Large Asteroid Habitat

• Habitat wheel, 2000 kg/m², W = 200 meters wide, R = 140 meters radius. Mass = 2 π R W dens = 3.5e8 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 = 2.52 rpm
• Edge velocity V = ω R = 37 m/s
• Angular momentum L = V R M = 1.81e12 kg m²/s
• Shield 20 m thick, density 1000 kg/m³ 150 meter inner radius, 170 meter outer radius, 220 meter inner width, 240 meter outer width.

• Shield Volume = πR₁²W₁ - πR₀²W₀ = π ( 170^{2*240 - 150}2*220 ) m³ = 1986000 m³, Mass ≈ 2e9 kg

• Volume of round asteroid = 1986000 m³ = 4 π R³ / 3 so R ≈ 78 meters
• Surface gravity of round asteroid = G M / R² = 6.67408e-11 m³/ kg s² × 2e9 kg / 78² m² = 2.2e-5 m/s²
• Maximum asteroid rotation rate ω = √ g/R = √ ( 2.2e-5 m/s² / 78 m ) = 5.3e-4 rad/s 3.3
• Maximum asteroid angular momentum L = 0.4 M R² ω = 0.4 × 2e9 × 78² × 5.3e-4 = 2e11 kg m²/s

We need a factor of 9 more ... hence the shielding must be at least 9 times heavier and thicker (1.8e10 kg), and the source asteroid larger than 160 meters diameter.

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

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