Orbital Bridges Hans Moravec The Robotics Institute Carnegie-Mellon University Pittsburgh, PA 15213 (412) 268-3829 Copyright 1986 by Hans P. Moravec Once upon a time, long before people could fly, a foolhardy few reached for the heavens with mountaineering and masonry. Mystics scaled peaks to commune with the gods and monarchs commissioned huge civil engineering projects to push penthouses into the sky. But their technology was modest and their successes minor. To this day, ridicule is their chief reward. By Newton's time humanity's bag of tricks had grown, and included powerful mass-launching weapons. Armed with these, and more importantly with his new mechanics and gravitational theory, Newton contemplated artificial satellites orbited by a big cannon on a lofty peak. The concept illustrated the relation between falling apples and the unfalling moon, but the equations showed no peak was high enough, nor cannon then powerful enough, to actually do it. The improved cannon of the nineteenth century, though still inadequate, were the most promising method for entering space. During World War I projectiles from long range guns grazed the top of the atmosphere. Rockets, cardboard or metal tubes stuffed with gunpowder, had been used for entertainment and war for centuries, but poor performance limited their utility until World War II. Calculations by the early space theorists showed that a rocket could, in principle, propel objects away from Earth more gently than a cannon. The required size was huge, and grew exponentially as the energy content of the propellant fell. Gunpowder, for instance, was terrible. To boost a ton to escape velocity a black powder rocket needs an initial weight of 200 million tons. This compares to a mere 15 tons for a rocket burning hydrogen and oxygen, one of the most energetic chemical combinations. Of late rockets have been so successful that the other roads to the sky have been nearly forgotten. Even exotic proposals such as nuclear pulse and laser propulsion are variations on the rocket principle. It is nevertheless true that the limitations on towers, cannons and rockets are about the same. All methods limited by chemical bond energies (including combustion, light, electricity, magnetism and passive structures) must be pushed to extremes to lift objects out of Earth's gravity well. The alternatives have been considered for the easier tasks of leaving the moon and moving in free space. The lunar mass driver in Gerard O'Neill's space colonization plans (described in the book {\bf The High Frontier} is a magnetic cannon, while tethered satellites, such as NASA will dangle from the space shuttle to observe the ionosphere, and solar sails are relatives of the tower philosophy. If the technology is pushed to its theoretical limits, the other methods will also work for Earth. Calculations in the 1970s by Rod Hyde and Lowell Wood of Livermore, and independently Henry Kolm of MIT, indicate that a terrestrial electromagnetic mass driver can send objects into the solar system through the atmosphere. The mass driver must boost payloads to somewhat beyond Earth escape velocity. The ablation-shielded capsules would plow through a kilogram of air for each square centimeter in their frontal surface area. This section is about developments on the Tower of Babel front. The structures discussed are not made of brick, stone or steel, for that would be like powering interplanetary rockets with gunpowder. They use the strongest and lightest materials available. While all the proposals involve cables under tension, the more traditional compressional towers are also possible, in principle. The technology of super strength structures is less mature than that of ultra energetic chemical reactions. Hydrogen/oxygen combustion, which powers the space shuttle, is nearly the most powerful chemical reaction known. Meanwhile the strongest materials produced in quantity are twenty times weaker than the theoretical limits, though tiny samples of substances with half the ultimate strengths have been synthesized in laboratories. Crystalline graphite is the hydrogen/oxygen of materials. It's theoretically twenty times as strong as conventional steel and four times less dense, making it 80 times as good. Graphite fibers embedded in epoxy binders are aerospace's new wonder materials. The space shuttle main engine owes its unprecedented power to weight ratio to their use in the combustion chamber and nozzle. Though strong, they are ten times weaker than theory predicts. The reasons for this should become better understood in the years to come. A further factor of two or three improvement will make them adequate for terrestrial orbital towers. They are already more than strong enough for such towers (the tensile variety of which I will call skyhooks) on the moon and in free space. Graphite composites are being challenged by a new class of synthetics, the aramid fibers, introduced by the DuPont company. Kevlar, a prototype of the class, is as strong as most existing composites. The carbon backbone of the polymer molecules bears the load and future aramids will likely be even stronger. Kevlar is being used in large quantities for bullet proof clothes, radial tires, parachutes and other applications previously served by nylon. Its strength, durability, availability and relatively low cost make it a prime candidate for near term skyhook projects. \sect{Synchronous Skyhooks} Here we have the classical Tower of Babel approach, updated for sixteenth and seventeenth century discoveries in physics and astronomy. In ``Speculations between Earth and Sky'', written early this century, Konstantin Tsiolkovsky discussed a hypothetical tower built from the equator to tremendous heights. A person climbing the structure would experience decreasing gravity (and air) with increasing altitude. 