The Challenge of Relativistic Spaceflight
posted by Adam Crowl on March 3, 2014
Riding a Beam to the Stars
The stars are, at minimum, tens of thousands of times further away than the planets. Presently flights to the planets take a year or more, thus to reach the stars in years, rather than millennia, requires speeds tens of thousands of times faster – a large fraction of the speed of light, what physicists call relativistic speeds. Chemical fuels have sufficient energy content to propel rockets to perhaps 15 kilometres per second. To reach 150,000 kilometres per second, 1/2th the speed of light, require fuels with an energy content at least a 100 million times greater than what mere chemistry can achieve. Fortunately, thanks to Einstein’s theory of relativity, we know that matter itself contains billions of times more energy than chemical bonds.
Philosopher Olaf Stapledon imagined the first realistic starships in his multi-billion year history of the Cosmos, “Star Maker” (1937). Intelligent species develop interstellar travel after the invention of “sub-atomic energy” – the total conversion of mass into energy. After they develop artificial planets – what we now call “space colonies” – they then combine the two and launch forth to explore the Galaxy. The fastest artificial planets achieve half the speed of light, which would require them to convert two-thirds their mass into energy. Stapledon’s starships, propelled by beams of sub-atomic radiation, are known nowadays as Photon Rockets.
Photon rockets have featured in astronautical discussions almost since the discovery that light has momentum and can produce push . Stapledon’s advanced alien civilizations learnt the trick of turning raw matter into pure energy, then directing it in a useful beam, but his description was rather short on details for serious engineering purposes. As a means of propulsion, pure photon thrust is very power intensive, requiring 300 megawatts of energy for every newton of thrust. Power is defined as the rate at which energy is used/released per unit time – one watt is one joule of energy used per second. Humanity presently uses about 20 trillion watts from all sources, other than food. Thus a thousand ton starship accelerating at 10 metres per second squared (just over 1 Earth gravity or “gee”) would require a photon power of at least 3 quadrillion watts – roughly 150 times the total power output of human civilization.
Instead of carrying the photon-making machines, why don’t we send the photons to the starship? This idea was explored in fiction  decades before a means of projecting photons across immense distances in tight beams was found. The first way of doing so was invented in 1960 – the Laser. A photon-propelled starship would then be an immense reflective “sail” that rode on a tight laser beam of photons. This concept, the Laser-Sail, was first seriously proposed by physicist Robert Forward in 1962 . Other physicists studied the concept through the 1960s and 1970s [4, 5], usually considering x-ray lasers as the preferred means of sending a tight laser-beam over the large distances needed to accelerate a laser-sail.
To accelerate to close to the speed-of-light, denoted as c by physicists, requires a large acceleration distance – at 1 Earth gee a laser-sail would need to accelerate over 0.15 light-years (about 1.4 trillion kilometres) to reach 0.5 c. The distance can be shortened by increasing the acceleration, but the light-intensity quickly becomes greater than known materials can stand. This was one difficulty identified in the laser-sail discussions of the 1970s. Another problem at that time was that no one could conceive of a plausible means for slowing the sail down. Then P.C. Norem  conceived of a way of turning using the magnetic field of the Galaxy, so one could slow the vehicle down with the same laser than accelerated it, but modern measurements of the galactic magnetic field have shown this to be impractically slow.
Robert Forward produced a series of new laser-sail concepts from 1982 to 1985 . His first break-through was the use of an immense Fresnel Zone Lens to increase the useful range of optical frequencies of laser light. Prior to this suggestion, laser propulsion advocates had suggested x-ray lasers would be needed to beat the diffraction limit on useful laser range. Due to diffraction, which causes the laser wave-front to spread out, the range of optical lasers would be limited to just astronomical units of distance. Useful range was inversely proportional to the wavelength of the laser-light, so very short x-ray wavelengths would be needed to reach across the vast light-years of distance until Forward’s lens allowed the more tractable optical wavelengths to be used.
Perhaps more significantly Forward demonstrated a means of braking laser-sails to a halt at their destination with his invention of the Stage-Sail – a laser-sail composed of successively smaller sails to be pushed via light reflected from the larger sail surrounding it. In Forward’s analysis, this allowed for the exciting prospect of reaching nearby stars, like Epsilon Eridani, at 0.5c, and then returning the vehicle to the solar-system. Laser-sails could thus be used for fast round-trip missions.
