** **Tocompute the moment of inertia for a torus being revolved around the z axis, theequation I=(¾R^{2}+r^{2})M can be used, where R is the majorradius, r is the minor radius, and M is the total mass of the torus, or ρV[ref 47]. In the below equations, R=major radius and R_{1}=minor radius.Assuming the colony is a solid torus with density 100 kg/m^{3}with a major radius of 2000 meters, and a minor radius of 255 (including theradiation shield), the moment of inertia can be found.^{17} kg·m^{2}.

Volume of torus: V=2π^{2}Rr^{2}

I_{1}=(¾R^{2}+r_{1}^{2})·M= [¾·(2000m)^{2}+(255m)^{2}]·100kg/m^{3}·2π^{2}·2000m·(255m)^{2}

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