3 ms·

So if my back of the envelope math is correct (and I've probably screwed something up as it's past midnight here), to accelerate a 100 kg probe to the speed of

So if my back of the envelope math is correct (and I've probably screwed something up as it's past midnight here), to accelerate a 100 kg probe to the speed of the object (30 km/s) at a maximum of 1000 m/s² using a steel spring would require a spring of modulus about 0.11 kg/s². (For reference, a slinky is less "stretchy" at 0.8 kg/s².) It would take about 47 seconds, and the spring would elongate by a maximum of 530 km. To withstand this tension (100 kN), the steel wire (ultimate tensile strength ~400 MPa) would need to have a cross-sectional area of 250 mm², or diameter of 16 mm. Given this wire diameter, and a Young's modulus for steel of 200 GPa, the spring itself would require a diameter of ~42 cm and ~200,000 turns, if we allow it to stretch completely during acceleration. Fully relaxed, the spring would be 3.2 km in length. This works out to at least 130 m³ of steel, or 1000 metric tons, which is somewhere around USD$500k. Eminently affordable. Of course, that's a drop in the bucket compared to the cost of launching a 3.2 km long, 1000 metric ton slinky into outer space.

ncmncm 7y ago
Steel is not usually chosen when elasticity or tensile strength per unit mass are goals. I am actually more worried about the propagation of tension in the tether being restricted to the speed of sound in the material. It seems like the end would just snap off, for any realizable material.
- SiempreViernes 7y ago
  Are there materials available with three orders of magnitude better properties?
  - ncmncm 7y ago
    The speed of sound in graphene is 22 km/s. If your tether were made of monocrystalline carbon fiber, it looks like you would have to boost the whole apparatus to 8+ km/s first to catch a 30km/s object, and you could then leave the solar system at something less than 52 km/s. For comparison, the New Horizon probe to Pluto and beyond left at 23 km/s. With a thousand km of graphene-fiber tether standing perpendicular to the object's path, it would take 45s to accelerate the probe at a peak of 484 km/s/s. For a 10kg probe, that would put 4.8e9 N of tension on the tether. Graphene has a tensile strength of 130000 MPa, or 1.3e11 N/m^2, so the cable would need to be some 20cm thick. Boosting to a higher speed would reduce the cable thickness needed proportionally. At 19 km/s, quite doable, it's 10 cm. However, boosting 1000 km of 10cm cable to 19 km/s would take quite a fair bit more fuel than just boosting the probe itself to the target speed of 41 km/s.

ncmncm 7y ago

Steel is not usually chosen when elasticity or tensile strength per unit mass are goals. I am actually more worried about the propagation of tension in the tether being restricted to the speed of sound in the material. It seems like the end would just snap off, for any realizable material.

SiempreViernes 7y ago
Are there materials available with three orders of magnitude better properties?
- ncmncm 7y ago
  The speed of sound in graphene is 22 km/s. If your tether were made of monocrystalline carbon fiber, it looks like you would have to boost the whole apparatus to 8+ km/s first to catch a 30km/s object, and you could then leave the solar system at something less than 52 km/s. For comparison, the New Horizon probe to Pluto and beyond left at 23 km/s. With a thousand km of graphene-fiber tether standing perpendicular to the object's path, it would take 45s to accelerate the probe at a peak of 484 km/s/s. For a 10kg probe, that would put 4.8e9 N of tension on the tether. Graphene has a tensile strength of 130000 MPa, or 1.3e11 N/m^2, so the cable would need to be some 20cm thick. Boosting to a higher speed would reduce the cable thickness needed proportionally. At 19 km/s, quite doable, it's 10 cm. However, boosting 1000 km of 10cm cable to 19 km/s would take quite a fair bit more fuel than just boosting the probe itself to the target speed of 41 km/s.