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Copyright © 2009 by Gaylen Hinton. Published by The Mars Society with permission.
THE COLONIZATION OF MARS VIA A MARTIAN SPACE ELEVATOR
Gaylen Hinton Durham, North Carolina [email protected]
ABSTRACT
An initial colony on Mars could be established through a Martian space elevator (MSE) that was sent from earth along with the colonists. The MSE and the colony could get into areosynchronous orbit (ASO) with the expenditure of less than 600 m/s of delta V. Once in ASO, the MSE would be made operational by simultaneously lowering a base station to Mars and extending the counterweight. The base station would be mobile in order to maneuver it to the right location. The colony would be based about 10° off of the equator in order to position the MSE where the Martian moons would not affect it.
It would probably not be practical to send an MSE to Mars unless there was a space elevator (SE) on earth first, due to the mass involved. In order for an earth-based SE to give a craft the delta V necessary to get to Mars, the craft would have to be released about 25,000 km past geosynchronous orbit (GSO). At that point the net force is only about 1/40g. Therefore huge loads, assembled at GSO, could be sent to Mars with minimal loading on the cable. Also, multiple loads could be sent and collected together in transit. Therefore, the initial colony could be composed of hundreds of people, the MSE, and all their supplies and equipment.
MARTIAN SPACE ELEVATOR BASICS
An areosynchronous orbit (ASO) is the altitude where the force of gravity and the centrifugal force of an object fixed with respect to the surface of Mars are equal:
This is less than half the elevation of a synchronous orbit on earth.
The load on the cables from the surface to ASO would be, for a cable of uniform thickness of mass λ/m:
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That is only about 1/5 of the specific strength required of a space elevator (SE) on earth. Because of this, it would not be necessary to have a tapered cable for an MSE. Cables of uniform thickness could be easily reeled out to construct the MSE. Also, because gravity on Mars is only .38g, the cables would only have to be 38% as thick to carry the same load as on earth. Actually, with the reduced loading of the cable on itself, the final cable would only have to be about 1/3 the size of an earth SE.
A serious problem for a Mars SE (MSE) is that there are two moons in the way. Phobos is less than half the ASO distance, and Deimos is just slightly outside ASO, but both would get in the way of the MSE and its counterweight.
The redeeming factor is that both moons only have an inclination of about one degree to the Martian equator. As they are only 15 – 25 km in diameter, these moons would only affect a narrow band around the equator.
Deimos is 23500 km from the center of Mars, and makes an angle of about one degree with the equator. So it actually travels
km on either side of the equator.
In order to make sure that that the MSE will always be clear of Deimos with a safety factor, and because the orbit of Deimos precesses somewhat with respect to the plane of the equator, we would want to have the closest point of the MSE at least 500km from the equatorial plane.
The moon Phobos is about 9500 km from the center of Mars. Its orbit makes an angle of 1.09 degrees with the equator. Therefore, it travels
km on either side of the equator – much less than Deimos.
Therefore, in order for the MSE to clear the moons of Mars, it needs to be positioned off the Martian equator. Figure 1 below shows the relationships between an MSE with a base station at latitude C above the Martian equator, a space station at ASO, the MSE counterweight, and the moon Deimos. Phobos is not shown because if the MSE can clear Deimos, it will easily clear Phobos.
We can see by this figure that the approximately one degree angle that Deimos makes with the equatorial plane requires a very much larger angle of latitude for the base station in order for the MSE to stay out of its path.
In the above figure, the length of the MSE tether from the surface to the ASO station is L, and it makes an angle B with the plane of the base station latitude. The radial distance of the ASO station from the center of Mars is r, and it makes an angle A with the equatorial plane. The
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radius of Mars is R, so the separation of the plane of the base station latitude from the plane of the equator is RsinC.
The outward force, CF, on the ASO station is provided by the centrifugal force on the station and counterweight. The gravitational force, mg, on the ASO station tends to counter that centrifugal force. The tension and gravitational forces are balanced when the ASO station assumes a position where:
We also have the relationship:
These two equations can be solved to get:
For a satellite in orbit, mg = CF. Therefore, if there were a massless cable going to Mars from an ASO satellite, then angle A would equal angle B. However, with any tension on the cable from the counterweight, the angles will not be equal.
