by ARTHUR C. CLARKE
Chancellor, University of Moratuwa, Sri Lanka
-- Fellow of King's College, London.
THE PROBLEM OF MATERIALS
As we go upwards, gravity falls off according to Newton's inverse square law. But the effective weight ofthe cable diminishes even more rapidly, owing to the centrifugal force on the rotating system. At geostationary altitude the two balance and the net weight is zero; beyond that, weight appears to increase again -- but away from the Earth.
So our cable has no need to be strong enough to hang 36000 km under sea-level gravity; allowing for the effects just mentioned, the figure turns out to be only one-seventh of this. In other words, if we could manufacture a cable with sufficient strength to support 5000 km (actually, 4960) of its own length at one gee, it would be strong enough to span the gap from geostationary orbit to Equator. Mathematically -- though not physically -- Jacob's ladder need be only 5OOOkm long to reach Heaven.... This figure of 5000km I would like to call 'escape length', for reasons which will soon be obvious.
How close are we to achieving this with known materials? Not very. The best steel wire could manage only a miserable 5O km or so of vertical suspension before it snapped under its own weight. The trouble with metals is that, though they are strong, they are also heavy; we want something that is both strong and light. This suggests that we should look at the modern synthetic and composite materials. Kevlar (Tm) 29, for example  could sustain a vertical length of 200 km before snapping -- impressive, but still totally inadequate compared with the 5000 needed.
This 'breaking length', also known as 'rupture length' or 'characteristic length', is the quantity which enables one to judge whether any particular material is adequate for the job. However, it may come as a surprise to learn that a cable can hang vertically for a distance many times greater than its breaking length!
This can be appreciated by a simple 'thought experiment'. Consider a cable which is just strong enough to hang vertically for a hundred kilometres. One more centimetre, and it will snap....
Now cut it in two. Obviously, the upper 50 km can support a length of 50 km -- the identical lower half. So if we put the two sections side by side, they can support a total length of 100 km. Therefore, we can now span a vertical distance of 150 km, using material with only 100 km breaking length.
Clearly, we can repeat the process indefinitely, bundling more and more cables together as we go upwards. I'm sure that by now you've recognised an old friend -- the 'step' principle, but in reverse. Step rocketsget smaller as we go higher; step cables get bigger.
I apologise if, for many of you, I'm labouring theobvious, but the point is of fundamental importance and the rocket analogy so intriguing that I'd like to take it a little further.
We fossils from the pre-space age -- the Early Paleoastronautic Era -- must all remember the depressing calculations we used to make, comparing rocket exhaust velocities with the 11.2 km 5' of Earth escape velocity. The best propellants we knew then --and they are still the best today! -- could provide exhaust velocities only a quarter of escape velocity. From this, some foolish critics argued that leaving the Earth by chemical rocket was impossible even in theory.
The answer, of course, was the step or multi-stagerocket -- but even this didn't convince some sceptics. Willy Ley  records a debate between Oberth and a leading German engineer, who simply wouldn't believe that rockets could be built with a mass-ratio of twenty. For Saturn V, incidentally, the figure is about five hundred
We escaped from earth using propellants whose exhaust velocity was only a fraction of escape velocity, by paying the heavy price demanded by multi stage rockets. An enormous initial mass was required for a small final payload.
In the same way, we can achieve the 5000 km 'escape length', even with materials whose breaking length is a fraction of this, by steadily thickening the cable as we go upwards. Ideally, this should be done not in discrete steps, but by a continuous taper. The cable should flare outwards with increasing altitude, its cross-section at any level being just adequate to support the weight hanging below.
With a stepped, or tapered, cable it would be theoretically possible to construct the space elevator from any material, however weak. You could build it of chewing gum, though the total mass required would probably be larger than that of the entire universe. For the scheme to be practical we need materials with a breaking length a very substantial fraction of escape length. Even Kevlar 29's 200 km is a mere 25th of the 5000 km goal; to use that would be like fuelling the Apollo mission with damp gunpowder, and would require the same sort of astronomical ratio.
So, just as we were once always seeking exotic propellents, we must now search for super-strength materials. And, oddly enough, we will find them in the same place on the periodic table.
Carbon crystals have now been produced in the laboratory with breaking lengths of up to 3000km -- that is, more than half of escape length. How happy the rocket engineers would be, if they had a propellant whose exhaust products emerged with 60% of escape velocity!
Whether this material can ever be produced in the megaton quantities needed is a question that only future technologies can answer; Pearson  has made the interesting suggestion that the zero gravity and vacuum conditions of an orbiting factory may assist their manufacture, while Sheffield  and I  have pointed out that essentially unlimited quantities of carbon are available on many of the asteroids. Thus when space mining is in full swing, it will not be necessary to use super-shuttles to lift vast quantities of building material up to geostationary orbit -- a mission which, surprisingly, is somewhat more difficult than escaping from Earth.
It is theoretically possible that materials stronger -- indeed, vastly stronger -- than graphite crystals can exist. Sheffield [153 has made the point that only the outer electrons of the atoms contribute, through their chemical bonds, to the strength of a solid. The nucleus provides almost all the mass, but nothing else; and in this case, mass is just what we don't need.
So if we want high-strength materials, we should look at elements with low atomic weights -- which is why carbon (A.W.12) is good and iron (A.W.56) isn't. It follows, therefore, that the best material for building space elevators is -- solid hydrogen! In fact, Sheffield calculates that the breaking length of a solid hydrogen crystal is 9118 km -- almost twice 'escape length'.
By a curious coincidence, I have just received a press release from the National Science Foundation headed 'New form of hydrogen created as Scientists edge closer to creating metallic hydrogen'. It reports that, at a pressure of half a million atmospheres, hydrogen has been converted into a dense crystalline solid at room temperature. The scientists concerned go on to speculate that, with further research -- and I quote -- "hydrogen solids can be maintained for long periods without containment".
This is heady stuff, but I wonder what they mean by 'long periods'. The report adds casually that 'solid hydrogen is 25 to 35 times more explosive than TNT'. So even if we could make structures from solid hydrogen, they might add a new dimension to the phrase 'catastrophic failure'.
However, if you think that crystallitic hydrogen is a tricky building material, consider the next item on Dr. Sheffield's shopping list. The ultimate in theoretical strength could be obtained by getting rid of the useless dead mass of the nucleus, and keeping only the bonding electrons. Such a material has indeed been created in the laboratory; it's 'positronium' -- the atom, for want of a better word, consisting of electron-positron pairs. Sheffield calculates that the breaking length of a positronium cable would be a fantastic 16,700,000km! Even in the enormous gravity field of Jupiter, a space elevator need have no appreciable taper.
Positronium occurs in two varieties, both unfortunately rather unstable. Para-positronium decaysinto radiation in one-tenth of a nanosecond -- but orthopositronium lasts a thousand times longer, a whole tenth of a microsecond. So when you go shopping for positronium, make sure that you buy the brand marked 'Ortho'.
Sheffield wonders wistfully if we could stabilise positronium, and some even more exotic speculations are made by Moravec . He suggests the possible existence of 'monopole' matter, and hybrid 'electric/magnetic' matter, which would give not only enormous strength but superconductivity and other useful properties.
Coming back to earth -- or at least to this century -- it seems fair to conclude that a small cable could certainly be established from geostationary orbit down to sea level, using materials that may be available in the near future. But that, of course would be only the first part of the problem -- a mere demonstration of principle. To get from a simple cable to a working elevator system might be even more difficult. I would now like to glance at some of the obstacles, and suggest a few solutions; perhaps the following remarks may stimulate others better qualified to tackle them.