SPECULORUM

Luca's Cone (the "Cone of Luca")

The space enclosed between the circumference of the Sun and the circumference of the Earth.

• Etymology: "Luca" derives from Latin lux, lucis (light) — literally the "cone of light".
• Definition points: NS / MS / SS — North / Middle / South of the Sun; NT / MT / ST — North / Middle / South of the Earth. These points change continuously with respect to the cone.
• Key relations: MS–MT = shortest distance between the two semicircles; NS–SS and NT–ST = the diameters of the Sun and the Earth with respect to the cone.
• Three baptismal names: Luca's Astral Cone, Luca's Sidereal Cone, Luca's Stellar Cone.

The cone is the channel of solar energy: fundamental for our planet.

The energy challenge

• Current anthropogenic (greenhouse-gas) forcing: ≈ +2.7–3.0 W/m².
• Full compensation via solar reduction would require ≈ 1.2–1.5 % of the solar constant (1361 W/m²).

Modular strategy

• Module 1 (0.5 %): ΔS ≈ 6.8 W/m² → forcing ≈ −1.2 W/m² (≈ 40–45 % of current forcing; avoids ~0.6–1.0 °C at equilibrium).
• The swarm can grow in +0.5 % modules or shrink: the climate "knob" is adjustable and reversible.
• It does not replace decarbonization (it does not cure ocean acidification).

The geometry of Luca's Cone

The Sun is not a point source: the Earth-bound light beam converges; the closer the shade is to Earth, the smaller it can be.

• Beam radius at fraction f of the distance: R(f) = R_Sun·(1−f) + R_Earth·f.
• At 1/3 of the distance: ≈ 3.4×10⁹ km² would be needed (0.5 %) — impractical.
• Near L1: only ≈ 3.0×10⁶ km² — ~1,100 times less.
• Nominal position: ~1.6 million km from Earth (classical L1 + ~100,000 km sunward due to residual light pressure β).

Symmetric diverging Fresnel lens, ~1°

• Function: spreads the light over ~28,000 km after 1.5 million km → nearly all of it misses the Earth.
• Why not mirrors or disks: light pressure (β up to 0.3) would push them millions of km out of position.

Gen-1 specifications

Stability and control

• Transverse: Earth's tidal gravity acts as a weak "spring" → natural oscillations with a period of ~6–7 months → self-confinement within the beam disk (radius ≈ 13,800 km).
• Axial: saddle point with e-folding time ~3 weeks → continuous trim required.
• Photonic rudders (reflective trim tabs, ~1 % of the area): authority ≈ 9×10⁻⁶ m/s² ≈ 280 m/s per year, propellant-free; real budget only a few m/s per year (margin ~25×).
• The swarm is always on the sunward side: never in Earth's shadow.

An ordered system, not a chaotic "gas"

• Ordered lattice (correlated oscillation phases): relative velocity ≈ mm/s.
• Mean spacing: ≈ 14 km between elements.
• Collisions: autonomous avoidance via photonic rudders; residual impacts only a few per year, tolerated by the thin film.
• Emergency response: shading 0.5 % → 0 in a few days (edge-on rotation) — the safety valve, e.g. after a major volcanic eruption.
• Onboard autonomy (sun sensor + simple logic); radio delay from Earth ≈ 5 s.

Mass and production

• Total mass (first 0.5 % module): 15 million tonnes (3 million elements × 5 t).
• Per-element breakdown: 2–3 µm glass lens ≈ 4 t · booms/tethers ≈ 0.7 t · control package ≈ 0.3 t.
• 94 % of the mass from the Moon: glass from regolith (abundant Si, O). 6 % high-tech from Earth (~0.9 M t ≈ 6–9 thousand heavy launches over 10 years).
• Logistics: lunar mass driver (2.4 km/s, ~3 MJ/kg) + reusable electric tugs; average power ≈ 140 MW — negligible.
• Steady-state rate: 300–450 thousand elements per year, including ~300 thousand scheduled replacements (10-year lifetime).

• Economic estimate: R&D + Phase 0: $50–100 B · Lunar infrastructure: $300–800 B · Production/deployment: $1,000–3,000 B · O&M: $100–300 B/year.
• Total first 0.5 %: ≈ $1.5–4 T over 15–20 years ≈ 0.1–0.3 % of world GDP per year.
• Comparisons: global military spending ≈ $2.4 T/year; current climate damages ≈ $0.5–1 T/year and rising.
• Cost/benefit potentially favorable, if combined with (not substituted for) decarbonization.

Continuous improvement

• Gen-2: areal density reduced to 1–2 g/m² (sub-micron films, 2D materials) → mass and costs ÷3–5.
• Materials: polymers from carbonaceous asteroids (C, H) for advanced optics.
• Scalability: each +0.5 % = ~3 M additional elements in the same lattice, with no orbit redesign.
• Design and manufacturing improve module after module, by project philosophy.

• Fast reversibility (off in days) → management of natural shocks (volcanoes); gradual ramp-down avoids "termination shock".
• Acts mainly on the tropics — complementary to the polar pattern of CO₂ forcing.
• Global governance of the climate "knob" is required: decision rules, monitoring, protocols.
• The swarm is repairable and replaceable piece by piece: no single point of failure.

From Luca's Cone to planetary infrastructure

• A consistent preliminary feasibility study across geometry, orbit, masses, energy and costs.
• Required deep-dive studies:

1. Qualification of 2 µm glass film + Fresnel prisms at 1 AU.
2. Simulation of the lattice and autonomous control of 3 million bodies.
3. Definition of the international governance framework.

• Luca's Cone evolves from a geometric definition into a modular planetary infrastructure.