Since the separation of the MSE cable from the equatorial plane is , and we want that separation to be at least 500 km, we would have,
Without any initial tension from the cable, mg = CF, so
At ASO, the mg force is only 1/36 of what it is at the surface. Therefore, if we assumed sufficient tension in the MSE to support a 15,000 kg load at the surface, that tension would balance 540,000 kg at ASO. So with a 540,000 kg ASO station and the ability to lift 15,000 kg, we would have . Substituting this in we get:
If we assumed , then the ASO station could have a mass of 270,000 kg or double cables (for a moving MSE) with a mass of 540,000kg then,
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As a load is being carried up the MSE, its weight will also affect the position of the cable. Figure 2 below shows a load on the cable of the MSE.
For a load being carried up the MSE, with a tension T on the cable, figure 2 gives the following relations, with being the weight of the load at the point shown:
These can be solved to give,
A load at the distance L’ from the base station pulls the cable from the plane of the base station latitude towards the equatorial plane by the amount . With no load at all, the cable would be a distance of from the plane of the base station. ( can be determined by the initial conditions using equation 2 – typically about .007.) So the difference, , with the load m’ on the cable is:
But to the first approximation, , so we would have:
With the maximum load at the surface, but it diminishes as as the load rises. Therefore, at any height,
Substituting into equation 3, we get,
The above equation can be iterated to show that the maximum movement due to the load on the cable is when the load is about 1600 km up. This movement from the maximum load would be 70 to 90 km, depending on the initial location of the base station.
Also, this same basic equation can give an estimate of the effect of the weight of the cable itself on the position of the MSE station. Another 15 km or so would be added to any movement caused by the load.
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Therefore, during worst case conditions, about 100 km needs to be added to the displacement of Deimos in order to clear the MSE. With the 410 km maximum movement of the moon itself, 500 km of clearance would not leave enough of a safety factor. Likely the use of the MSE would need to be restricted during a Deimos alignment of maximum excursion in order to maintain a sufficient safety factor. In addition, the use of the MSE would have to be timed to dampen any oscillations, rather than increase them.
In any event, depending upon the initial mass of the ASO station, the MSE would need to be positioned about 10 or 12 degrees north or south of the equator.
An alternate plan to an off-‐equator MSE would be to put the base on a movable platform with wheels. In order to avoid the moons (up to 25 km across) the platform would have to be able to move north and south at least 30 km. That would restrict the location of a Mars colony to a location with a smooth surface for 30km. Also, this plan would put very strict requirements on maintenance, reliability and backup systems for the moving platform. If the mobile base ever failed to move properly just one time, the MSE would be destroyed.
The moons of Mars make their maximum excursions from the equatorial plane once each orbit. However, that maximum is not at the same place each time, relative to the surface, due to the different orbital and rotational periods. Relative to the surface of Mars, those maximum excursions appear to rotate around the planet.
The ratio between Mars’ rotation and Deimos’ orbital period is . Therefore, if a point on the surface and Deimos were initially aligned, after one Martian day (sol) Deimos will be orbits behind. In order to line up again it would take,
Therefore, every 5.3384 sols Deimos would be in a position to potentially interfere with an MSE. However, if the initial alignment was with the location of maximum excursion of Deimos from the equatorial plane (410 km), then at the second alignment, Mars would have rotated radians. (That is 121.8° past the point of maximum excursion.) So, at the nth alignment, Mars would have rotated radians, and the distance of Deimos from the equatorial plane would be:
km (3)
Knowing the distance of the mobile MSE from the equator, and the diameter of the moon, we can compare to the distances of equation (3) to see when there would be an interference with Deimos. By going through all the values of n from one alignment to hundreds, we can determine how many sols there are between times of interference.
The worst case scenario (for a mobile MSE near the point of maximum departure) would be a move every sixteen sols (every third alignment) for five or six times, followed by a wait of 267 sols. For a mobile MSE on the equator, there would be thirty one
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alignments (165 sols) until a move was required, followed occasionally by another move sixteen sols later.
The ratio of Phobos’ orbit to Mars’ rotation is 3.2171. Doing the same exercise for Phobos as Deimos gives,
and the distance of departure from the equatorial plane at the nth alignment:
By going through the values of n, we can determine how many sols between times of interference with Phobos. Typically, there would be seven to eleven alignments between required moves, with an occasionally longer wait. That would mean that a mobile MSE would have to move twice each three to five day period. (Once to move away from Phobos, and then again to move back.)
Perhaps a compromise between an off-‐equator MSE and a mobile MSE could be made. A lot of movement is required for a mobile MSE to avoid Phobos, but only half the latitude is required to avoid it completely compared to Deimos. An MSE could be placed far enough from the equator to avoid dealing with Phobos, but still have a mobile base to deal with the occasional moves required by Deimos.
Even if the initial MSE was set with a fixed base, because the orbit of Deimos precesses with respect to the equatorial plane, eventually the base platform may have to be made mobile to avoid it.
