dyson sphere
a structure that captures a star's whole output. the practical form is a swarm — countless independent collectors in layered orbits, assembled incrementally. the rigid 1 AU shell is a cartoon of the limit, not a build plan; layers grow outward from the star as collectors and proof allow.
territory base: the photosphere
in the space doctrine a celestial body is a state and its territory is a measurable surface that can be titled. for the Sun that base is the real stellar surface — the photosphere — not a hypothetical shell at Earth's orbit:
R_☉ = 6.957×10⁸ m (IAU 2015 Resolution B3)
A_☉ = 4π R_☉²
≈ 6.082×10¹⁸ m²
≈ 6.082×10¹² km²
= 6.082 trillion km²
that is the number on the ledger next to the Sun: ~6.08 trillion km². it is about twelve thousand Earth surfaces, and it is the natural unit for distribution — the first layer of claim against which later orbital layers settle.
layers, not one shell
a full-power swarm still intercepts $L_\odot \approx 3.83\times10^{26}$ W. energy capture and land title are different meters:
| meter | quantity | role |
|---|---|---|
| territory | $A_☉ \approx 6.08\times10^{12}$ km² | base surface for title and share |
| capture envelope (asymptote) | spheres at increasing $r$ | where collectors orbit as layers |
| power | $L_\odot$ | what a mature layered swarm can claim |
ownership is ring-and-atmosphere: orbital-slot or collector-flow anchors in the Sun's co-moving frame, each layer grounded as real collectors are proven. the token mints against the grounding coefficient so the economy grows with the swarm.
a 1 AU sphere would span $4π · (1.496×10^{11},\mathrm{m})^2 \approx 2.81\times10^{17}$ km² — forty-six thousand times the photosphere. that figure measures an eventual capture surface if the whole shell were filled at Earth distance; it is not the land base for the ledger.
see your share of the sun for equal-division yardsticks on the photosphere base, and space doctrine for the ownership mechanism.