36,000 kilometers above the ground the centrifugal force of the earth's rotation equals the lessened gravity, and it becomes possible to let go of the tower and float freely beside it. Beyond this synchronous point the centrifugal force dominates, and the climber is pulled outwards, away from the earth. To Tsiolkovsky it was a mental exercise, to illustrate concepts in celestial mechanics. Actual construction was dismissed as an obvious impossibility with known technology. The tallest artificial structure of the day, the Eiffel Tower, was 300 meters high. Discussions of the concept once centered on its self evident absurdity. There are problems in physics texts which ask the reader to show how a tower built up to the sky, or a cable dangling down from it, could not possibly support its own weight. Similar problems demonstrate the inanity of interstellar flight, and earlier textbooks disproved the possibility of journeys to the moon, and of heavier than air flying machines. Although a compressional tower may be possible using some active means to prevent buckling, a cable under tension is a simpler structure. In 1960 another Russian, a young Leningrad engineer named Y. N. Artsutanov, published calculations about a cable grown from a synchronous satellite. One end would be extended towards the earth, and would weigh the satellite down. The other end would be extruded upwards, lifting the satellite by virtue of the orbital centrifugal force. If the extrusion rates of the two were carefully controlled the net pull could be kept nil. Eventually the lower end would reach the ground. At that time the outer end of the cable would be 150,000 kilometers away from Earth. Tidal force would keep the structure stretched and vertical, and it would hover just above the surface, in perfect equilibrium. The bottom end could then be anchored to the ground, and a large counterweight attached to outer tip. Being far beyond synchronous orbit, this counterweight would pull on the cable, and thus on the anchor. The cable, under full tension, can now support elevator cabs running up and down its length. At synchronous height they may let go to become synchronous satellites. The energy for achieving the orbit comes partly from the long climb, but also from Earth's rotational energy, which accelerates payloads to orbital velocity by a small deflection of the cable. Cabs continuing beyond the synchronous point are pulled along by the ever increasing centrifugal force. They can extract energy from the ride, and on reaching the ballast can have recovered the energy of the climb to synchronous altitude. Such full route passengers are powered entirely by Earth's angular momentum. The ballast is 150,000 kilometers from the center of the earth and moving with a velocity of 11 Km/sec. A cab released from there has enough momentum to coast to the orbit of Saturn on a Hohmann minimum energy trajectory. No known substance can support its own weight from synchronous orbit if it's simply fashioned into a uniform rope. To make the concept barely feasible the cable must be trimmed of all excess mass. At each height the cross section should be just large enough to support the local tension. The skyhook takes on the form of a distorted bell curve, narrow at the ends, tapering to maximum area at synchronous altitude. The taper (the ratio in cross sectional area between the middle and the ends) is exponential in the weight to strength ratio of the material, which means that if you halved the strength or doubled the density the taper would square. If it was 10 before, it would be 100 after, if it was originally 100 it would become 10,000. The skyhooks' size, and very feasibility, is extremely sensitive to the strength of the material one proposes to use. A synchronous cable made of steel has to be $10^{50}$ times bigger in the middle than at the ends and weigh $10^{52}$ times what it can support. Astronomical results like these are the basis of physics text skyhook impossibility proofs. Rockets are similarly sensitive to the energy content of their fuel, and open to the same kind of ridicule. A coal fired steam rocket needs to weigh a 100 billion times as much as its payload, to achieve escape velocity. Per unit weight, Kevlar is 5 times stronger than steel. A synchronous Earth skyhook made of it needs a taper of $10^{10}$ (ten billion), and weighs $10^{13}$ times what it can lift. Better than steel, but still ridiculous. Single crystal graphite whiskers with 50 times the strength to weight of steel have been grown in laboratories. Bulk material as strong would permit a synchronous cable with a taper of only 10, and a mass ratio of 400. Half this strength is perfectly adequate for an Earth synchronous skyhook. Artsutanov's results were printed in popular