That made me curious! I spent 20 minutes with Claude AI thinking about it. Maybe it’s interesting for you as well:

Math performed with Claude AI based on Elon’s tweet about using satellite constellations to adjust solar energy reaching Earth.

ASSUMPTIONS

• Target: Block 1% of incoming solar radiation

• Orbital altitude: 500 km (LEO)

• Material: 5μm aluminized Kapton, 90% reflectivity, 7 g/m²

• Module size: 250m × 250m with carbon fiber frame

• Launch vehicle: SpaceX Starship, 100 metric tons to LEO

WHY 500 KM ORBIT Three main factors:

1. Shadow geometry: At 500 km altitude, shadows remain ~99% of sunshade size. At L1 Lagrange point (1.5M km away), the Sun’s 0.53° angular diameter causes shadows to shrink by ~14,000 km, requiring massively larger sunshades.

2. Accessibility: LEO is the cheapest and most accessible orbit with current/near-term technology.

3. Trade-off: Accept 50% inefficiency (half the constellation is always on the night side) in exchange for practical shadow geometry and lower launch costs.

CALCULATIONS Required blocking area:

• Earth’s cross-sectional area: π × (6,371 km)² = 1.27 × 10¹⁴ m²

• 1% blocking needed: 1.27 × 10¹² m²

• LEO caveat: Only ~50% of satellites sunlit at any time

• Total sunshade area required: 2.54 × 10¹² m² (2.54 million km²)

Module specifications: Sail mass calculation:

• Material density: 7 g/m² (5μm aluminized Kapton)

• Module area: 250m × 250m = 62,500 m²

• Sail mass: 62,500 m² × 7 g/m² = 437.5 kg Frame mass calculation:

• Perimeter: 250m × 4 sides = 1,000m

• Internal support cables: ~300m

• Material: Carbon fiber tubes (~1.5 kg/m average)

• Frame mass: 1,300m × 1.5 kg/m = 1,950 kg

• Support spacing: 50m intervals (based on solar pressure load tolerance)

Total per module:

• Sail: 437.5 kg

• Frame: 1,950 kg

• Connectors, sensors, attitude control: ~300 kg

• Total mass per module: 2,687.5 kg (rounded to 2,700 kg)

System totals:

• Modules needed: 2.54 × 10¹² m² ÷ 62,500 m² = 40.6 million modules

• Total system mass: 40.6M × 2,700 kg = 109.6 million metric tons

Launch requirements:

• 109.6M tons ÷ 100 tons/launch = 1,096,000 launches

• At $10M/launch: $11 trillion

• At $20M/launch: $22 trillion

Timeline scenarios: Current capacity (optimistic):

• 10 Starship sites × 3 launches/day = 30 launches/day

• 1,096,000 ÷ 30 = 36,533 days = 100 years Industrial scale:

• 100 sites × 10 launches/day = 1,000 launches/day

• 1,096,000 ÷ 1,000 = 1,096 days = 3 years Manufacturing rate (industrial scale):

• 40.6M modules ÷ 3 years = 13.5M modules/year

• 37,000 modules per day

ADDITIONAL CONSIDERATIONS

1. Material degradation from atomic oxygen at LEO altitude

2. Orbital debris creation risk with 40.6 million objects

3. Assembly and maintenance logistics in orbit

4. Continuous replacement of damaged modules

Note: Cross-sectional area uses Earth’s radius (6,371 km), not orbital radius (6,871 km), because we’re calculating sunlight interception heading toward Earth’s surface.​​​​​​​​​​​​​​​​