However to send laser-light usefully concentrated across 10 light years or more, the beam would need to be focused by an immensely large Fresnel Zone Lens – about 50,000 kilometres in diameter. The lens itself, which shaped the wave-front of the beam via alternating rings of light and dark, need only be made of thin space-capable material, but such an immensity would still mass half a million tonnes. The Laser Stage-Sail itself would mass 75,000 tonnes and be 1,000 kilometres in diameter, requiring a pushing power of many thousands of terawatts of laser-energy. So where would those trillions of watts of laser-energy come from? Forward suggested a vast array of energy collectors and laser generators in orbits close to the Sun.
The discovery in 1986 of high temperature superconductors allowed astronautical engineers to contemplate use of superconductivity for creating low-mass magnets on a grand scale. One such application was the Magnetic-Sail. Jonathan Vos Post, Dana Andrews and Robert Zubrin, had discovered  the long-sought braking system for laser-sails from interstellar speeds. Coupled to a laser-sail, a magnetic-sail would allow deceleration from relativistic speed in a couple of decades or less, without the problems of focusing laser-light across light-years in order to brake as required by Forward’s Stage-Sail design. In the late 1980s NASA scientist Geoffrey Landis  studied high temperature laser-sail materials that would allow much shorter acceleration track-ways to be used, reducing the scale of the focusing optics to more manageable sizes. In one analysis, by Zubrin & Andrews , a focusing mirror and mag-sail equipped laser-sail as “small” as 50 kilometres across would achieve the same performance as Forward’s 1,000 kilometre Fresnel Lens/light-sail combination for a mission to Epsilon Eridani. The laser power would be about 5,000 terawatts – just 250 times present day energy production levels.
Could lasers be used to go even faster? If a laser-sail could maintain continuous acceleration from departure to destination, then the full benefits of relativistic time dilation would be available to the passengers. According to Einstein’s Special Relativity, the passage of time for observers traveling close to the speed of light decreases relative to observers who are stationary. A starship could accelerate at 1 gee from here to Alpha Centauri, then the travel-time experienced by the passengers would be just under 4 years, but observers on Earth would experience six years of time.
To increase the useful range of lasers and to maintain constant acceleration, independent researcher Charlls Quarra has recently proposed a series of laser Starways – effectively booster stations for laser-sails – to maintain pointing accuracy and thus beat the diffraction limitation. This will require careful heat management and advanced optical technologies, but faces no serious physical difficulties.
Alternatively the lasers could be entirely done away with and a small magnetic-sail could be pushed via a particle or pellet beam. Charged particle beams tend to be susceptible to deflection by the ambient magnetic fields around them, which limits their useful beam range. A beam composed of heavier particles would deflect less, if at all. One of the earliest concepts using pellets was Clifford Singer’s Interstellar Pellet-Launcher.
Developed at roughly the same time as Forward’s Stage-Sail, Singer  proposed using small pellets to project momentum to a star-ship. His concept used a very large magnetic accelerator, spread out over a very large track-way, to propel small particles to relativistic speeds and then push against the magnetic-field of an interstellar vehicle. The advantage of the pellets was that they were too big for the feeble magnetic fields of interstellar space or random impacts of interstellar gas and cosmic-rays to deflect from their path to the starship. Being so numerous, the loss of a few pellets to random dust collisions wouldn’t impact the system’s performance significantly.
Then in the 1990s, as nano-technology was becoming a part of the conceptual landscape, a new pellet-propulsion concept emerged, championed by USAF researcher Gerald D. Nordley. Instead of “dumb pellets”, externally steered and shot towards a starship, Nordley  proposed nano-technological “Smart-Pellets” which could maintain themselves in the beam path to a starship via a simple artificial intelligence and tiny single-atom rockets for course correction. Such a stream of Smart-Pellets pushing a Starship can be called a Mass-Beam.
