The history of momentum-exchange tethers goes back many, many years but is bound by a common thread that, until recently, limited the realization of this technology. That common thread is the need for high specific tensile strength.
The first idea of concept of a tether dates back to the imagination of Konstantin Tsiolkovsky, the Russian schoolteacher who first developed our modern concepts of rocketry and first derived the rocket equation. In the late 1800s, Tsiolkovsky visited Paris and saw the Eiffel Tower. He was so impressed by the sight that he imagined a tower reaching up far into space. He calculated the height at which such a tower would have to be before the centrifugal force from the Earth’s rotation balanced the pull of gravity (inadvertently calculating the altitude of geosynchronous orbit).
Tsiolkovsky, of course, could not conceive of any material that could withstand the compressive forces of such a structure, but sixty years later, a Russian engineer named Yuri Artsutanov picked up the thread of Tsiolkovsky’s work and first worked out the engineering principles of what is now called a “space elevator”, a long tether hanging all the way from geosynchronous orbit to the surface of the Earth. The space elevator required materials with specific tensile strength far in excess of any known material, and still does. Further conceptual engineering work on the space elevator concept was done in the early 1970’s by American engineer Jerome Pearson.
The space elevator was a hanging tether, and payloads were required to traverse its length in order to achieve orbit. The beginnings of rotating momentum-exchange tethers date to the late 1970s, when Hans Moravec, a robotics researcher at Stanford University (now at Carnegie-Mellon) was intrigued by a suggestion of his friend John McCarthy of a satellite that “rolled like a wheel” around the Earth. Moravec began a scientific investigation of the concept, which he first called a “non-synchronous orbital skyhook” and later a “Rotovator”. Like the space elevator, it reached all the way to the surface of the Earth, but unlike the elevator, it rotated about its axis a number of times per orbit. A payload would be picked up by the tip at the surface of the Earth and then thrown half a rotation later into an interplanetary trajectory. The Rotovator was a good deal shorter than the space elevator (~4200 km vs. 40, 000 – 100,000 km) but was not much better in terms of materials required. Moravec published a paper on the subject in the Journal of Astronautical Sciences where he speculated on advanced forms of matter that might have the strength needed to build the Rotovator.
About a year after the JAS paper was published, Dupont’s development of Kevlar excited Moravec to the possibilities of Rotovators built with conventional materials. He wrote a short paper called on the subject which was never published. The paper showed that Kevlar skyhooks were not feasible around the Earth but could be reasonably built around the Moon and Mars. In an appendix to this unpublished paper, Moravec speculated on the possibility of skyhooks built in interplanetary space that would assist spacecraft traveling between the Earth and Mars. To the great benefit of future tether researchers, his equations for the cross-section of a tether, in the absence of a gravitational field, could be integrated in closed-form. Thus, the Moravec “tether equation” was first derived.
Moravec was able to derive analytical expressions for the area of the tether as a function of its distance from the rotational center. He then numerically integrated the area expression along the length of the tether to calculate volume and mass. As an aside, in an appendix, he considered the case of a tether spinning in free space. When the tension on the tether was only due to centrifugal forces, the area expression could be analytically integrated to a closed-form solution. Thus the Moravec mass ratio was derived.
The equation could be simplified by realizing that fundamentally, the mass ratio is a function only of the velocity ratio, which itself is the ratio of the tip velocity of the tether and the characteristic velocity of the tether material.
Further insight into the value of the equation was gained by comparing it to the rocket equation and noting the similarities and differences.
Moravec wrote a few articles on the subject for space-themed publications, but basically returned to his robotics work. Nevertheless, Moravec’s equation still serves as a foundation to all momentum-exchange tether work to this day.
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