Trebuchet Cosmonautics — a method of launching cargo into space not by rocket but by a throwing device: an enormous rotating sling that the author called a "space trebuchet." It was proposed by Nizhny Novgorod engineer-physicist Igor Knyaginichev, known under the pen name Professor Rastolkovskiy.[1][2] The idea and the term itself emerged in 2005–2006.[2] The author does not reject the rocket outright — he proposes that it retain the role of a vehicle for leaving the atmosphere, while acceleration to orbital velocities is handled by a rotating rod that exploits the potential energy of lunar material in Earth's gravitational field.[1]
The Concept
The trebuchet was the most powerful throwing weapon of antiquity: a counterweight falls, and a long lever accelerates the projectile. Knyaginichev transfers this principle to orbit, replacing the falling weight with lunar material and the lever with a rotating rod sharpened at both ends. Spacecraft hook onto its tips and release from them already at the required velocity — in theory, two stations of equal mass can exchange orbits with almost no fuel expenditure.[1][3]
The author attributes the high cost of spaceflight to the low payload fraction of rockets: almost all of the mass launched is propellant and the rocket's own structure. A sling, unlike a rocket, does not carry its energy source with it — it draws energy from the difference between the potential energies of bodies falling toward Earth and toward the Moon.[1]
From the same idea grew the author's related concepts: Space Trebuchet and Nizhny Novgorod Lunar Trebuchet — a device for exploiting cislunar orbit; Razgonoplan (Boost-Plane) — a glider with a water-jet engine serving as an atmospheric-exit stage; and Aerometro — urban transit based on the same rotating-carousel principle, but at ground level.[2]
The carousel is stopped and the cosmonaut steps down onto the surface of the Moon.
The Author
Igor Knyaginichev was born on July 16, 1960, in Yakutsk.[2][3] From 1977 to 1982 he studied at the radiophysics faculty of Lobachevsky University, specializing in celestial mechanics.[2] He worked at the Nizhny Novgorod Lenin Television Plant, where he developed optics and electronics for high-precision machine vision systems.[2]
He adopted the pen name "Professor Rastolkovskiy" for the popular presentation of his ideas — under it he published booklets, maintained an author's blog on the city portal nn.ru, and gave talks at Nizhny Novgorod venues.[1] Since the mid-2010s he has lived in Moscow and the Moscow Region; from January 2018 he has published on Habr, where he presents himself as a specialist in the application of slings in space systems and as the developer of an orbit-exchanging space sling.[3]
Fate of the Idea
The concept has never been given engineering form: it remains the author's own conception, set out in booklets, online publications, and calculation tables of material properties for space slings.[1][3] Below is a description of the concept in the author's own words, as he published it.
Author's Description of the Invention
It is common knowledge: THE HIGH COST of all forms of space activity is connected with the low payload fractions of rocket-space systems (for example, the Soyuz launch vehicle, the Proton, or the American Shuttle).
The aim of this article is to draw attention to the remarkable potential and effectiveness of one propulsion-based method of spaceflight, which will make it possible not only to increase the effectiveness (i.e., the payload fractions) of rocket-space systems, but also to use the potential energy of any lunar material in Earth's gravitational field to launch spacecraft into orbit. This energy is the difference between the potential energies of bodies falling toward Earth and toward the Moon — and these energies can in turn be expressed through the kinetic energy corresponding to the escape velocity for Earth and the Moon respectively.
This is clear because the kinetic energy of a body moving at the escape velocity near a planet's surface tends to zero as the body moves away from the planet — that is, it converts into the potential energy of gravitational attraction. Consequently, the work that can be obtained by transferring a unit mass (1 kg) from the Moon to Earth can be calculated as the difference between the kinetic energies corresponding to the respective escape velocities.
The escape velocities are: 11.2 km/s for Earth and 2.4 km/s for the Moon (error < 0.1 km/s). The energy obtainable by transferring a unit mass (1 kg) from the Moon to Earth is therefore: (11.2 km/s)²/2 − (2.4 km/s)²/2 = 59.84 MJ/kg, i.e., nearly 60 MJ/kg — one-third more than the energy released by burning hydrocarbon fuel, or six times more than the energy density of hydrocarbon rocket propellant (i.e., paired with the oxidizer, which must be 3.5 times greater by mass than the kerosene or hydrazine, etc.).
I INTEND TO SHOW HERE HOW THIS ENERGY CAN BE USED TO LAUNCH SPACECRAFT, AND TO PROVE THE FEASIBILITY OF THIS POSSIBILITY AT THE CURRENT LEVEL OF TECHNOLOGY.
Imagine that we have launched into low Earth orbit a one-thousand-ton (If such large masses in orbit seem entirely unrealistic to you, recall that material can be accumulated in Earth orbit by launching it from the Moon. Transferring it from an elongated elliptical orbit that reaches the Moon onto a low circular orbit is easy if the orbit is slowed down pass by pass by grazing the upper atmosphere at perigee. When the orbit has become nearly circular, a small prograde impulse at apogee will raise the perigee and eliminate the atmospheric grazing.) long, thin, and strong rod (of a length on the order of kilometers — the exact figure does not matter for now), with docking nodes — or more precisely, hooks — for spacecraft at both ends, rotating about its center of mass. The linear velocity of the tips during rotation, relative to the center, is measured in hundreds of meters per second, meaning that the resulting centrifugal forces create tensile stresses comparable to the ultimate strength of the rod's material.
Let the plane of the rod's rotation coincide with the plane of the orbit. The entire picture of motion will then be two-dimensional and more intuitive, since the rod remains constantly in one plane — the plane of the diagram — although there is in fact no real necessity for these two planes of rotation to coincide.
Spacecraft may attach to the docking nodes — the sturdy hooks. This can happen only during the brief moment when two velocity vectors coincide: the velocity of the tip-hook, whose direction of motion along the circle is continuously changing, and the velocity of the spacecraft, which is moving in a straight line tangent to the circle and uniformly relative to the rod's center. In other words, docking requires coincidence both in space and in velocity — and this task has always been solved in automatic docking operations.
The only difference is that the time available for completing the docking (i.e., the hooking) is reduced many times over, but there is nothing inherently impossible about this. The real difficulties lie elsewhere: in the generation not only of overloads, but also of powerful oscillations. We shall leave the complexities for later, and for now examine what benefits we gain — benefits that are worth the effort of overcoming these challenges.
It is clear that the purpose of this device is to save characteristic velocity for the launch vehicle carrying our spacecraft. The linear velocity of the docking node's rotation is exactly the amount by which the spacecraft's velocity before docking can be less than the velocity of the rod's center. Obviously, the velocity of the center of mass equals, or is slightly greater than, the first cosmic velocity. And if it were possible to spin the rod's tips up to a velocity of, say, 3 km/s, then the required characteristic velocity of the launch vehicle for putting satellites into orbit would be reduced by that same amount compared with the currently required characteristic velocity of at least 9.3 km/s.
This last figure exceeds the first cosmic velocity (≈7.8 km/s at an altitude of 200 km) because it accounts for the cost of lifting the spacecraft 200 km above Earth's surface (characteristic velocity 8.05 km/s) and gravitational losses, which today are generally no less than 1.25 km/s.
Thus, by subtracting 3 km/s, we can use a two-stage — or so-called one-and-a-half-stage — launch vehicle (or even a single-stage one) with a characteristic velocity of about 6 km/s, and achieve a payload that is 3–4 times greater than that of conventional space rockets.
The relative cost of recovering the elements of such a system (i.e., of maintaining the reusability of the launch vehicle) is considerably lower, since reentry into the atmosphere for braking will occur at a substantially lower velocity: 5.2 km/s rather than 8 km/s. Moreover, when the launch vehicle with the spacecraft approaches the docking hook, it is possible not only to transfer the spacecraft onto the hook but also to remove some mass from that hook and transfer it to the recoverable launch vehicle, in order to deliver that mass back to Earth.