Russian literature, and showed up in the US in several Soviet published English language books and magazines, where they were widely ignored. In 1966 John Isaacs, Allyn Vine, Hugh Bradner and George Bachus from the Scripps and Woods Hole Institutes of Oceanography independently derived the properties of an Earth skyhook. They managed to get their results published in {\it Science}, along with a note from the editors effectively apologizing for printing such a grandiose and futuristic idea. Their paper elicited a letter from an officer of the Novosti Press agency pointing to and claiming credit for Artsutanov's earlier work. The time for skyhooks was still not ripe. The idea was again forgotten, and no new work appeared for a decade. In 1975 Jerome Pearson, an engineer working at the Flight Dynamics Laboratory of Wright Patterson Air Force Base, again independently derived and published the concept, this time in Acta Astronautica, an international astronautics journal. Undaunted on discovering the idea was already in the literature, he published a second paper in 1976 outlining an operational mode for the Earth skyhook, analyzing its dynamic response to moving payloads. He found that certain elevator velocities excited resonances in the cable, but that a cab could safely accelerate through these speeds, and that the system was generally workable. In 1977 and 1978 Pearson published papers about synchronous skyhooks on the moon. At first glance a lunar skyhook seems even more absurd than a terrestrial one. The moon rotates very slowly, once a month, and synchronous altitude is 400,000 kilometers, the Moon-Earth distance, above the lunar surface. A Moon skyhook apparently has to be much bigger than an Earth model. Fortunately the Earth-Moon interactions come to our aid. In 1772 comte Joseph Louis Lagrange, a French mathematician, tackled the interactions of two heavy masses and a very light one in Newton's newfangled physics. There are five places near two heavy bodies in circular orbits about each other where gravitation and the orbital centrifugal force cancel. A small object with the right velocity in any of these locations will whirl around with the big bodies and appear stationary with respect to them. In the Earth-Moon system, the first point, dubbed L1, is on the line joining the center of the earth to the center of the moon, closer to the moon than to the earth. At L1 centrifugal force and lunar gravity team up to cancel the earth's pull. L2 is behind the moon, where the centrifugal force cancels the combined pull of the earth and moon. L3 is similar, but behind the earth. L4 and L5, well known to future space colonists, form the third points of two equilateral triangles whose other vertices are the centers of the earth and moon. The gravitational and centrifugal forces at L4 and L5 point in different directions. The Lagrangian points in a two body system are analogous to the synchronous orbital altitude of a single body. L1, L2 and L3 are unstable, which means that any positioning error will cause a satellite to drift away. Synchronous satellites of single bodies have the same problem, requiring continual corrections by tiny thrusters to stay put. L4 and L5, on the other hand, are stable. They are actually the centers of shallow, disembodied potential wells, and mass placed there will remain. Skyhooks anchored to the lunar surface can be built passing through, and with maximum thickness at, the L1 and L2 points. Pearson calculated that a lunar skyhook through L1 would be twice as long, 300,000 kilometers, as an Earth hook. The lunar gravity well is very shallow and far less demanding of skyhook construction materials. Existing substances such as Kevlar and graphite composites are strong enough, and result in mass ratios (ratio of skyhook mass to maximum payload mass) of a few hundred. An L2 skyhook is 550,000 kilometers long, and twice as heavy as a similar L1 hook. If the the moon didn't block Earth's view of L2, a communications satellite there could link Earth and the lunar farside. The idea has merit because it's possible to put objects into circular orbits, called halo orbits, around the unstable Lagrangian points. The plane of a halo orbit is perpendicular to the line joining the two massive bodies, and from Earth an L2 halo satellite appears to be circling the lunar disc. Recently a satellite called the international Sun-Earth explorer was put into a halo orbit around the Sun-Earth L1 point to observe the solar wind. While L1 itself is visible from Earth, it is obscured by radio noise from the solar disc behind. Halo satellites must use fuel to counteract drifting. Pearson proposes anchoring a lunar farside satellite to the moon's surface with a very thin, truncated, L2 skyhook. The satellite, a little beyond L2, would not need to station keep. Needing no fuel, its lifetime could be indefinite. The closer to L2 the satellite is, the smaller are the restraining forces needed to keep it there, and the more delicate can be the tether that holds it. The tether mass can be made arbitrarily smaller than the mass of the satellite it restrains. A limitation is the extreme thinness of the lower end of the skyhook. Suppose we are building with a graphite composite material that needs a taper of 30:1 between L2 and the ground, and