Power for the Starships
Nordley’s proposed crewed Mass-Beam Starships would cruise at 0.87c, the speed at which time-dilation halves the experienced travel-time. Accelerating at 5 gees, to minimise the acceleration distance, a 1000 tonne Mass-Beam Starship would require about 50 petawatts (50 x 1015 watts) of mass-beam power at maximum. In space one power source dominates all others: the Sun. Earth absorbs, every second, about 122.2 petawatts (122.2 x 1015 watts) from the Sun. Using the energy that falls on Earth alone we could power starships, but covering the Earth in solar arrays is problematic, at best. In 1968 physicist Peter Glaser  proposed building immense solar arrays in space, Solar Power Satellites, or Power-Sats. Glaser imagined that Power-Sats would beam energy back to Earth via microwave beams or lasers. Building Power-Sats was imagined in late 1970s studies by NASA to involve every component being launched into orbit via rocket, and each Power-Sat assembled piece-by-piece via teams of astronauts. The cost would be trillions of dollars to supply, perhaps, a few gigawatts of power to a ground receiver. Alternatively the materials could be mined on the Moon, but the cost of setting up the manufacturing infrastructure on the Moon seemed daunting. For starships something much, much cheaper is needed.
The intensity of sunlight increases with the inverse square of the distance from the Sun. At Earth’s orbital distance about 1400 watts of sunlight power falls on every square metre. At the orbit of Mercury the intensity of sunlight increases 10-fold. At just 0.1 AU (1/10th the Earth-Sun distance) the intensity is 100-fold higher. Thus to get more useful power for the same mass of equipment the Power-Sats need to be moved closer to the Sun. High-temperature photovoltaic materials can be made to operate in such conditions, but at higher temperatures converting raw sunlight into useful electrical energy can use highly efficient thermoelectronic conversion .
A 1,000 tonne Power-Sat that produces a gigawatt (1/1000th of a terawatt) at Earth’s orbit could produce 100 gigawatts at 0.1 AU. To produce the 50,000 terawatts (50 petawatts) for a mass-beam propelled starship to fly to Alpha Centauri, about 500,000 Power-Sats would be needed. Launching the required 500 million tonnes of Power-Sat into orbit just doesn’t seem feasible.
No starship designer has ever seriously proposed launching so much material from Earth, but translating sufficient traditional industrial capacity into a more conducive location in the Solar System, like Mercury or the Moon, seems an equally Herculean task. Current world solar-power manufacturing capacity is only a 100 gigawatts or so, thus many thousands of years of manufacturing would be required using present day techniques. Instead of traditional manufacturing technology, relocated to space, something new is needed.
Gerald Nordley  has suggested that we utilize a self-replicating factory to build enough factories and Power-Sats, deriving materials from the asteroids in space. Two questions arise:
(1) What difference does self-replication make?
(2) Can it really be done?
To answer the first, we’ll use Gerald Nordley’s scenario slightly modified – a self-replicating factory (a SeRF) that can make a copy of itself and a Power-Sat, situated inside the orbit of Mercury and generating a 100 gigawatts, in one year. Thus, at the end of the first year, we have two SeRFs and a Power-Sat. At the end of two years we have four SeRFs and two more Power-Sats. At the end of ten years there are 1024 SeRFs and 1023 Power-Sats – thus more than a 100 terawatts (1014 – a hundred trillion – watts) of power-generating capacity. At the end of year Twenty there will be 1,048,576 SeRFs and 1,048,575 Power-Sats producing over a 100 petawatts (1015 – a thousand trillion – watts). Thus in just 20 years enough power to propel two starships to Alpha Centauri at 0.87 c. This is the power of exponential growth and seems the only way enough infrastructure could be created.
The implications for improving human civilization’s prospects, if exponential manufacturing is developed for use in space, are profound. Consider, Earth intercepts from the Sun about 175 petawatts of energy, thus in 21 years more usable energy will be available than is received by the Earth. Nikolai Kardashev, a Russian astronomer, proposed a scale for measuring civilizations based on their energy usage. In the Kardashev Scale a Type I Civilization utilizes the energy equivalent to that received by its home planet from its star. A Type II Civilization utilizes the total energy produced by its star, while a Type III utilizes the total energy produced by its home Galaxy.
