All outputs are rough engineering estimates for ideation. Real asteroid mining and fusion propulsion involve far more variables (orbit mechanics, extraction tech, delta-v budgets, shielding, etc.).
(a) Asteroid-Mining Economics
Volume V = (4/3)·π·(d/2)³
Mass m = V · ρ, ρ = 3000 kg/m³
Metal m_metal = m · (fraction/100)
Gross value = m_metal · price ($/kg)
Assumptions: spherical body; uniform density 3000 kg/m³; 100% metal recovery assumed — optimistic (real recovery < 100%);
no cost for reaching/extracting/returning material; price is a single flat value with no market saturation effect.
(b) Fusion-Propulsion Travel Time (brachistochrone)
Constant acceleration a, flip at halfway:
t = 2·√(d / a)
Peak velocity at flip: v_max = √(a·d)
a in m/s² = (acceleration in g) · 9.81
Assumptions: constant 1-g-style acceleration there and back with an instantaneous flip at the midpoint (no flip maneuver cost);
relativistic effects ignored; propellant mass, fuel burn, and delta-v budget are NOT modeled — real travel takes longer/more fuel.