Tuesday, September 5, 2023

The weight of our world

Once I've spun this rubblepile, I need maths for what is going on downbelow / outside. I hadn't done that yet; so I'll sketch it, here. The rock pushes down with... its density, multiplied by the equation of centrifugal force, integrated (sigh) over height, here radius-of-spin.

[REPLACEMENT 9/6: As a maximum force on the bottom, I'll just go with how much tonnage is on it, from Bennu's 1190 kg/m3 which is then 1190 kg/m upon a square meter. If there's 300 m, that's 357 T/m2 of sheer mass. So if 3.14 m/s2: 1122 kN/m2. That's a maximum, for sanity-checking. I'll have to reverse-engineer the real equation from SpinCalc on account my calculus-fu failed me Tuesday.]

To limit that difference of h against r0, if we are keeping SOME constant distance between them for colonists to live, and allowing for expansion in the other two dimensions... requires a flattened curve. Like the parabola.

FIXED IT 9/8: ρ * ω * ω * r * (r-h) = 1190 * 0.0712 * 0.0712 * 620 * (620 - 320) = 1122k. I reckon I did better here.

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