Large Asteroid Habitat
Bad example, not enough asteroid angular momentum
- Habitat wheel, 1000 kg/m², W = 200 meters wide, R = 140 meters radius. Mass = 2 π R W dens = 1.8e8 kg
- Assume 1 gee, 9.8 m/s² = ω² R = ( 2 π freq )² R, so ω = √0.07 = 0.26458 rad/s, so freq = 0.042 Hz = 2.53 rpm
- Habitat Edge velocity V = ω R = 37 m/s
- Angular momentum L = V R M = 9.1e11 kg m²/s
- Assume Shield thickness 20 m thick, density 1200 kg/m³
- 150 meter inner radius, 170 meter outer radius, 220 meter inner width, 260 meter outer width
Shield Volume = πR₁²W₁ - πR₀²W₀ = π ( 1702*260 - 1502*220 ) m³ = 2360000 m³, Mass ≈ 9.7e9 kg
- Volume of round asteroid = 1986000 m³ = 4 π R³ / 3 so R ≈ 124 meters
- Surface gravity of round asteroid = G M / R² = 6.67408e-11 m³/ kg s² × 9.7e9 kg / 124² m² = 4.2e-5 m/s²
- Assume maximum centrifugal acceleration 0.8 × gravity
thus ω < √( 0.8 × 4/3 × G × ρ ) = 5.18E-4 rad/s → 3.37 hours period
- Maximum asteroid rotation rate ω = √(g/R) = √( 0.8 * 4.2e-5 m/s² / 78 m ) = 5.18e-4 rad/s
- Maximum asteroid angular momentum L = 0.4 M R V = 0.4 × 2e9 × 78² × 5.3e-4 = 3.1e10 kg m²/s
We need a factor of 30 more ... hence the shielding must be at least 8 times heavier and thicker (1.8e10 kg), and the source asteroid larger than 245 meters radius and spinning fast.
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Near Earth asteroid 101955 Bennu has a mass of 7.3e10 kg, a mean density of 1200 kg/m³, a mean radius of 245 m, and a rotation period of 15500 seconds. L = 0.4 M R² ω = 7e11 kg m²/s, not quite enough!