than the colony.

On the Moon, with one-sixth of Earth's gravity, such a grandiose structure might be practical. On Mars, it is not quite so clear that a gigantic mirror could be erected and remain stable. Worse yet, not only does Mars have an atmosphere, but as amateur astronomers who try to view Mars at those oppositions at which it is closest to Earth well know, Mars is famous for its ferocious dust storms.

Solutions are possible; one could replace a large parabolic mirror by a horizontal strip from an even larger parabolic mirror, and one could devise ways in which the mirror could close like a fan, or split up and spread out to flatten upon the ground, so as to protect itself from dust storms.

Alternatively, since the immense size of the parabolic mirror is the main problem, one could have multiple smaller parabolic mirrors, each with their own heliostat farm, and simply place multiple relay mirrors so as to send the light from each parabolic mirror down to the underground base. This solution is illustrated in the diagram provided above, but in practice more than perhaps four mirrors, as suggested by that diagram, or seven, but rather hundreds would be needed, so as to make a significant difference between the size of the base and the size of the parabolic mirrors.

This is derived from the space colony design on the preceding page, but it seems to me that similar designs may well have appeared in science-fiction magazines of the nineteen-thirties.

Incidentally, one potential flaw in the design shown may not have escaped notice. If, to ensure structural strength of the overlying bedrock, only a small hole, drilled like that for an oil well, perhaps less than a foot in diameter, connects the habitat to the surface, would it not take an awful long time to excavate the rock that would need to be removed to create a hemispherical cavity for the habitat which might be a mile in diameter?

It is envisaged that several nearby colonies would be linked by horizontal tunnels containing roads. A similar horizontal tunnel could link a habitat with a valley or a cliff face lying close to it and poleward from it, and that tunnel would be considerably larger than the vertical shaft used for admitting sunlight.

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