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Home , Escape velocity, Momentum exchange tether, Skyhook (structure)

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The performance of a chemical rocket can be improved less, a momentum-exchange tether system would still re- by using a fuel with a higher specific impulse. The most duce the ∆v needed for chemical rockets to reach escape powerful chemical fuel ever tested was a lithium, fluo- velocity by twice the rotational speed of the tether, even rine, and hydrogen mixture with Isp = 542 s (Arbit et al. if it does not rotate at the orbital velocity. 1968). This fuel would decrease the of a rocket The functional limit of a is launched from a large super-Earth to 164. However, given by a characteristic speed of the material, vc, which the technical and supply considerations of a fuel con- is the maximum speed at which an untapered cable can taining large amounts of fluorine and lithium mean that rotate without breaking. (Tapering the tether would add this would not be a great improvement in terms of cost. additional strength, but for this paper, we use the unta- Thus, it is unlikely that the technology of chemical rock- pered strength and assume any tapering is used to pro- ets alone can support a space program on a super-Earth. vide a safety margin.) The characteristic speed is given Another option is not to attempt to reach escape ve- by: locity, but instead to reach a low . Once in orbit, 2σ v = , (2) a spacecraft can move away from the planet slowly us- c r ρ ing a much more efficient , which requires negligible fuel compared with chemical rockets (Jahn where σ is the tensile strength of the tether material, 1968). The orbital velocity in low orbit is given by and ρ is its density. The strongest known material for vorb vesc/√2, so for a large super-Earth, the orbital constructing such a tether is carbon nanotubes. Pugno velocity≈ is 19.2 km s−1. For a chemical rocket with (2006) estimates the tensile strength of a macroscopic cable made out of carbon nanotubes at σ = 22 GPa and Isp = 400 s, a mass ratio of 134 is needed to reach low or- −3 −1 ρ =1.5 g cm , which result in vc 5.4km s . bit. This is still more difficult than launches from Earth, ≈ but readily achievable with current technology. 4. LAUNCH SYSTEM 3. MOMENTUM EXCHANGE TETHERS A hybrid launch system would involve a suborbital One proposed alternative to chemical rockets is a chemical rocket to reach a momentum-exchange tether space-elevator, which extends a tower or cable from the in low orbit, where the ∆v requirement to reach orbit is planet’s surface to beyond the , allow- reduced by the rotational speed of the tether. The space- ing an electric vehicle to climb and reach orbit or even craft would dock onto the end of the tether and rotate it at no fuel cost. However, construting around until it is released at the top of the arc at a higher a cable that can hang under such stress would require speed. At that point, additional chemical rockets would materials with immense tensile strength that may not be used to reach escape velocity (although an ion thruster be realizable even for Earth, and would almost certainly would also work at this point). With a rotational speed not be able to withstand the stronger gravity of a super- of 5.4 km s−1 for a tether orbiting a Earth (Pugno 2006). large super-Earth, the required ∆v for chemical rockets A momentum exchange tether is a cable system that would be reduced from 27.1 km s−1 to 16.3 km s−1. For does not have a fixed end, but instead rotates in orbit this ∆v, the mass ratio of an average hydrogen-fuelled around a planet (Moravec 1977). In such a system, a rocket evaluates to 64, similar to the , so this spacecraft docks at one end of the tether and rotates system would be in line with launches from Earth. around to the opposite position, where it is released, ac- Building a momentum-exchange tether without an ex- celerating it relative to the planet by the exchange of isting tether-assisted system in place would be slightly , again without any fuel cost. While more complicated. However, for this purpose, a small the tether loses angular momentum in the process, caus- “seed” tether could be launched into orbit conventionally ing its orbit to decay, this angular momentum can be by chemical rockets, which can reach low orbit without recovered in several ways at very little cost, includ- assistance. After this, robotic climbers could be launched ing a momentum exchange in the other direction with on suborbital rockets to dock onto the tether and add an incoming payload to the planet, a fuel-efficient ion more strands, thickening it and increasing its maximum thruster to raise its orbit, or