Such an unusual method of bringing the products of space research down to Earth is far cheaper, and it also has the advantage of transferring part of the momentum of that mass to our orbital thousand-ton rod. Of course, the rod need not necessarily have a mass of 1,000 tons — that is merely a convenient thought experiment, making it conceivable to attach, for instance, a 6.5-ton Soyuz spacecraft to such a rod. The large mass is needed so that the attachment of the spacecraft's mass does not knock the rod out of orbit due to its deceleration by several tens of meters per second, which occurs in accordance with the conservation of momentum. No such deceleration will occur at all if the masses exchanged (transferred) are equal!
And that is where the solution to the problem of braking our rod by the attached spacecraft is hidden. It lies in the exchange of equal masses! AND THEN 1,000 TONS WILL NOT BE REQUIRED — TENS OF TONS WILL SUFFICE.
And where is one constantly to obtain masses for such an exchange? The obvious answer is to use lunar soil.
That is, before each docking, the hook at the end of the rod must carry a mass (a billet or a bag) of lunar soil equal to the mass of the spacecraft being attached. This lunar soil is released at the moment of docking, freeing the hook of the docking node for the spacecraft being launched. It is entirely unnecessary to recover this lunar soil — it can burn up like a meteorite (not oxidize, but melt, evaporate, and disperse) from aerodynamic heating in the atmosphere.
Even more sensible would be to fashion some kind of structure from this lunar material prepared for release, and to use it as a heat shield protecting the recoverable upper rocket stage of our two-stage (or one-and-a-half-stage) reusable launch vehicle during entry into the dense atmospheric layers — by attaching this shield (until it evaporates) in front of the upper stage.
You can now understand why such a spacecraft-catching machine as our rod was not invented earlier. The idea had long been "in the air," but could not gain strength and solidity until it had been thoroughly worked through and calculated, and so such ideas had until now faded away and been lost to society. For example, the idea was criticized on the grounds that using such a "carousel" in orbit (its ground-based use for launching spacecraft was already rejected by Tsiolkovsky because of the low strength of materials available at the time) would bring no benefit, since the momentum gained by the spacecraft upon launch is taken from our rod-carousel. This momentum must be restored for the next use, and doing so would allegedly require rocket propellant that could be obtained from nowhere but Earth.
This apparently creates a vicious circle: even if we learn to use fuel somewhat more efficiently on a large thousand-ton space station than on a launch vehicle — that is, by using an engine of low thrust but with a high exhaust velocity (higher specific impulse) — the energy required would be far greater than any propellant can contain. An additional energy source would then be needed, but solar panels would add extra drag, i.e., velocity losses from atmospheric friction at an altitude of 200 km. And the many-kilometer rod itself presents considerable drag.
In addition, there are the high overloads — especially at the rod's tips — and the need to overcome them when transporting a spacecraft toward the center. Placing a nuclear reactor as a power source on a device already under such structural stress seems exceedingly dangerous. No president would authorize it — although reactors did fly in space not infrequently during the Cold War, and a nuclear power unit and the rod can be kept well apart.
But it turns out that nuclear energy is not needed here at all. All the problems are solved by the use of extraterrestrial material, and we have this inexhaustible resource: the Moon. Moreover, the strength of materials has grown by approximately two orders of magnitude in the 70 years since Tsiolkovsky's death, which means that the achievable tip velocity of a rotating rod has become more than ten times greater than the velocity of the "carousel" about which Tsiolkovsky wrote (he cited the figure of 200 m/s).
Let us now return to describing the operating principles of "this rod" — our spacecraft-catching machine — and proceed directly, without dwelling too long on the technical details of solutions I have already rejected.
First, it would be desirable to eliminate the lengthy procedure of moving the spacecraft toward the center of rotation of the rod. This procedure is associated with a multitude of problems: prolonged overloads (while the spacecraft is traveling toward the center — a distance of kilometers), their probable range of 5–30 g, complex mechanisms generating the forces needed for movement and applying lateral compressive forces on the slender rod, numerous elements subject to friction and wear, the need to supply electrical power to the drive, and the gradual change in the moment of inertia and the shift of the system's center of rotation.
And all of this against the backdrop of the powerful oscillations arising at the moment of each docking, which require damping. Then our "vertical-travel locomotive" (to call it anything else would be dishonest — it is not an elevator; an elevator has a reeling cable… and if we were to reel in the rod like a cable, we would spin up even faster to the point of catastrophe — think about what would happen if we concentrated the entire enormous rotational momentum into a single point) would also have to navigate around the vibration dampers on its way to the center, which would either complicate its design and/or the dampers twofold, and increase their weight.
All these problems vanish if, half a revolution after the spacecraft attaches to the rod, we release it. Our spacecraft will then find itself not on a circular orbit, but on an elliptical one, with its perigee at the point of release. You might say: "But that is not where we wanted to go, and it is wasteful: we are taking double the momentum — and two to three times more energy — from the rod, and how are we now to return to a circular orbit?" But I prefer the elliptical orbit!
I understand why you want a circular orbit — that is where all cosmonauts have been flying to the ISS so far. Well, even if we don't send people this way, at least we could send useful packages of food and equipment to the ISS. Quite right — food withstands any overloads, and in my opinion it would be better to transfer the ISS itself to this elliptical orbit just once, using the same lunar-soil energy. Alternatively, a new station could be built on this orbit from lunar soil — or, more naturally, the ISS could be moved to an elliptical orbit and used as a base for constructing a new station, with an additional outer shell initially added from lunar soil, since cosmonauts need protection from high-energy protons when passing through the radiation belts.
They shouldn't have to sit in cramped radiation shelters for half an orbit at a time. But this also depends on which ellipse we put the station in: the trajectory at the perigee section may pass through the gap between the radiation belt and Earth's atmosphere, while at apogee it bypasses the radiation belts on the outside. Such an ellipse would need to be quite elongated — and this might not be achieved immediately — but converting the ISS into the main base for processing lunar soil would be very much the right thing to do. In the initial period, when the ISS orbit has not yet been changed or is still intermediate during apogee raising, the cheaper packages for the ISS — i.e., those launched with the help of the rod — will have to be decelerated either by the upper atmosphere in the old-fashioned way, or by another rod operating analogously but to decelerate the orbital motion of the spacecraft, and a much smaller one at that.
It is smaller because it needs to change the spacecraft's velocity by half as much. For after the first rod releases the spacecraft, it imparts to it a velocity exceeding the first cosmic velocity (or more precisely, the velocity of the rod's center of rotation) by exactly the amount the spacecraft lacked before docking with the rod (this is a first approximation, but a sufficiently accurate one — and with equal mass exchange, an exact one). The second rod must have an intermediate center velocity, midway between the spacecraft's high (elliptical) velocity and the first cosmic velocity or the ISS's velocity. One must also keep in mind that the ISS flies at an altitude of about 400 km, while the point of capture of the spacecraft by the first rod is at an altitude of 200 km, and the release point is higher by the length of the rod (if, as we assumed initially, the rod is symmetric). In other words, the velocity calculations must in principle also account for changes in altitude (the conversion of kinetic energy into potential energy), if we wish to be precise.
Second: we can prevent deceleration of the rod mainly by equal mass exchange at all dockings and undockings. One could, of course, restore its velocity using reaction engines, using lunar soil to manufacture rocket propellant. But on reflection, one can see that all such manipulations with lunar soil (braking it in the atmosphere, then chemically processing it, etc.) only reduce the efficiency of the possible direct use of its momentum, which at approach to Earth equals the product of its mass and the escape velocity. The remarkable fact is that the difference between the escape velocity and the first cosmic velocity is only 3 km/s. Equally remarkable is that such a tip velocity is achievable with certain modern materials, especially if the rod is made to taper toward the ends.