With any SE, the minimum counterweight mass is when there is no lump weight at all, but simply a cable extended outward from the synchronous orbit. The total tension for the MSE would be the maximum allowable load on the cable.
From equation (1) we know that it takes of force to balance a uniform cable at ASO. However, we can use that same equation to determine how far a cable of uniform thickness would need to extend out from ASO to provide the initial tension. The initial tension at the surface, and therefore the maximum load carrying capacity of the MSE would be,
If we assumed that the maximum allowable load on the cable was , (or the allowable specific strength was ), we can set F in equation 1 and change the limits of integration out to a distance r:
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If the maximum allowable load on the cable was , then .
Therefore, if we wanted the maximum cargo capacity on the MSE to be 15,000 kg, we would have, with a cable of strength ,
So the cables of the MSE would have a total mass of
If the MSE were made with movable cables, there would be one cable going up and another coming down, so the total mass would be double that. Also, a tapered cable would require more mass.
As an elevator car left the surface of Mars and got closer and closer to ASO, the gravitational force on that car would diminish as . Because of that, with a cargo capacity of 15,000 kg at the Martian surface, there could be a total load of six elevator cars of 10,000 kg each, evenly spaced between Mars and the ASO.
THE COLONIZATION OF MARS VIA A MARTIAN SPACE ELEVATOR
If a complete MSE was sent from earth with the first Mars colony, then all the equipment, supplies, habitats, and colonists could be lowered directly down to the base station from ASO. A tremendous amount of effort would be saved because everything could come down to the surface with little or no concern for aerodynamics, reentry, landing, or protection.
The fact that the cables of an MSE might have a mass of 200,000 kg or more seems daunting. All of the mass of the equipment, supplies, habitats and colonists would be added to those 200,000 kg. Such a large amount of mass would be prohibitive if it had to be sent to Mars via chemical rockets. However, if there was an SE on earth first, then all of that mass could be easily sent to Mars to provide the first colony with everything they need to succeed.
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With an SE on earth, there is no energy cost to send a spacecraft to Mars beyond getting it to GSO. In fact, energy is gained by sending a load from GSO to the release point where it would be slung toward Mars. Typically, a load bound for Mars would need to be released about 25,000 km beyond GSO. That would give it the delta V necessary to escape earth and travel to Mars. At 25,000 km past GSO the net force on any object is only about 1/40 g. A 200,000 kg load would only apply 5,000 kg-‐force on the cable at the release point.
Therefore huge loads, assembled at GSO, could be sent to Mars with minimal loading on the SE cable. Also, multiple loads could be sent and collected together in transit. Therefore, the initial colony could be composed of hundreds of people, the MSE, and all their supplies and equipment. A drawing of the complete Mars colony en route to Mars is shown below in Fig. 3.
Dozens or even hundreds of loads of equipment, supplies, and people could be sent up the SE to be assembled together at a space station at GSO. Once assembled and prepared, the much larger colonial loads could be sent to Mars via the SE.
The same technology used to create a SE (carbon nanotubes?) could also create large, inflatable, rotating space craft that would bring the colonists to Mars with artificial gravity, and all the comforts of home. Also, this same technology could be used to make lightweight habitats for the Martian colonists on the surface.
The cables and equipment necessary to make the MSE would be sent along with the rotating space habitat, or be sent in separate loads and collected together in transit. In any event, by the time the colonists reached Mars, everything would be assembled together in one large load. As shown in Fig. 3, there would be a reel of cable to lower a mobile base station to Mars and another reel to extend the counterweight further out.
That large colonial assembly would be aero-‐captured into a large elliptical orbit around Mars. Then, using a bi-‐elliptic transfer, the assembly would be moved into an ASO around the equator using less than 600 m/s of delta V. Using common fuels, that orbital maneuver could be accomplished by having less than 20% of the initial mass as fuel.
Once in ASO, a base station would be lowered towards Mars at the same time the counterweight was sent further out. The two processes would be coordinated in order to keep the assembly at ASO until the base station reached earth.
Unfortunately the base station would reach Mars at the equator, but it needs to be located about 600 km north or south of the equator. Therefore, after a mobile base station reached the surface, it could be driven to the proper location, although that would require a 600 km free path. Another possibility would be to have thrusters on the base station, and those thrusters would move the station into its position before it even touched the ground. Even large propellers could serve as the thrusters to locate the base station at its correct longitude.
Once in the correct location, the base station would be firmly anchored in place. Then the correct tension could be adjusted on the MSE cables with the counterweight, and
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the colony would be ready to start unloading. At that point the MSE would be fully operational.