that a 4000 Kg satellite is being restrained by a 100 Kg tether. The 100 Kg is distributed over 70,000 kilometers, and most of it is near L2. The tether diameter at the ground is then only one hundredth of a millimeter, very tiny indeed. Of course a tethered satellite sticking out of the middle of the lunar farside can't be seen from Earth. If we give it a little sideways kick it will begin swinging like a giant pendulum. The plane of the oscillation will precess, and from Earth the satellite will seem to trace out a complicated lissajous pattern in the vicinity of the moon, being visible virtually all the time. Foremost among the planets, Mars seems to have been designed with a synchronous skyhook in mind. It has a gravity well just deep enough to make a conventional matter skyhook interesting, a simple gravitational environment, and a high rotation to keep the hook short. Kevlar is almost strong enough for the job. A Martian Kevlar skyhook would have a taper of 15,000 and a mass ratio of a million. A material twice as strong would give a taper of 100 and a more reasonable mass ratio of 6000. Some graphite composites occasionally achieve that. Arthur Clarke, in {\it The Fountains of Paradise} suggested that Deimos, 3000 kilometers above synchronous orbit, is in exactly the right place to provide a mass anchor for a truncated Martian skyhook. Using it would permit a skyhook with one third the mass of an equivalent full length cable. The dynamics are similar to Pearson's tethered lunar satellite. \sect{Non-Synchronous Skyhooks} The Stanford Artificial Intelligence Lab was frequently a hotbed of extreme, usually technical, ideas. The premier extremist was John McCarthy, the lab's founder. In the 1950s he conceived a series of ideas about space travel. A synchronous Earth skyhook was among them. Looking up the strongest material to be found in the CRC Handbook, which in those days was steel, he did a rough calculation on the required taper and got the $10^{50}$ figure that has probably nipped hundreds of potential skyhook theorists in the bud. Chagrined, he tried to think of cheaper variants. One involved starting with a satellite in a lower than synchronous orbit. Earth's orbital velocity is extremely high, so simply dangling a cable from a low orbit to the ground doesn't work. But if the satellite with two cables (for balance) spins so that the rotation cancels the orbital velocity when the tips get near the ground, the worst effects disappear. The cables then move like two spokes of a huge wheel rolling on the surface. The concept trades the extreme size of a synchronous skyhook for high spin induced centrifugal forces. While it didn't seem to offer economies dramatic enough to offset the $10^{50}$ figure, it was a cute idea, and McCarthy told it to whoever seemed receptive, including me. My late edition CRC Handbook had a new entry, a NASA table listing the mechanical properties of single crystal whiskers of various substances. Graphite whiskers have a much higher strength to weight than steel, and a little effort seemed worthwhile. Using Macsyma, a huge and very clever computer program written at MIT that does for algebra and calculus what desk calculators do for arithmetic, I derived formulas for synchronous skyhooks, and plugged in the strength of graphite whiskers. A graphite Earth synchronous skyhook could be built with a taper of only 100, and is able to support payloads 1/6000 as massive as itself. Amazing. Even more amazing, a few weeks later I stumbled across Pearson's original 1975 paper, hot off the presses, containing the same results, and then some. It encouraged me to work on the more complicated rolling skyhook. A non-synchronous (rolling) skyhook isn't able to tap its planet's rotational energy the way the synchronous variety does. If it picks up a payload during a ground contact and launches it with more than escape velocity a half rotation later, the energy must come from the skyhook's orbital velocity and rotational momentum. It drops closer to the ground. Conversely a skyhook gains energy when it intercepts a speeding mass with its high velocity outer tip and lowers it to the ground. The variations in orbital altitude make it almost mandatory that the skyhook maintain a safe distance from the surface. A relatively tiny vehicle would be adequate for achieving a rendezvous with a slow moving cable tip at an altitude of fifty kilometers. Burke Carley of Indian Harbour Beach and I worked out a more intimate combination of rockets with skyhooks. The mass ratio of each method is exponential in the velocity change it provides. If the job of achieving orbit is broken up equally between the rocket shuttle and a skyhook, the combined initial mass is minimized. The mass of the rocket and of the skyhook is about the square root of what it would have been had either been used exclusively. The skyhook material strength requirements are halved. The forces on a non-synchronous hook are constantly changing. Maximum stress happens when a cable touches down, and gravity and spin centrifugal force work in the same direction. Making the skyhook shorter decreases the interval over which the forces sum up, but increases the required spin rate, and centrifugal force, in a way that eventually offsets the decreased length. Taper and