This favorable circumstance makes it possible to carry out the mass exchange at the moment of releasing the spacecraft. That is, at the moment when the spacecraft's velocity at the top of the circle reaches 11.1 km/s (8 — velocity of center + 3 — rotational velocity), we must bring to that point a billet of lunar soil equal in mass to the spacecraft, and carry out a re-docking — i.e., exchange the spacecraft for the billet on the hook. This is possible because the billet, traveling from the Moon, has a velocity of 11.1 km/s. Our spacecraft will then transfer to an orbit with a velocity of 11.1 km/s, tangent at apogee to the Moon's orbit.
I have added a small decimal digit for the sake of precision-minded readers (of whom I am one myself), but such a high level of precision is not yet needed to understand the essence of the method. In reality, the center velocity is not 8 but 7.8 or 7.7 km/s, and the rotational velocity required may be somewhat more than 3 km/s, which will noticeably affect the material strength requirements for the rod and may call for greater tapering of its ends — but this is not important for understanding the operating principle of the system. That is why I have allowed such rounding. Is it possible to carry out such docking operations and "deliveries" at the current level of technology? Why not? Radio-navigation methods accurate to 10 cm on a global scale have been perfected for over a decade. Astronomy has long astonished us with the brilliant precision of planetary position predictions.
So bringing a massive billet sent from lunar orbit toward Earth to within even a millimeter of the docking hook will present no insurmountable problem. The process will be carried out by the standard method of successive approximations — trajectory corrections; to increase the accuracy of the billet's location, we simply reduce the radio wavelength; the navigation systems will be more modern, but the principles will be the old ones. Of course, the navigation and reactive guidance equipment installed on the billet while still in lunar orbit for its guidance need not necessarily be discarded into the atmosphere and burned up. It should be sent back to the Moon for reuse.
In this way, each piece of guidance equipment can be used once every 10 days (that is approximately the orbital period of an orbit tangent at apogee to the Moon's orbit, neglecting the time spent on operations near both bodies). For each reuse, it must be relaunched from the rod's tip in the direction of the Moon's new position in its orbit. The Moon completes one revolution in 27 days, meaning that in 10 days it will have moved approximately one-third of an orbit — more precisely, 133° — and the apogee direction must be rotated forward by that same amount; i.e., the perigee must be rotated by the same angle, since the perigee is the starting point for the next trip to the Moon.
In other words, the starting point for the guidance unit heading out for the next batch of lunar soil (which I call a "billet," as artillerists call a simple projectile — a piece of metal) is shifted 133° ahead of the billet's attachment point in the direction of travel, meaning one must wait more than one-third of an orbit — that is, 33 minutes — between the attachment of one billet and the launch of the next. Dividing 24 hours by 33 minutes gives 43 such periods. This means 43 spacecraft can be launched per day (without interfering with one another), and consequently 43 billets can be received. To keep the rod in continuous use, one would need 430 units of guidance equipment, constantly traveling back and forth between Earth and the Moon. In principle, spacecraft launches can be carried out even more frequently — on every revolution of the rod — but in that case the guidance units would have to be used only once a month (every 27 days), since their orbital axes (ellipse axes) would no longer rotate by one-third of a revolution.
It follows that if such a system were set in motion even once (with a single tether), cargo flows into space could grow to scales utterly unimaginable today. And if the pricing for launching payloads into space were to become comparable to that of air freight, the cost of putting one tonne into orbit would approach the price of 2 tonnes of kerosene plus 7 tonnes of liquid oxygen. That is sufficient (you can verify this using the Tsiolkovsky equation, taking the exhaust velocity as 3 km/s) to accelerate one tonne to 6 km/s by reaction propulsion (plus 410 kg of launch vehicle structure per tonne of payload — though in this case I believe 8–20% for structure is adequate, rather than 41%). As for the other cost components — lunar regolith, for example — there is no floor to how cheap they can become, since they will be produced ever more frequently away from Earth, at ever greater scale, and using unmanned technologies.
The question arises: WHAT IS THERE TO SEND INTO SPACE given such enormous capability? (And a related sub-question, which we will address a little later: is it convenient to travel along orbits extending all the way to the Moon, or how best to take advantage of that?) In the early period, equipment must be sent into space: guidance vehicles; lunar launching equipment for firing lunar regolith from the Moon's surface (launch velocity 600–900 m/s); lunar orbital launching equipment — the same tethers (but of far lower velocities and smaller dimensions) for catching and dispatching lunar regolith toward Earth; and equipment for establishing a space-based industry producing construction materials from lunar regolith: glass for greenhouses, fiberglass, and metals (iron, titanium, aluminum) for building orbital habitats.
All this equipment will, however, only keep the ever-growing Earth-to-space launch capacity busy for a limited time. A moment will quickly come when the greater part of this equipment — the more massive portion — can be manufactured in space from lunar materials using remotely operated facilities. The logical consequence of this must be the delivery of the consumers of these resources into space — that is, the steadily growing transport of people to these elliptical orbits.
But can we launch people into space using the orbital tether described? After all, as noted earlier, the overload lasts only a short time — just half a rotation of the tether. Perhaps we can somehow reduce the g-forces to acceptable magnitudes and durations. One may also recall that immersion in liquid makes overloads of 20–30 g (200–300 m/s²) tolerable. Or perhaps it will be possible to make the first launching tether universal — suitable for launching both the most highly trained cosmonauts and equipment that is not of the most rugged construction — which would be more economical. And the return of cosmonauts to Earth by tether is not only cheaper but, I believe, safer as well.
As any school physics course teaches: overloads are determined by acceleration (divide the acceleration by g = 10 m/s², ±2% aside), and accelerations in curvilinear circular motion are defined as the square of the linear velocity divided by the radius of curvature. (Recall: a = ωv, ω = v/R, therefore a = v²/R, and consequently aR = v² — a constant.)
Indeed, the linear velocity of the tips of our tether is constant, and therefore the product of acceleration and radius is constant — but just how large is it? Enormous, of course: v² = (3…3.2 km/s)² ≈ 10⁷ m²/s², or 100 m/s² × 100 km. (Impressive, isn't it?) This means an acceleration of 100 m/s² (or 10 g) at a radius of 100 km. And what is so frightening about that? — Space is vast.
One can choose a perfectly tolerable overload of 5 g and a radius of 200 km. The total length of the tether would then be 400 km, which fits neatly between altitudes of 200 and 600 km — that is, between the upper boundary of the atmosphere (the lower boundary for spaceflight), at approximately 140–200 km, and the lower boundary of the inner radiation belt at 600 km above the equator. The lower boundary of the inner radiation belt above the equator actually lies somewhat higher: 600 km above South America and 1,500 km above Australia, compared with mid-latitudes around 40°, where it stands at 400 km. Consequently, when launching in the equatorial plane (or into orbits inclined up to 20° to the equatorial plane), overloads of 5 g suffice — and almost anyone can withstand that in a reclined position, since the inertial forces act from within the body, not as though four additional people were lying on top of you. (Top-level aerobatic pilots have been known, in the heat of competition, to pull turns at 12 g — i.e., 120 m/s² — at which point the wings of aerobatic aircraft have snapped off. After three such incidents, aircraft of that type began to be designed for 15 g.)
For launches at angles greater than 40° to the equatorial plane, the gap through which the tether must pass between the atmosphere and the edge of the radiation belt is approximately 200 km, and the tether length will probably need to be halved to 200 km, the radius to 100 km — in which case the acceleration will have to be raised to 10 g. Sustaining that for 100 seconds is problematic, though Gagarin reportedly endured 12 g during training. The 10-g variant is somehow inconvenient — immersing the cosmonaut in liquid is not yet necessary, but very few people would be able to fly even in an anti-g suit with assisted breathing.