At the end of year Thirty there will be over a billion SeRFs and 100 exawatts (1020 watts) being produced by over a billion Power-Sats, enough to launch 20,000 laser-sail starships at half-lightspeed per year. To reach Kardashev Type II, mathematically speaking, the SeRFs would require just 52 years of self-replication to fully envelope the Sun in an energy gathering shell. At 1,000 tonnes per SeRF and Power-Sat, however, we may use up the available mass floating free in space in the form of asteroids. To merely power thousands of star-ships will require a tiny fraction of what is available.
Clearly self-replicating technologies can make an immense difference in a relatively short span of time.
In answering Question (2) “can it really be done?” we must step back to the late 1970s when President Jimmy Carter directed NASA to study what would be needed to build a self-replicating factory on the Moon, with the final report being delivered in 1980, edited by Robert Freitas and William Gilbreath [16, 17]. For a Seed mass of 100 tonnes, using robotic and manufacturing technology just ahead of 1970s technology, the study considered all the aspects of how to gather, process and manufacture an Automated Factory’s components on the Moon. An important aspect that determined the level of difficulty was parts/component closure – what proportion of parts could be manufactured on site, from Lunar resources, and what had to be imported from Earth. Closure of 90-95% was considered straight-forward. More challenging would be 100% closure, with the Lunar Factory being totally autonomous of inputs from Earth. Chiefly the difficulty of producing computer chips meant, in the early days, that they would be easier to produce on Earth. Eventually even this could be moved to the Moon.
A more recent study, from 2011, by NASA researchers Philip Metzger, Anthony Muscatello, Robert Mueller and James Mantovani , re-examined the concept, updating it with modern 3-D Additive Manufacturing techniques, concluding that the Seed mass could be considerably reduced. Instead of immediate 100% closure of parts & components, the system would evolve through several generations of improving robotics and industrial techniques, adapting to the local resources. For a Seed mass of 41 tonnes the system could produce 100,000 Robonauts in 20 years to sustain industry on the Moon, eventually expanding to the Asteroid belt and beyond. Human beings would remain a part of the process, with teleoperation – advanced remote control – of the Robonauts a key part of the process leading to increasing autonomy of the robotic systems. Humans would train the automation and remain key to the whole system’s evolution as it expands.
Once a Space-based industrial infra-structure is well underway, with the corresponding experience growth in manufacturing and prospecting techniques, then a more focused effort on developing self-replicating Power-Sat factories can begin. Gerald Nordley  has plotted the following development time-table over the next century, as follows.
Initially the resources of the asteroids will be prospected, as various ‘New Space’ companies, like “Planetary Resources”, are already planning to do. Next step will be refining materials in situ, with teleoperated (remote-controlled) machinery at first, but also by developing ever more capable robotics as activities move beyond speed-of-light control-range. In Nordley’s starship architecture an early stage is a high-speed flyby of Alpha Centauri (and other target star-systems) to confirm the necessary resources are available. Then a robotic base is launched which will send out a Braking Trail of slow-pellets for the following starship to brake against. As the Braking Trail pellets are much slower than the accelerating pellets, the robotic base doesn’t need to produce Power-Sats for decades to build-up to full-power. Once the Braking Trail is confirmed to be in place, the first crewed Starship to Alpha Centauri will depart, arriving in about 6 years.
Key to powering that first Starship, as we have seen, will be developing the Solar System’s resources. Exponential bootstrapping of Space Industry make Starships possible and immense potential wealth is opened up for the human species, with the relocation of bulk industry into space. For this potential to become actual the broader public will need to be involved every step of the way. Prospecting thousands of asteroids will need thousands of “Citizen Scientists” analysing the data. Operating thousands of teleoperated Robonauts on the Moon – and beyond – will need thousands of people on Earth, and eventually in space as we move further afield and the lightspeed communication limit makes teleoperation difficult. Co-ordinating and maintaining the immense Power-Sat arrays that will power the Starships will also need human supervision.
And the limit? Consider for a moment the power of the Sun – some 400 trillion trillion watts, which is a total power sufficient to propel 20 billion Mass-Beam Starships to 0.87c per year. Harnessing a tiny fraction of that power allows everyone to go to the stars.
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