mass ratio are roughly minimized when the radius of the skyhook is one third the radius of its planet. Skyhooks longer or shorter than this optimum are fatter and weigh more, for the same lifting capacity. Hypothetical graphite whisker material that permits a 100:1 taper Earth synchronous skyhook gives us an optimum size version with a taper of 10, weighing only 50 times as much as it can lift. If built to support 1000 tons, it would be about as long as a transatlantic telephone cable but smaller in cross section and considerably lighter. It orbits once every two hours, alternate tips touching down every 20 minutes. The huge size makes the approaches, cusps of a cycloid, appear essentially vertical. The satellite end descends with a 1.4 g deceleration, comes to a full stop, then ascends again with the same acceleration. There is negligible horizontal motion. The moon's slow rotation does not handicap a non-synchronous skyhook the way it does a synchronous one. An optimally sized lunar version built of ordinary Kevlar has a taper of 4, and masses a mere 13 times its lifting capacity. The modest size makes it a fine alternative to rockets for getting supplies and personnel to and from the lunar surface. The proposed lunar mass driver is unsuitable for this because of its 1000 g accelerations, small payload unit and inability to decelerate incoming capsules. Operating a lunar transportation system based on a rolling skyhook will require occasional adjustments of the satellite's orbital and rotational velocity, even if on the average the amount of mass raised equals the amount lowered. Solar powered high specific impulse ion rockets in the skyhook's midriff are one solution. The lunar mass driver (an electromagnetic cannon proposed by Gerard O'Neill) offers another possibility. There is an orbit which takes a projectile launched parallel to the lunar surface by a mass driver to a perfect, velocity matched, rendezvous with the tip of a lunar skyhook. At the instant of rendezvous the skyhook is almost exactly horizontal, halfway between touchdowns. If the intercepted mass is released at the upper extreme of the tip's trajectory, it flies away with more than escape velocity and the skyhook loses energy. If, instead, the mass is retained until the tip's next ground contact, then dropped, the skyhook gains. The required precision in position, time, and velocity will necessitate some kind of terminal guidance. Ability of the mass driver to deviate its launch angle from the purely horizontal would also help, as would the existence of a catcher's mitt at the skyhook's end. Docking with a non-synchronous skyhook will be nothing at all like connecting with an orbiting spacecraft. The ground end of an Earth skyhook is subjected to 1.4 g of centrifugation and 1 g of gravity, for a net acceleration of 2.4 g. A lunar skyhook grounds with half a g. Unless the docking spacecraft has plenty of fuel to waste chasing the receding tip, the mating will have to occur within seconds. The Air Force's Big Bird spy satellites used to deliver pictures by ejecting film packets which decelerated and re-entered the atmosphere. As a pack parachuted down an airplane with a big hook would fly by, snag the chute lines, and snatch it from the sky. I visualize skyhook docking techniques as refinements of this technology, combined with the computerized guidance methods of surface to air missiles. \sect{Free Space Skyhooks} The concept of a non-synchronous skyhook works even in the absence of a planet. A large cable rotating in empty space can catch a spacecraft with one of its tips, hold onto it for a certain length of time, subjecting it all the while to centrifugal forces, and then release it with altered velocity. Maximum velocity change, twice the velocity of the cable tips with respect to the middle, is achieved when the spacecraft is carried through a skyhook rotation of 180 degrees. Planetary skyhooks need to be of a certain size and strength just to exist in their gravity wells. Free space skyhooks are liberated from this constraint, and can be made arbitrarily large or small. The cross section of a well designed free skyhook varies along its length as a perfect normal (bell) curve. For a given material the mass ratio is exponential in the square of the skyhook tip velocity, and independent of its length. The skyhook can be either short and fat and rapidly spinning, imparting high accelerations for short periods, or very long and thin and slowly rotating, taking a long time to deliver its momentum change. The long thin ones give more time for docking, subject their payloads to lower accelerations, and are probably the best kind to build first. The shorter ones can transfer payloads more frequently, and may be useful when the solar system traffic warrants the extra difficulty. The extreme dependence of mass ratio on tip speed means that a material with a given strength/weight ratio is useful only up to a certain velocity. Kevlar can be made into skyhooks with a tip speed of one quarter Earth escape velocity, and a mass ratio of 400. Material twice as strong would permit the same performance with a mass ratio of 20. Built to heft the 50 ton mass of Skylab, a quarter Earth escape velocity Kevlar free skyhook would weigh 20,000 tons. It could be 100 kilometers in