And if one is going to immerse the cosmonaut in a water-filled capsule, it becomes more interesting — and perhaps more practical — to push the acceleration to 30 g, or perhaps even beyond that through various expedients such as surgical reinforcement of the parts of the human body most susceptible to g-forces, or by regulating pressure in individual body compartments. At 30 g the radius would be 33 km and the length 66 km. That is still very long, and the tether more closely resembles a thread or a cable. It cannot resist transverse bending.
Yes, in reality this will be a massive and strong cable of enormous length. Why have I been calling it a rod all along? Simply because it will be kept permanently taut by centrifugal forces to such a degree that one can scarcely tell the difference — it will always be straight, or nearly always, when in operation (that is, except during transport and preparation for spin-up). To help the general reader understand the launch process and the use of lunar regolith slugs, it is more convenient to treat this cable as a rigid rod. This avoids errors and misconceptions about the nature of the motion, which would easily arise if I had said from the outset that it is a cable — for a cable has an infinite number of degrees of freedom.
If the mass exchange at the ends of our spun-up cable is always equal, its tension will remain constant, its length will remain constant, and no oscillations (or waves) will arise at the moments of mass-exchange operations. It will therefore behave like a rigid rod. And someone with a secondary education can understand how it works — no mathematical physics required; school mechanics from Year 9 (formerly Year 8) is sufficient, along with Kepler's First Law from the astronomy curriculum.
I do therefore hope that even in our time of minimal interest in spaceflight — a time of mockery and even condemnation of those who pursue it in a quixotic spirit and try to bring others along — I can arouse the interest of those who are still searching, as best they can, for points of spiritual support and for ideas that unite the nation and humanity regardless of the scientific background of the people involved. Very few today (they are simply irrational by current standards) are prepared to engage with problems of spaceflight; it is unfashionable and demands mental effort. The Mass Media neither discuss nor write about it — and so the public's minds go untrained, relaxed to a porridge-like consistency.
This situation must be changed, and it can be. If we do not do it, we will lose the future — that is, a worthy future — while space technologies will be developed (by whom?) and space settlements and cities will be built from lunar regolith within 10–15, at most 20 years. All of this will be done by the present-day schoolchildren of other countries, not ours.
At this point we shall break off our digression from the main subject and return to describing the operating principles of space-based throwing machines — which would be a simpler name for what we have been examining than "catching-and-throwing spacecraft vehicles." To shorten the name further, I propose a term commensurate with the scale of the device: the space trebuchet.
A trebuchet is a huge, multi-tonne medieval siege engine capable of battering fortress walls from a distance of 200 metres, striking stone cannonballs weighing a hundredweight with considerable accuracy again and again into the same spot on a wall. There were no rubber or spring materials capable of storing sufficient energy for such a throw at the time (nor can one purchase such a colossal shock absorber today). Yet engineers of that era solved the problem: the gravitational energy of eight tonnes of lead (or even fifteen tonnes of sand and stone) raised several metres by a simple mechanism — a well-sweep with a sling attached to its long end — was converted into the kinetic energy of a stone cannonball. I believe there is a very close and instructive analogy here.
But is our rod-cable of a grand cosmic sling not too long? And what does length even matter to it — it runs into nothing and touches nothing as long as it is shorter than 200–400 km. Does longer mean more time to unwind? It will unwind on its own at the very start of spin-up. Do you think longer means heavier? Pardon — there is weightlessness there, so we are speaking of mass. At one and the same cable mass we can have very different lengths, and conversely, at one and the same cable length we can have very different masses, depending on the cross-section and density of the material. Mass equals density times volume, and volume is the integral of cross-section along the length.
In the present case, then, the admissible payload that can be attached at the cable's ends — measured as a percentage of the total mass of the tapered cable — is completely independent of length. What matters is the square of the linear velocity at the tips and its ratio to the specific strength, i.e., the quotient of the material's ultimate tensile strength divided by its density. All of this applies, of course, to a properly designed cable — one manufactured according to the optimal law of cross-sectional variation along its length. In that case the entire cable material, throughout its volume, will be uniformly stressed to a level equal to the ultimate tensile strength.
It is purely for the convenience of mathematical reasoning that we set the stress equal to the ultimate tensile strength. In practice, of course, some safety margin must exist, and it must be uniform throughout the cable's volume in order to minimise the probability of failure at any point. But this is equivalent to assigning the material a lower, reduced ultimate tensile strength and solving the problem with zero safety margin throughout the volume. In such a critical structure operating at its limit, we must know almost everything about the material at virtually every point and at every moment in order to forestall the onset of failure. And this does not — alas — mean there is any possibility, as is customary in construction, of taking a safety margin substantially greater than unity.
That would lead to a very large multiple increase in cable mass. As is customary in cables, the load of accidentally broken strands is taken up by neighbouring strands — but our cable must be designed far more intelligently than an ordinary one, so that when a single strand breaks its stress is instantaneously redistributed not merely to four or six neighbours but equally across a hundred strands at that cross-section.
In this way we can reduce the safety margin to 1–2%, or equivalently bring the safety factor to 1.01 — which any structural engineer today would regard as absurd (they customarily design with safety factors of 10–20, treating percentage-level margins as negligible). Once such a break occurs (one strand in a hundred), it is necessary to smoothly reduce the cable's load by 1–2% (so as not to excite oscillations) and carry out an automated repair — by a micro-robot, for example. The robot could be delivered to the break location by a mini-rocket to speed up the repair. I consider it thereby already demonstrated that accident-free operation of such a structure is possible with a safety factor of only 1.01, although more technologically elegant methods of repair or self-healing are also conceivable. How is the 1–2% load reduction accomplished? The slug gradually sheds all of its 1–2% of lunar regolith in tiny chips, which immediately burn up in the atmosphere so as not to create hazardous micro-meteoroids. One could go on at great length providing details, but this is already becoming tedious.
More interesting is the question of which modern materials could be used to manufacture the cable so as to achieve a tip speed of 3 km/s — and what percentage of payload one can expect at such speeds. Would it turn out to be merely a pea's worth per tonne of cable? There is such a danger, even when using the very best material at less than its full — i.e., maximum — stress. For the cable cross-section decreases from the centre according to the formula e^(−kx²), or exp(−kx²).
This is a qualitative representation of the dependence (the exact and detailed version comes later), but it already makes clear that once a certain threshold is crossed the cable's cross-section — and with it the payload at its end — becomes microscopic. This happens when kx² exceeds roughly… 4 or 6.
It turns out that suitable materials for such a cable have existed for several decades, and it is remarkable that no one noticed this sooner. Fiberglass has existed for about forty years and could have been used to make a cable with a tip speed of 1.5 km/s. That would already have provided a very significant boost to the payload capacity of launch vehicles, and hence to spaceflight as a whole. In those days, orbital nuclear power plants were viewed with considerably more favour as well.
Why did no one realise that the momentum lost by the rotating rod-cable upon attachment of a spacecraft could be restored as many times as desired from one and the same orbital nuclear rocket engine (a development of the 1960s–70s)? That is precisely where its real applicability and safe reusability lie. Its exhaust velocity is 9 km/s (hydrogen at 2,500°C with a nozzle efficiency of ≈78%), not the standard 3 km/s of most chemical engines in conventional launch vehicles — three times the specific impulse. Yes, one would have had to carry liquid hydrogen into space with every spacecraft — about 17% of its mass (1/6 of the spacecraft's mass on average, but not necessarily on every flight) — but the total spacecraft mass would then have increased by only 65% when using the same launch vehicle.