While the equipment in the assembly at ASO was being unloaded down to the surface, the majority of the colonists would remain in the rotating space craft. That rotating craft would remain as a permanent part of the ASO space station. It could have a permanent manned presence, or simply be an empty station waiting for occupants to arrive. However, the colonists would likely leave it as an empty shell, taking everything they can down to the surface.
One of the first loads to come down the MSE would have to be a crane. Unlike loading and unloading in zero-‐g, people in space suits could not man-‐handle large objects on Mars. A 10,000 kg piece of equipment on Mars would weigh the same as a 3800 kg load on earth. Therefore, the crane would have to move and position each load that came down the MSE.
Once the habitats came down the MSE and were assembled by the initial crew, then the rest of colonists could begin to come down and also work on the surface. Each person could then start setting up his own work and living areas.
Having a large initial colony greatly enhances the possibility of success. First of all, with more people there could be more professions and disciplines, with their respective equipment, represented. Therefore there would be more likelihood that all needed skills and materials would be present on Mars. Also, with larger numbers, the possibilities of personality conflicts are reduced.
The only practical way to set up an MSE is to send it in its completed form from earth. Even a colony of one million people on Mars would still be so resource-‐limited that it is unlikely that they could ever build an MSE on their own.
The MSE would facilitate much more economical transportation to and from earth because no rockets would be needed. A load would simply be sent out on the MSE cable about 20,000 km farther than the ASO station and released. That would give the load sufficient delta V to get back to earth.
The initial cost of the MSE would be part of the setup cost of the colony, and would probably be paid for by the elimination of the reentry/landing vehicles that would otherwise be required.
Martian landing vehicles are very costly, complicated, and risky machines comprised of heat shields, parachutes, thrusters, aerodynamic surfaces, and maneuvering devices. Eliminating landing vehicles would eliminate a tremendous complication and cost for a Mars colony. The landing vehicles would be one the most difficult parts of a non-‐MSE colonization effort. Also any provision for vehicles to return to space from the surface would add a great deal more to the complication.
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In addition, using an MSE to lower the colony to the surface would eliminate any possibility that a load missed its landing site and ended up in an unretrevable location. Even if every landing hit its designated site, there would still be transportation issues in bringing each load to the colony site. On the other hand, the MSE would deliver every load to the exact same spot.
With a 200,000 kg MSE, and a location of 12° north or south latitude, the initial mass of the whole colony assembly could be 540,000 kg. With an even larger initial mass, the MSE could be located farther away from the equator, or the equipment and habitats could be in separate loads from the colonists.
After the majority of the colonists and the equipment on the first load were lowered to the surface, those additional loads could dock with the ASO station. Those loads would initially be in a non-‐equatorial synchronous orbit. Near the point of maximum departure from the equatorial plane, they would be captured as needed by the ASO station and their cargo lowered down to the Martian surface.
Even with a mass of 200,000 kg, the MSE could still end up being only be a small portion of the total mass of the initial colony. Therefore, the MSE could end up having less total mass than the mass of the required reentry vehicles for landing the same colony.
The bottom line is that an MSE could end up being simpler, cheaper, less risky, and require less mass than using reentry vehicles for colonizing Mars.
Because the MSE would have already paid for itself in the initial colonization effort, any subsequent use would just involve the incremental cost of operating it. Therefore, goods and materials could be shipped from Mars to earth rather cheaply. The primary cost would be a container capable of surviving earth reentry.
Future transports from earth could dock with the ASO station by entering a non-‐equatorial synchronous orbit, just like any multiple loads from the original colony. After unloading its cargo, the earth transport could then be reloaded with cargo and passengers from Mars, and then be sent back to earth.
However, even with an MSE and an SE on earth, the practical launch windows would still be about two years apart. Therefore, there would be a flurry of activity around those launch windows, but little use between them.
CONCLUSION
Space elevators are coming. The necessary material will be available sooner or later. It may be carbon nonotubes, or it could be some other allotrope of carbon like graphene, colossal carbon tubes, linear carbyne, or polycumulene. Even lowly polyethylene, the material of garbage bags, could be made strong enough to make space elevators if the molecular chains were long enough and the chains aligned. Several polymers of boron could also be strong enough to make a space elevator. One way or other, it will happen.
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An MSE would be the most practical means of getting a large, well equipped colony established on Mars, and would provide the means for economical transportation back and forth from earth. It is the opinion of the author that Mars will be colonized by an MSE long before it could be colonized by any other means.
Figure 1
Figure 2
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Figure 3