2620
Comment:

2620

Deletions are marked like this.  Additions are marked like this. 
Line 7:  Line 7: 
 {{ attachment:homewheel.png   width=600 }}  {{ attachment:homewheelmirror.png   width=150 }}    {{ attachment:homewheel.png   width=600 }}  {{ attachment:homewheelmirror.png   width=180 }}  
Large Asteroid Habitat
The habitat geometry is a large cylinder, illuminated by diffusing mirrors on the axis from an external focusing mirror. The habitat is surrounded by a thick shield of dustball asteroid material.
Dustball asteroid rotation rates are quite limited by centrifugal disassembly. For 1200 kg/m³ and a 1.25x safety factor, the rotation period must be longer than 3.37 hours or equatorial material will spin away. The dustball asteroid 101955 Bennu has a rotation period of 4.3 hours, close to the limit, and most asteroids rotate more slowly. Asteroids do not spin too fast; if you hope to spin up a habitat with the angular momentum in the shielding mass, they spin too slowly.


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 ( 170^{2*260  150}2*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 = 6.67408e11 m³/ kg s² × 9.7e9 kg / 124² m² = 4.2e5 m/s²
 Assume maximum centrifugal acceleration 0.8 × gravity
thus ω < √( 0.8 × 4/3 × G × ρ ) = 5.18E4 rad/s → 3.37 hours period
 Maximum asteroid rotation rate ω = √(g/R) = √( 0.8 * 4.2e5 m/s² / 78 m ) = 5.18e4 rad/s
 Maximum asteroid angular momentum L = 0.4 M R V = 0.4 × 2e9 × 78² × 5.3e4 = 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.
Libreoffice Calc ods spreadsheet . . . . (download free, open source libreoffice here )
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!