Thus, for every kilogram of matter (propellant for the engine) launched into space, one would have obtained three times the reactive impulse compared with the standard approach. And by releasing the spacecraft at the top of the tether's rotation, one would give it a velocity 1.5 km/s above the first cosmic velocity. Ignoring the altitude gain and the higher launch point, the spacecraft would enter a 3.5-hour orbit with an apogee at 1.5 Earth radii altitude (2.5 R from the centre of the planet). From that orbit, heading for the Moon is only natural — one need only add 1.6 km/s. By saving a combined 3 km/s, we gain a factor of e ≈ 2.72 in payload (comparing with an ideal rocket whose engine and structure have minimal — i.e., zero — mass and whose exhaust velocity is the standard 3 km/s; this is close to reality in the present context).
I read in V. I. Levantovsky — whom I regard as the finest Soviet writer-teacher on the mechanics of spaceflight for those who wish to understand spacecraft trajectories and rocket engines — already in the 1970s about the real possibility of building and widely deploying low-thrust nuclear interorbital tugs with accelerations of 0.01–0.5 g (we will not discuss electric-propulsion tugs of ultra-low thrust, 10⁻³–10⁻⁵ g, here). These tugs were to transfer space cargo by nearly ideal impulsive manoeuvres between low Earth orbit and higher orbits — including near-lunar orbit — via intermediate elongated elliptical orbits. The author noted (in the spirit of pre-Chernobyl times) that there would be no radioactive contamination of Earth from such tugs, since they would never return to Earth.
Their key advantage is the high exhaust velocity of 8–10 km/s, which yields the benefit of dramatically expanding the possibilities for space exploration by lightening and cheapening all space transport operations. Moreover, a tug is by definition a reusable vessel. Their purpose would be "eternal" landing-free wandering in near-Earth space out to no farther than lunar orbit, with periodic refuelling with liquid hydrogen in low orbit from Shuttles. And it would be desirable to use them as frequently as possible for maximum economic benefit. When the service life of a reactor (tug) ends, it could be dispatched to a storage location 400,000 km from Earth at one of the Lagrange points, where the radioactive waste of the entire civilisation is planned to be stored.
Yet even the fact that the risk of accidents and contamination of any territory on Earth is extremely small does not, in our time, give the green light to deploying nuclear tugs in low Earth orbit. A failure of automation or the ever-present human factor — and a "nuclear rubbish bin" falls from space next to some populated locality. Since we already know (are informed) that space can be developed without nuclear energy — specifically, drawing on the energy potential of lunar material — I think it is permissible to reason about the use of nuclear tugs and compare their parameters with those of the space-trebuchet cargo transport system.
To bring a malfunctioning geostationary satellite back to a Shuttle, having refuelled from the same Shuttle, a tug would require 8.5 km/s of characteristic velocity (this is Levantovsky's figure; I calculate 7.81 km/s plus 200 m/s for corrections and manoeuvres, totalling 8 km/s). This would require liquid hydrogen amounting to ~157% of the tug's mass plus ~97% of the satellite's mass. If the same operation were conducted using a space trebuchet made of 1970s materials (tip speed 1.5 km/s) and if the tug were refuelled with propellant from the trebuchet itself, we would save 3 km/s of the tug's characteristic velocity (1.5 km/s at the start and end of the operation), reducing the required characteristic velocity to 5.5 km/s.
The nuclear tug would then require liquid hydrogen amounting to ~84% of the tug's mass plus ~49% of the satellite's mass — roughly half as much as without the trebuchet. Moreover, by returning the tug with the satellite to the trebuchet, we recover most of the momentum that the trebuchet lost when launching the tug together with its fuel — or rather propellant. The tug in this case need not even dock with the trebuchet; it only needs to exchange a cargo for fuel while flying, at the moment of the handover operation, not far by space standards from the trebuchet at the same relative velocity of 1.5 km/s. Docking or precise guidance of the satellite to the trebuchet's docking end can be performed by a miniature guidance vehicle of the same type used for directing lunar slugs.
And the jettisoned propellant (a Dewar flask of liquid hydrogen under low pressure) the tug will catch after a small manoeuvre. Their orbit is, after all, a shared one: speed 1.5 km/s above the first cosmic velocity, period 3.45 hours, apogee 10,000 km. If two identical trebuchets are used in sequence (tip speed 1.22 km/s — meaning the trebuchets would be of far lesser mass than at 1.5 km/s), the tug could be dispensed with entirely: the characteristic velocity drops to 500 m/s, which any ordinary chemical rocket engine can easily handle.
Imagine the second of our trebuchets travelling along an elliptical orbit that is tangent at perigee to the orbit of the first trebuchet (a low circular orbit) and at apogee to geostationary orbit at an altitude of 35,800 km. At apogee it would drop off and pick up retired geostationary satellites, and at perigee it would exchange these cargoes with the first trebuchet. At this point (perigee) the difference in the velocities of the centres of mass of the two trebuchets is approximately 2.44 km/s. It makes more sense, in order to save trebuchet mass, to split this velocity difference equally between them — between their tip speeds. That is precisely how the tip speed of 1.22 km/s arises.
Admittedly, the satellite will be slightly uncomfortable spending the entire 5-hour interorbital transit under g-load while hanging from the end of the second trebuchet — but at the apogee point, after release, its velocity will have received an increment of 1.22 km/s from T2's tip speed, leaving it only 250 m/s short of the circular geostationary velocity. A small tug with a characteristic velocity of 500–600 m/s is therefore needed here (with conventional propellant at an exhaust velocity of 3 km/s, approximately 20% propellant mass).
The small tug will collect its propellant from T2 (picking up a propellant tank from its tip as it flies past), deliver the old satellite to that same trebuchet (attaching it, along with the empty propellant tank, to the tip), pick up a new satellite, and place it into geostationary orbit (spending only 250 m/s), then slowly drift at up to 50 m/s toward another old geostationary satellite (it is understood that this last velocity is given relative to those satellites). After braking, it will take on that satellite and wait for the moment of closest approach with T2. It will then apply a reactive impulse of minus 250 m/s (against its orbital velocity) to match its speed with that of the docking tip of T2 — and the entire process, from the beginning of this paragraph, repeats itself.
Such a system of two trebuchets and numerous small tugs (and the tugs could be replaced by quite small trebuchets T3 rated at 250 or even 125 m/s) can periodically, orbit by orbit, supply and generally service even a crewed geostationary station with large cargo flows — and that is, after all, the pole of inaccessibility of near space: stopping there is harder than flying to Mars or crashing into the Moon. The system can be used once every 10.5 hours — that being the orbital period of T2. And it can, in principle, be used every single time. The only complication arises from the fact that the orbital periods are not in exact ratio: if the periods were 12 h and 24 h, for example, T2 would service only two diametrically opposite points on geostationary orbit, but it would do so daily.
The trick here is that if the station and the trebuchet (when in apogee) do not happen to be in the same location (approximately), the cargo will simply have to wander in a waiting orbit for a long time — anywhere from one day to a week. Fortunately, after being released from the trebuchet at geostationary altitude, the cargo has a velocity that differs from the geostationary velocity by 250 m/s. Within less than a day it will therefore return to geostationary altitude but at a point with a different geostationary coordinate (longitude). Over the course of a week it will thus make sufficiently close approaches to all points on geostationary orbit, requiring only the necessary corrections.
In this case, ensuring that both trebuchets converge at the perigee of the second trebuchet's orbit at each pass for cargo transfer proved straightforward, since 10.5 hours is a multiple of 1.5 hours — the orbital period of a low orbit. That is, the first trebuchet completes seven revolutions in a low orbit at 280 km altitude during the time the second trebuchet completes one revolution along its elongated ellipse from perigee and back to the low point of the orbit. This guarantees repeated rendezvous. At these moments it is even possible to perform an instantaneous exchange of cargo between the maximally close ends of the trebuchets. Through successive correction maneuvers, achieving such extreme proximity is entirely feasible if all types of orbital perturbations are accounted for — and this too is possible.
This makes an interesting process viable: the exchange of equal masses, which avoids jerks at the moment of reconnection and hence eliminates oscillatory loads on the trebuchet cables. And if the masses exchanged are not equal but at least comparable — or better still, close — even then we substantially reduce the magnitude of the oscillations that must be damped (which is very important!). Unfortunately, at the beginning of our large-scale (trebuchet-based) space construction program there are no masses available to compensate for the trebuchets' momentum losses and reduce oscillatory loads during transport in the direction away from Earth into space — more precisely, in the direction of increasing specific mechanical energy (K/m + P/m) and specific angular momentum (v·r, where v is the horizontal velocity component), both computed relative to Earth's center.
This explains why it is necessary to travel to the Moon to obtain lunar soil: any substance there possesses a large store of potential energy (as well as angular momentum) relative to Earth. Orbital space trebuchets will allow the exchange of momentum, energy, and indeed the entire subsequent trajectory (after the exchange) of two space objects: a spacecraft (payload) and an object made from any lunar material. This could be a bag of lunar sand, a roughly chipped lunar stone, or a geometrically shaped blank smelted from lunar sand or regolith on the Moon using a solar furnace. The only requirements are that these objects have the same standard mass for which our trebuchets are designed, sufficient strength to withstand the g-forces produced by the trebuchets without breaking apart, and a fastening point — a hook or a loop (all of which are relatively simple to fabricate).
But to make use of these objects — that is, to exploit their gravitational potential energy and angular momentum — one must first of all drop them from the Moon toward Earth, or more precisely transfer them to an orbit with a perigee 200–400 km above Earth's surface (a higher orbit is also possible if we need this raw material there as well — whether as an energy carrier, or more precisely a momentum carrier, as a building material, or most likely all of the above in combination).
The Moon itself moves at an orbital velocity of 1,020 m/s, and if an object is thrown with only escape velocity it will end up in the same lunar orbit as an Earth satellite. It must be thrown such that only 190 m/s of the Moon's 1,020 m/s orbital velocity remains (a reduction of 830 m/s), i.e., in the direction opposite to the Moon's motion. It is desirable to impart the full required space velocity to the object while it is still nearly at the Moon's surface: this saves almost 700 m/s compared with a two-stage acceleration. It follows that, if one wishes to avoid rockets (manufacturing rockets and propellant on the Moon is still a very distant prospect), a gun or catapult capable of launching objects at 2.51 km/s is required. But if a trebuchet in lunar satellite orbit is used, the required launch velocity from the Moon's surface decreases by a factor of three!
The lunar trebuchet has an orbital velocity of 1.68 km/s. We split this velocity in half to minimize the maximum tip speed of the two trebuchets: the first being a carousel-type trebuchet installed on the Moon's surface on an axle, serving as the catapult, and the second being the orbital trebuchet that catches the cargo thrown from the lunar surface by the first. By equalizing the tip speeds in this way we minimize the total mass of the cables of both trebuchets — i.e., the mass that must be delivered to the Moon first and foremost.
We impart the resulting velocity of 0.84 km/s to the rotating ends of the orbital trebuchet (relative to its center of mass). The lower end lags behind while the upper end outpaces the center. The trebuchet effectively rolls, and the speed of the tip at its lowest point equals half the speed of the center. At this moment the lower end slides above the Moon's surface at 0.84 km/s. An object launched by any catapult from the Moon's surface at this same speed of 0.84 km/s can be caught by the lower end of the trebuchet, and then released from the upper end when that end is at the top.
The lower end becomes the upper end in less than a minute, after half a revolution of the trebuchet. And its speed will then be 3 × 0.84 km/s = 2.52 km/s — even slightly greater than the 2.51 km/s we needed for departure toward Earth. This favorable outcome is almost coincidental, since we were only solving the optimization problem of catching with the trebuchet a cargo thrown from the Moon by another trebuchet.
The centrifugal loads on such trebuchets (with such tip speeds) are much lower than on a near-Earth trebuchet, which means that materials of substantially lower strength can be used here.
A bursting speed of 420 m/s for the rotating ring is already sufficient for these materials. This is not the 1,200–1,900 m/s required for a single-stage near-Earth trebuchet with a tip speed of 3,115 m/s. When using a material characterized by a bursting speed of 420 m/s — i.e., twice the tip speed — the mass of a symmetric trebuchet cable exceeds the mass of each end load by a factor of 35. This is quite considerable, but a mass margin is still needed so that the trebuchet does not fall onto the Moon immediately after a load is attached. In this case, attaching the load reduces the trebuchet's velocity by 1/70 of its value.
Consequently, an initial excess of the trebuchet's center-of-mass velocity over the lunar first cosmic velocity of 24 m/s (i.e., 1,680 m/s / 70) is required. The trebuchet's orbit before capture will be not circular but elliptical, with the capture point at its pericenter. After capture the orbit becomes circular, and the trebuchet — now a lunar satellite — must restore its original orbit and velocity by means of propulsive acceleration. For this purpose, part of the captured cargo can be used as reaction mass. To avoid chemical technologies on this satellite, lunar soil can be ejected in solid form, replacing the conventional gaseous exhaust jet.
The efficiency of the reaction jet approaches 100% when the ejection velocity equals the satellite's orbital velocity, since the ejected masses then fall to the lunar surface with zero horizontal velocity component and therefore carry away virtually no energy. An ejection velocity of 1,700 m/s is in this case more technologically feasible for solid objects. The energy source for such ejection of dust or pellets of lunar soil should be a solar power plant on the satellite. In total, 2/3 of the captured mass must be ejected, while 1/3 is launched toward Earth. This follows from the fact that we launch material from the Moon at 1/3 of the velocity required for departure toward Earth, and we transfer all the momentum to 1/3 of the ejected mass, bringing it to the required velocity. If we wish to change this useful fraction, we must either reduce the reactive efficiency or change the launch velocity from the Moon's surface — i.e., deviate from the optimum.
Regarding the throughput of the entire system launching lunar material toward Earth: the trebuchet satellite, in one orbit around the Moon lasting at least 1.8 hours, can fly over any given catapult only once. To increase its throughput, it must fly over many catapults in a single orbit. To increase the throughput of each catapult, as many satellites as possible should fly over it. The system throughput is determined by the product of the number of satellites in a single orbit and the number of catapults located on the Moon's surface in the plane of that orbit. If the catapults are stationary, the orbit must be equatorial.
Furthermore, once the number of satellites and catapults is sufficiently increased, the system throughput expressed in kg/h will be determined by the system's power supply, since launching 1 kg requires approximately 1 kilowatt-hour of electrical energy. This is precisely where an irrational preference for a polar orbit variant arises: if the catapults and orbit are positioned along the terminator, the solar power supply will be continuous — i.e., twice as large as at the equator. Moreover, we avoid problems with the more-than-100-degree midday lunar heat. That said, the catapults could be mounted on wheels. The Moon's rotation speed is modest: 4.6 m/s at the equator and negligible near the poles. By concentrating catapults on the polar segments of the terminator approximately within the lunar polar circles — 5–7° from the poles — we reduce the peak rolling speed of wheeled catapults in lunar winter and summer by a factor of ten. In lunar spring and autumn, when the terminator passes almost through the poles, this speed becomes negligible.
It is admittedly difficult to launch cargo directly from the lunar pole toward Earth. This is because the trebuchet throw must be made horizontally; otherwise the trebuchet or the cargo will fall back to the Moon. To solve this problem, the cargo must first be placed on a highly elongated elliptical orbit that extends beyond the Moon's sphere of influence. There, by maneuvering, the major axis of the orbital ellipse is turned 53° against the direction of motion, and then, departing from pericenter with a 53° lead, the cargo is directed toward Earth by departing the Moon's sphere of influence in the rearward direction at the usual 830 m/s. All these complications are more than compensated for by the doubling of sunlit time.