by electrodynamic propul- payload. Thus only a single conventional launch would sion, which generates thrust from the planet’s magnetic be needed to build a tether-assisted launch system. field (Katz et al. 1995). Once a momentum-exchange tether is in place and The most efficient form of momentum exchange tether, built up enough to carry large payloads, launching to sometimes called a “”, would be a tether that ro- space from a super-Earth would be much easier, albeit tates at the planet’s orbital velocity such that its ends still more difficult than on Earth. The ∆v required to trace out an epicycloidal path around the planet. In the reach the tether with chemical rockets would be 13.8 km frame of reference of the planet’s surface, the end of the s−1, and the docking would have to be achieved in the tether would descend vertically and come to a momen- span of a few seconds in which the spacecraft’s speed tary stop at a relatively low altitude, at which point a nearly matches the tether’s. From here, a climber could suborbital spacecraft could dock with it, before ascend- crawl to the midpoint of the tether, at which point it ing back to orbit. The tether would also be much smaller would be in low orbit, or the spacecraft could rotate than a possibly as short as a few hun- around and be released at the top of the tether’s arc. dred kilometers in length− compared with 100,000 km for From this point, an acceleration of a further 2.5 km s−1 a space elevator. However, rotating a tether to even the would be needed to reach escape velocity, but interest- low-Earth orbit speed of 7.8 km s−1 would require a simi- ingly, this is less than the 3.4 km s−1 needed to reach lar tensile strength to a space elevator, and such a system escape velocity from low-Earth orbit without tether as- would not be able to function on a super-Earth. Nonethe- sistance. 3

5. APPLICATION TO EARTH these planets would present a serious challenge to space A momentum exchange tether is an even greater ad- travel. For the largest super-Earths, most proposed vantage for spaceflight on less massive planets because systems (short of nuclear ) would the lower involved make it easier to reach or at range from infeasible to impossible for reaching escape least approach the of the planet. For Earth, velocity, although reaching low orbit would be possible. even with our current level of technology, a momentum However, a hybrid system combining chemical rockets exchange tether in Earth orbit would greatly reduce the and a momentu-exchange tether could put interplane- fuel cost for launches to orbit and elsewhere in the solar tary travel within reach for a civilization on even the system. Aramid-type fibers such as Kevlar are strong largest terrestrial planets, bridging the gap by combin- enough to achieve characteristic velocities approaching ing the maximum feasible contributions of each system 3.0 km s−1. Thus, a momentum exchange tether could to reach a sufficient velocity to escape the planet’s grav- reduce the ∆v required for chemical rockets to reach ity well. Combining chemical rockets with ion thrusters Earth orbit from 7.8 km s−1 to 4.8 km s−1, and the ∆v would also work, but would present less of an advantage. to reach escape velocity from 11.2 km s−1 to 5.2 km s−1. The same method could also reduce the cost of space A ∆v of 5.2 km s−1 with oxygen-hydrogen fuel could launches on Earth much more easily than with a space allow a mass ratio as low a 3.25 for an efficient enough elevator. While a space elevator requires roughly 100,000 engine and consequently a much smaller and less power- km of cable and a strength at the limit of what is physi- ful rocket. With such a system, even a suborbital rocket cally possibly, a momentum exchange tether in low-Earth could reach interplanetary space, making it a great im- orbit would require less than 1,000 km of cable and could provement on current rocket technology. boost suborbital launches to escape velocity using cur- rently available materials. 6. CONCLUSION The observed range of super-Earths extends up to 10 M⊕, and the high masses and surface gravities of ∼ REFERENCES Arbit, H. A., Dickerson, J. A., Clapp, S. D., & Nagai, C. K. 1968, Jahn, R. 1968, Physics of electric propulsion, McGraw-Hill series AIAA, 68, 618 in missile and (McGraw-Hill) Buchhave, L. A., et al. 2016, AJ, 152, 160 Katz, I., Lilley, Jr., J. R., Greb, A., McCoy, J. E., Galofaro, J., & Fulton, B. J., et al. 2017, AJ, 154, 109 Ferguson, D. C. 1995, J. Geophys. Res., 100, 1687 Heller, R., & Armstrong, J. 2014, , 14, 50 Moravec, H. 1977, Journal of the Astronautical Sciences, 25, 307 Hippke, M. 2018, ArXiv e-prints Pugno, N. M. 2006, Journal of Physics: Condensed Matter, 18, S1971