radius, with a diameter of 6 cm at the ends and 47 cm in the middle, rotating once every 4 minutes, subjecting payloads to 8 g of acceleration. Alternatively, with the same weight, its radius could be 20,000 kilometers, with a rotational period of 12 hours. It would then be half a centimeter thick at the ends, three in the middle, and the acceleration would be a puny four hundredths of a g. This kind of hook orbiting the sun at a distance of one AU (same as Earth) can match the velocity of a payload coming in from the orbit of Venus on a Hohmann minimum energy transfer and boost it into a Hohmann orbit to Mars. Eight such skyhooks could span the solar system. One would be needed in the orbit of Mercury, one halfway between Mercury and Venus, one each in the orbits of Venus, Earth and Mars, one in the asteroids, one by Jupiter, and a final one at Uranus. Each provides enough delta v to get a payload to the next one, and Uranus' accelerates to solar escape velocity. The trip from Mercury to Earth takes less than a year, as does Earth to Mars. An extra year and a half is needed to reach the asteroids, and the outer planet part of the journey takes decades. Such maneuvers need skyhooks in the right place at the right time. The required precision is greatly reduced if they have a little more than the bare minimum Hohmann velocity. There is then some leeway in launch angle, and consequently in arrival time and position. Having more than one skyhook in an orbit would also help. The navigational constraints can be further relaxed, and travel times considerably shortened, if other methods of propulsion, like ion rockets, are used between skyhook boosts. Outgoing Hohmann-Hohmann boosts don't affect the skyhook's rotation, but do steal orbital momentum. Although free skyhooks have much more leeway than their planetary relatives, the energy has to be returned sooner or later. The most convenient source is spacecraft moving inward in the solar system. The skyhook system could support solar system commuter traffic at no net energy cost. Outgoing spacecraft would borrow energy from the skyhooks, and return it when they came back. Large, nonrotating, solar sails attached to the skyhook middles might also be used to adjust the orbits. The hypothetical graphite material essential for Earth skyhooks can provide twice the velocity change of Kevlar. With it, solar system hopping would go about twice as fast. \sect{But, But ...} Even after the material strength objections are disposed of, skyhooks present many targets for the nit pickers. For one, they are BIG. The non-synchronous kinds are smaller than transatlantic phone cables, but phone cables don't whip around at orbital velocity. Apart from an occasional trawler or sperm whale, nothing ever runs into a phone cable. But the space around a planet is filled with orbiting objects, moving at relative velocities faster than speeding bullets. If one of these collides with a skyhook, the result is a spectacular mess. At the point of collision the skyhook separates into two parts. One flies off into deep space, the other crashes to the ground. On Earth the groundward fragment would burn up in the atmosphere like a meteor, producing a momentary sheet of flame in the sky. A lunar skyhook would impact the ground, possibly leaving an unusual linear crater. The silhouette of a skyhook is long but thin, with smaller total area than many big satellites, meaning the probability of a collision is very low. Still, skyhooks will operate mostly in the equatorial plane, where the heavy traffic is. The consequences of a collision could be very serious, especially to the colliding object and to payloads or passengers on the hook. Some kind of law of the sea will probably have to prevail. A skyhook is not very maneuverable, but its path can be predicted in advance. It will be the responsibility of other traffic, guided by a latter day Norad, to not get in the way. This seems unrealistic now, when most satellites are out of control once in orbit, but in the near future reusable spacecraft will dock with satellites routinely, to repair or retrieve them, or alter their trajectories. Free space skyhooks probably don't have to worry about traffic density, but are in danger from the very payloads they service. A docking gone awry can result in the spacecraft hitting the wrong portion of the hook with meteoric velocity. Fortunately the collision probability is low. In any case it takes the spacecraft very little energy to change its line of flight enough to miss the slender skyhook, a maneuver that should be planned for. The navigational calculations needed to keep a skyhook transportation system working are not trivial. Several big computers will be kept busy continuously predicting the orbit and rotation of a skyhook, taking into account such matters as skyhook stretch, payload sequences, solar wind and aging of the structural material. In addition they must plan skyhook dockings and energy adjustments, including the possibility of docking failures, and perhaps keep a lookout for collision hazards. Skyhooks are definitely a second generation system. In San Francisco horse drawn wagons preceded the cable cars. Analogously, in space, rockets are blazing the trails and skyhooks will be an early sign of dawning maturity. \end{document}