Initially, however, equipment will be delivered to the Moon via the exchange process. This process is only possible in orbits with a low inclination (5°) to the equator. Naturally, the transition will be made from the exchange process to a non-exchange stream of lunar soil launches in the equatorial plane, and only afterward will a near-polar launch system be established. A byproduct of this will be a lunar global transport system with transfers between orbits at the equatorial carousel through which the terminator passes at any given moment. This is a fast transport linking the equator and the poles. However, reaching an arbitrary point in the mid-latitudes is only possible once every two weeks.
Thus, the tip speed for the lunar trebuchet described above is 852 m/s, and the bursting speed for its material can be chosen as 426 m/s. Incidentally, such materials have always existed — one did not need to wait for the 21st century to be able to build a lunar trebuchet. Always, as in even before humans appeared on Earth: bamboo! Has it been tested in vacuum? I think not, and I hope that with some precautions it will not be damaged there either. But this is just a small joke — forgive me. After all, we intended to apply higher-order technology: namely, the processes of momentum and trajectory exchange, whereby the trebuchet receives no braking impulse and can therefore be made light — nearly equal in mass to the payload being attached.
When the cable strength is high, the total trebuchet mass approaches the mass of the two end loads, and the cable mass approaches zero. For example, when using a material with a bursting speed of 1,680 m/s (twice the tip speed of 840 m/s), the cable mass amounts to 54.4% of the mass of one load, or 27% of both. Thus the cable of our lunar trebuchet can be lightened by a factor of 65, and the counterweight load can even be delivered by the catapult using lunar soil. This means that to create a powerful exchange trebuchet in lunar orbit from modern materials — one capable of dropping significant masses of lunar material from the Moon in a single operation — it is sufficient to launch a cable satellite into lunar orbit with a mass of approximately 60% of the standard per-throw mass (60% − 54.4% = 5.6%). Then let 5.6% of the standard mass represent the mass of all other satellite systems, which amounts to 1/11 of the cable mass.
To commission this satellite, it must be transferred from the hyperbolic approach trajectory to the Moon onto a low near-circular orbit. The characteristic velocity of this maneuver is an impulse of 800–900 m/s near the pericenter of the approach hyperbola, which is placed by trajectory corrections at an altitude of 20–40 km above the far side of the Moon. This is in principle important for the exchange process, since the satellite is placed in an orbit whose direction of revolution around the Moon is opposite to the rotation of the Earth and the Moon around the Earth. Somewhere there, in the same direction, the Luna 10 station had been revolving since April 3, 1966, and in principle should still be revolving to this day (the world's first artificial lunar satellite, with an aposelene of 360 km and a periselene of 1,000 km).
Our trebuchet satellite, in order to be commissioned, must also be spun up and then gradually loaded at its ends with lunar material — needed to tension and balance the cable and to provide objects for exchanging with packages from Earth during reconnections, i.e., swapping them for blanks or bags of lunar soil. Only after the ends have been loaded (each to the standard mass, totaling 3.3 times the mass of our satellite) can the exchange process be initiated — a process that will be free of oscillations.
However, the process of gradually and incrementally loading both ends in small increments (on the order of 1/4 or less, but in no case more than 1/2 of the standard mass) will each time trigger powerful oscillations of the loads on the cable — either slowly or rapidly damped — as well as wave-like oscillatory processes of alternating tension and slackening along different sections of the cable. There is no particular need to equip the satellite with vibration dampers, as this would add unnecessary mass. Sufficient time is available for oscillations to die down: approximately 2 hours. Since loading is only possible at the moments when the trebuchet passes through periselene (the lunar analogue of perigee, from Selene — the Moon), the time available for oscillation decay equals the orbital period in lunar orbit (a minimum of 1.8 hours).
Even if the orbit were a low circular one just above the Moon's surface, loading more than once per orbit would still be impossible. Loading requires flying over the aforementioned lunar soil catapult. Its horizontal launch velocity must be 840–890 m/s, not counting the vertical velocity component of 100–400 m/s needed to loft the cargo upward to the trebuchet's orbital altitude — from 3 km to 50 km above the catapult. This minimum of 3 km (or more) of loft height must guarantee safe passage of the trebuchet in the event of certain emergency orbital perturbations, although the propulsion system should be used to compensate for these perturbations. In an extreme case, the trebuchet can shed a small fraction of its cargo from the lower end and, receiving a reactive impulse in return, raise its orbit by tens or hundreds of kilometers.
By alternately shedding small fractions of both loads from the lower points of rotation — where the ends have a rearward velocity of 840 m/s — our lunar trebuchet effectively becomes a rocket with an exhaust velocity of 840 m/s and can achieve an additional velocity of 1,225 m/s (by Tsiolkovsky's formula: 840 × ln 4.3). This increment is added to the existing circular velocity of 1,680 m/s, giving a total of 2,905 m/s. With such a reserve of characteristic velocity, our trebuchet could not only dodge any lunar mountain but could even fly to Mars or Venus.
Imagine: we first accelerate to the Earth-transfer velocity of 2,510 m/s; a reserve of 2,905 − 2,510 = 395 m/s remains, and this is spent five days later during a flyby at 200–300 km above Earth's surface for a perturbation maneuver. Oh wait — 100 m/s is not enough! We arrive at perigee at 10.9 km/s and depart at 11.3 km/s — and at that speed you cannot always reach Mars on its eccentric orbit. But in general, our exchange trebuchet should have a periselene velocity of 2/3 of 2,665 m/s — this being the velocity of the incoming exchange cargo (noticeably greater than the minimum required for Earth departure, 2,510 m/s) — and the tip speed is greater: 888 rather than 840 m/s.
Therefore at periselene the velocity is 1,777 m/s, which is 97 m/s above circular — and there are the missing 100 m/s needed to reach Mars. Of course, no one will allow a trebuchet to fly from lunar orbit to Mars (even for the sake of a record in the 2020 Guinness Book of Records) — who would answer for creating a swarm of hazardous meteoroids concentrated on the busy Earth–Moon space lane? However, if the particles are 1 mm or smaller in size, they will be braked by the residual atmosphere at 200–300 km altitude after 10–100 orbits, and since the maximum orbital period in that case does not exceed 8 hours, all such meteoroids will burn up within a month.
Those released near the Moon will simply fall back onto the Moon, since their velocity of at most 2,520 − 888 = 1,612 m/s is less than the circular velocity of 1,680 m/s — but this only holds up to a flight altitude of 150 km above the lunar surface; above that altitude we would also begin generating long-lived meteoroids.
But let us return to the main subject — the technological process of transferring lunar material to a Earth-transfer orbit. In addition to the trebuchet in low lunar orbit, we will need a carousel located on the Moon's surface. Not a children's merry-go-round with horses, of course, but simply a trebuchet cable spinning in a horizontal plane. The center-of-mass point has zero velocity — this is where we pass an axle through a bearing, on which this carousel will be mounted on some lunar peak or on a tower 10–50 meters tall. The tip speed of this carousel, or inertial catapult, is 800–900 m/s, and from this end the lunar blank can be released into flight toward the end of the orbital trebuchet (the lower end, moving at approximately the same speed).
But it is better not merely to release the cargo, but to exchange equal loads at the ends of both machines: this prevents cable oscillations from arising. Clearly, the exchange process allows only as much mass to be sent from the Moon as we send there. But at the initial stage of establishing a lunar base, this is already excellent! By sending some equipment there, we receive equal masses in return, which will feed the exchange trebuchet in near-Earth orbit. There, by means of a large trebuchet (tip speed 3,115 m/s), a gain of up to 6,230 m/s in the characteristic velocity of the rocket launching cargo can be achieved.
