Physical Constants

All values used in calculations for Project Helios.

Solar System

Solar Constant

Location Value Source
Earth (1 AU) 1,361 W/m² NASA Sun Fact Sheet
Mercury (orbit average) 9,287 W/m² Time-average: S₀/(a²√(1-e²))
Mercury (perihelion) ~14,444 W/m² Calculation: 1361 × (1/0.307)²
Mercury (aphelion) ~6,242 W/m² Calculation: 1361 × (1/0.467)²
Moon 1,361 W/m² Same as Earth (1 AU)
Mars 589 W/m² NASA Mars Fact Sheet

Note: The value 9,087 W/m² is the flux at mean distance (0.387 AU): S₀/a² = 1361/0.387². For energy calculations, we use the time-averaged orbit flux: ⟨S⟩ = S₀/(a²√(1-e²)) = 1361/(0.387² × √(1-0.2056²)) = 9,287 W/m². The time-average is higher than the mean-distance value because the planet spends more time closer to the Sun (Kepler’s 2nd law acts inversely for ⟨1/r²⟩).

Planetary Parameters

Planet Gravity Escape Velocity Distance from Sun
Mercury 3.7 m/s² (0.38g) 4.3 km/s 0.39 AU (57.9M km)
Moon 1.62 m/s² (0.16g) 2.4 km/s 1 AU
Mars 3.7 m/s² (0.38g) 5.0 km/s 1.52 AU
Earth 9.8 m/s² (1g) 11.2 km/s 1 AU (150M km)

Source: NASA Planetary Fact Sheets

Regolith Composition

See Why Mercury? — planet comparison for the project.

Materials

Aluminum

Parameter Value
Density 2,700 kg/m³
Melting point 660°C
Reflectivity (pure) 90–92%
Reflectivity (with MgF₂ coating) 95–96%
Emissivity (polished) 0.03–0.05
Emissivity (with black coating) 0.8

Steel

Parameter Value
Density 7,850 kg/m³
Melting point ~1,500°C

Silicon

Parameter Value
Density 2,330 kg/m³
Solar cell efficiency 18–22%

Physical Constants

Constant Value Symbol
Stefan-Boltzmann constant 5.67×10⁻⁸ W/(m²·K⁴) σ
Speed of light 299,792,458 m/s c
Light pressure (Mercury orbit) ~60 µPa (reflection, P=2S/c) —

Project Design Parameters

Swarm Mirrors

Parameter Value Source
Size 100 × 100 m (square) Design decision
Area 10,000 m²
Foil thickness 4 µm Technological minimum
Foil mass ~110 kg 10000 × 0.000004 × 2700
Corner masses (4 pcs) ~3 kg Iron or basalt
Tethers (4 pcs) ~2 kg Steel wire
Electrochromic layer (TiO₂) ~1 kg Mercury (500 nm coating × 10% area)
Electronics ~50 g Earth (import)
Total mass ~116 kg
Reflected power 84 MW 10000 × 9287 × 0.90

Dyson Swarm (Target Parameters)

Parameter Value Calculation
Number of mirrors ~1.1 billion Production plan (~9.5 years)
Total area 1.1×10¹³ m² (~11M km²) 1.1×10⁹ × 10⁴ m²
Total mass ~128 million tons 1.1×10⁹ × 116 kg
Specific mass 0.0116 kg/m² 116 kg / 10000 m²
Mass Drivers ~1,000
Production timeline ~9.5 years accounting for degradation
Intercepted power ~102 petawatts 1.1×10⁹ × 93 MW
Reflected power ~92 petawatts 1.1×10⁹ × 84 MW
Power on Earth ~18 petawatts 102 PW × 18% efficiency

Mass Driver

Parameter Value Source
Target velocity 5 km/s Escape velocity + margin
Tunnel length 1 km (base)* Maximum construction speed
Acceleration 12,500 m/s² (1275g)
Acceleration time ~0.4 sec
Installation mass ~500 t
Efficiency (aluminum coils) 40% Conservative estimate
Margin vs proven 25,000g 20× McCormick Stevenson GNC

*When reducing load: 2 km (637g, 875 t) or 3 km (425g, 1300 t)

Gen-2 Robots (Optimized Fe/Al Hybrid)

Parameter Crab-M Centaur-M Mole-M Average
Total mass ~1,000 kg ~380 kg ~1,500 kg ~960 kg
Iron (critical components) ~350 kg (35%) ~80 kg (22%) ~1,250 kg (83%) ~560 kg (58%)
Aluminum (frame, body) ~470 kg (47%) ~235 kg (63%) ~220 kg (15%) ~310 kg (32%)

Optimization principle: - Steel only for critical components: wheels, bucket, bearings - Aluminum frames and bodies — sufficient strength at lower mass - At 5 robots/day: ~1.5 t Al + ~2.8 t Fe

Ground Zero Factory

Parameter Value
Power consumption (peak) ~165 MW
Concentrator area (6 launches) 105,000 m²
CPV system mass ~10.5 t (5.25 t foil + 2 t GaAs + 3.25 t structure)
Specific power ~14.4 kW/kg (at Mercury orbit)
Available power ~151 MW
Surplus over factory (no MD) ~27 MW
Silicon panel output ~1.4 kW/m²
Dome area ~1,500 m² (~50×30 m)

Constants Usage

These values are used in calculations: