Cast iron 7.8 | 3,500 | 4.5
Manganese steel 7.8 | 16,000 | 21.
Drawn steel wire 7.8 | 42,000 | 54.
KEVLARTM 1.4 | 28,000 | 200.
Silicon whisker 3.2 | 210,000 | 660.
Graphite whisker 2.0 | 210,000 | 1,050.
no one has yet built a beanstalk. The strongest steel wire is a hundred times too weak. The best candidate materials that we have today, silicon and graphite dislocation-free whiskers, fall short by a factor of five.
This is no cause for despair. The strength of available materials has increased throughout history, and we can almost certainly look for strength increases in the future. A new class of carbon compounds, the fullerenes, are highly stable and seem to offer the potential of enormous tensile strength.
We would like to know how much strength is reasonable, or even possible. We can set bounds on this by noting that the strength of any material ultimately depends on the bonding between the outer electrons of its atoms. The inner electrons, and the nucleus, where almost all the mass of the atom resides, contribute nothing. In particular, neutrons in the nucleus add mass, and they do nothing for bonding strength. We should therefore expect that materials with the best strength-to-density ratios will be made of the lightest elements.
TABLE 2
Potential strength of materials
Element pairs* | Molecular weight (kcal/mole) | Bond strength (kms) | Support length
Silicon-carbon 40 | 104 | 455
Carbon-carbon 24 | 145 | 1,050
Fluorine-hydrogen 20 | 136 | 1,190
Boron-hydrogen 11 | 81 | 1,278
Carbon-oxygen 28 | 257 | 1,610
Hydrogen-hydrogen 2 | 104 | 9,118
Muonium 2.22 | 21,528 | 1,700,000
Positronium 1/919 | 104 | 16,750,000
*Not all element pairs exist as stable molecules.
TABLE 2 makes it clear that this argument is correct. The strongest material by far would use a hydrogen-hydrogen bond. In such a case, each electron (there is only one in each hydrogen atom) contributes to the bond, and there are no neutrons to add wasted mass.
A solid hydrogen cable would do us quite nicely in beanstalk construction, with a support length about twice what we need. However, solid crystalline hydrogen is not available as a working material. Metallic hydrogen has been made, as a dense, crystalline solid at room temperature — but at half a million atmospheres of pressure.
It is tempting to introduce a little science fiction here, and speculate on a few materials that do not yet exist in stable, useful form. The last two items in TABLE 2 both fall into the category of Fictionite (also known as Unobtainium), materials we would love to have available but do not.
A muonium cable would be made of hydrogen in which the electrons in each atom have been replaced by muons. The muon is like an electron, but 207 times as massive, and the resulting atom will be 207 times as small, with correspondingly higher bonding strength. Unfortunately the muonium cable is not without its problems, quite apart from the difficulty of making it in solid form. The muon has a lifetime of only a millionth of a second; and because muons spend a good part of the time close to the proton of the muonium atom, there is a good probability of spontaneous proton-proton fusion.
Time to give up? Not necessarily. It is worth remembering that a free neutron, not forming part of an atom, decays to a proton and an electron with an average lifetime of twelve minutes. Within an atom, however, the neutron is stable for an indefinite period. We look to future science to provide means of stabilizing the muon, perhaps by binding it, as the neutron is bound, within some other structure or material.
Positronium takes the logical final step in getting rid of the wasted mass of the atomic nucleus completely. It replaces the proton of the hydrogen atom with a positron. Positronium has been made in the lab, but it too is highly unstable. It comes in two varieties, depending on spin alignments. Para-positronium decays in a tenth of a nanosecond. Ortho-positronium lasts a thousand times as long — a full tenth of a microsecond.
We are unlikely to have these materials available for some time. Fortunately, we don’t need them. A solid hydrogen cable will suffice to build a beanstalk. Its taper factor is 1.6, from geostationary height to the ground. A cable one centimeter in diameter at its lower end is still only 1.3 centimeters across at geosynchronous altitude. To give an idea just how long this thin cable must be, note that our one-centimeter wire will mass 30,000 tons. And it’s strong. Slender as it is, it will be able to lift payloads of 1,600 tons to orbit.
TABLE 3
Beanstalks around the solar system
Body | Radius of stationary satellite orbit* (kms) | Taper factor (hydrogen cable)
Mercury 239,731 | 1.09
Venus 1,540,746 | 1.72
Earth 42,145 | 1.64
Mars 20,435 | 1.10
Jupiter 159,058 | 842.00
Saturn 109,166 | 5.11
Uranus 60,415 | 2.90
Neptune 82,222 | 6.24
Pluto** 20,024 | 1.01
Luna 88,412 | 1.03
Callisto 63,679 | 1.02
Titan 72,540 | 1.03
* Orbit radius is planetary equatorial radius plus height of a stationary satellite.
** Pluto’s satellite, Charon, is in synchronous orbit. If so, a beanstalk directly connecting the two bodies is possible.
Beanstalks are much easier to build for some other planets. TABLE 3 shows what beanstalks look like around the solar system, assuming we use solid hydrogen as the construction material. As Regulo said, Mars is a snap and we could make a beanstalk there with materials available today. Kim Stanley Robinson included a Mars beanstalk in his Mars Trilogy, Red Mars, Green Mars, Blue Mars. My only objection is that he destroyed the stalk cataclysmically in Red Mars, and in so doing obliterated the town of Sheffield that stood at its tether point.
Building the beanstalk
We cannot build a beanstalk from the ground up. The structure would be in compression, rather than tension, and it would buckle under its own weight long before it reached geostationary height.
We build the beanstalk from the top down. In that way, by extruding cable simultaneously up and down from a production factory in geostationary orbit, we can preserve at all times the balance between outward and inward forces. We also make sure that all the forces we must deal with are tensions, not compressions.
The choice of location for production answers another question raised earlier: Where will we obtain the materials from which to make the beanstalk?
Clearly, it will be more economical to use materials that are already in space, rather than fly them up from Earth’s deep gravity well. There are two main alternatives for their source: the Moon, or an asteroid. My own preference by far is to use an asteroid. Every test shows the Moon to be almost devoid of water or any other ready source of hydrogen. Two of the common forms of asteroid are the carbonaceous and silicaceous types, and coincidentally carbon and silicon fibers are today’s strongest known materials. A small asteroid (a couple of kilometers across) contains enough of these elements to make a substantial beanstalk.
If the solid hydrogen cable proves to be the only acceptable answer, then we need to seek farther afield for construction materials. Hydrogen is readily available in the solar system, but not on small asteroids whose orbits bring them anywhere near the Earth. Their volatile materials have long since boiled off due to solar heating. However, if we look farther out, hydrogen as components of water and methane becomes plentiful. A comet, which is little more than a huge dirty snowball, would serve us very well to make a beanstalk; and quite a small comet, with a head a few kilometers across, is big enough.