This is remarkable! But at this stage we are unlikely to have such a massive trebuchet (e.g., 46 standard masses — see the table). Here too, however, a compromise can save us: use a universal trebuchet for launch to GEO (tip speed 2.4 km/s, 13 standard masses), with the remaining 700 m/s covered by a rocket, and somewhat later a small trebuchet (tip speed 350 m/s) with a 12-hour orbital period — a multiple of 1.5 hours, the period of the main trebuchet in low orbit.
And we must also make use of all the space debris and spent equipment that has accumulated in orbits around the Earth (most likely what has piled up at GEO, but not only that) to launch progressively larger trebuchets, in order to lay, first and foremost, a trebuchet road to the Moon and back — and as we have seen, it is two-way. After all, trebuchets work best when equal masses move in opposite directions in terms of orbital energy, exchanging momenta, energies, and orbital trajectories while still revolving in the same direction around Earth's center, thereby reducing the difference in velocities.
And could we not break the required velocity difference (i.e., the characteristic velocity needed to fly to the Moon from low Earth orbit) into 3, 4, 5, or however many trebuchet acceleration stages as needed? We can, if the orbits of the trebuchets are properly synchronized; and the more trebuchets there are passing the cargo from one to the next (or performing exchanges), the smaller the velocity increment falling on each one, and hence the smaller the required tip speed (which equals half the velocity increment for a given trebuchet), the lower the centrifugal forces, and the much lower the mass of each trebuchet. Many small trebuchets will have a total mass far less than one or two large ones.
This is related to the fact that even before the exponential factor (exp(−kx²)) governing the cable taper becomes noticeably significant, the cable mass — at constant load mass — grows proportionally to the square of the tip speed, i.e., to the kinetic energy of the load. This seems natural if one regards the cable material as a kind of energy accumulator. In that case, N identical small trebuchets providing sequential acceleration with a total velocity increment equal to that of one large trebuchet will have a combined mass N times smaller than the mass of the large trebuchet.
When the exponential factor does make itself felt, the mass of the large trebuchet will grow even faster — disproportionately so — because the cable mass greatly exceeds the load mass, and the greater part of the rotational kinetic energy belongs to the cable rather than to the load. Consequently, the more trebuchets the entire system comprises, the lighter its total mass, and the easier it will be to launch into space (each trebuchet to its own orbit). The g-forces and the required cable lengths can also be reduced many times over through such trebuchet cascading.
In this system of exchange trebuchets, in a first approximation, all perigees and all major axes of all elliptical orbits of all trebuchets approximately coincide (they need not be identical — indeed they will differ, to match orbital period ratios and velocity relationships).
For the cascade transfer of the payload launched from Earth — from trebuchet to trebuchet for immediate dispatch to the Moon — all trebuchets must gather at approximately the same place at approximately the same time: at the common perigee of all their orbits. There the process of sequential transfer of the cargo to ever-faster trebuchets will take place rapidly, accelerating the payload from just below the first cosmic velocity to nearly the second — an increase of more than 3,000 m/s. Meanwhile, the lunar blanks will travel from the faster trebuchets to the slower ones, and each blank will shift down by one trebuchet level for each unit of cargo accelerated. This resembles the process of hole conduction in semiconductors. Thus, in the limit of many trebuchets in the acceleration cascade, their combined mass will be negligibly small — these are just the cables that need to be placed in their respective orbits, while the counterweight loads at the ends can be collected and towed from space debris.
Surely such a solution to the problems of space transportation is not without its brilliance? There is, of course, a challenge: an ultra-precise (precision) guidance system (space navigation in the broad sense) must be developed. But this problem is, as already noted, solvable in principle. The load on the navigation system simply increases in proportion to the number of trebuchets. But for computers it makes no difference whether an algorithm is run once or a thousand times. A certain reduction in reliability due to complexity is not catastrophic — a failed exchange operation can be remedied within a few hours or days. The main drawback of this approach, however, is that we lose the gain of approximately 2,000–3,000 m/s in acceleration up to the first cosmic velocity that would be possible with a large first trebuchet.
And so it turns out that the most immediately relevant option is to build the compromise transportation system described above, consisting of two trebuchets (with tip speeds of 2.4 km/s — for GEO — and 350 m/s). Initially, two identical trebuchets with a tip speed of 1.03 km/s and a mass of 1.2 standard units according to the table can be launched — though they can also be heavier, i.e., with a substantial safety margin. One goes to low orbit, the other to a six-hour orbit (period ratio of 4). Together with the two lunar trebuchets already described, this already constitutes, in a first approximation, a genuine exchange pathway exploiting the energy of lunar soil. It reduces the characteristic rocket velocity required for a round trip to the Moon from 17 to 8 km/s! A further 1.4 km/s will be gained later when the compromise trebuchet is launched. Add to that the savings on the descent vehicle (5 km/s is not 11), and what about the effect of reusable launch vehicles? And we are still hesitating?!
Incidentally, is it really necessary to bring the trebuchets' orbits so dangerously (?) close together? The cargo transfer could be carried out via an intermediate cargo orbit, without bringing the trebuchets near each other at all. This also provides an additional degree of freedom and greater flexibility in selecting orbital parameters to achieve the desired ratio of the trebuchets' orbital periods — though it does somewhat slow down the acceleration process.
Also regarding the ratio of orbital periods: the transfer orbit to GEO (10.5 hours) and the low orbit. If such a fortunate coincidence did not exist, one would presumably have to adjust the periods by raising the apogee of the first trebuchet or introducing a second transfer ellipse. In any case, the commensurability of the trebuchets' orbital periods (here with a factor of 7) only marginally reduces cargo delivery time (relative to the roughly one week needed to reach any point on GEO, and in comparison with it). This is perhaps why similar projects that may have arisen in the past were buried in their infancy, never gaining the momentum of serious development. The real, politically funded purpose of spaceflight back then was intimidation — implicit intimidation. And to have such a system in orbit means living in constant fear of it being shot down or damaged. It seems that revolutionary ideas only come to those who have nothing to lose.
You have probably noticed that the strength of all existing materials is insufficient to build the famous space elevator of Yury Artsutanov (or Tsiolkovsky, or Arthur Clarke) — a tether extending beyond geostationary orbit, i.e. more than 35,800 km above the equator. And materials capable of withstanding the stresses associated with both the second and first cosmic velocities are not expected anytime soon. And that is where the thinking stopped. Who funds space exploration? Politicians, and the military to a small degree. More physically complex concepts simply do not fit inside their heads — and if they do, those concepts are immediately classified. It was only the appearance of the atomic bomb in America that pushed space exploration forward in the Soviet Union; before that, the leadership had no need for anything orders of magnitude more powerful than Katyusha rockets.
You have to show a political leader how it goes "boom" first — then he will give you the money. That is why the V-2 could never have appeared in the Soviet Union without bourgeois capital; but once it went boom, it immediately became useful — especially as a freebie in the form of a trophy. That, I imagine, is when Korolev was summoned back from Kolyma to figure out the V-2 and report back, and to do so without unnecessary expense. From that moment, practical spaceflight began — and it ended with the end of the global standoff. New driving political forces are now needed, along with fresh ideas and people. The political forces (those common to all humanity) are still embryonic and blind. So let ideas awaken people, and let those people push forward — or shape — the political force of a united humanity. I hope that Russia will not find itself trailing somewhere at the tail end of the world.
Sources
- rastol.nn.ru — Igor Rastolkovskiy's personal blog on the city portal (archive)
- razgonoplan.nnewer.ru — Professor Rastolkovskiy, pen name of engineer-physicist Igor Knyaginichev (archive)
- habr.com — Habr — Profile of Igor Rastolkovskiy-Knyaginichev (archive)