The Data Centers in LEO

Appendix A — Constants, formulas and conventions

Quantity

Value used

Solar constant at 1 AU

1,361 W/m²

Stefan, Boltzmann constant σ

5.670 × 10⁻⁸ W/m²K⁴

Standard gravity g

9.80665 m/s²

Earth gravitational parameter μ

3.986 × 10¹⁴ m³/s²

Orbital velocity at 650 km

≈ 7.53 km/s

Aluminium density

2,700 kg/m³

Multi-junction cell efficiency

30%

Radiator emissivity ε

0.85

Effective LEO sink temperature

200, 270 K

Radiator areal mass

5, 12 kg/m²

Array specific power

~150 W/kg

Rack convention

200 kW, 1.4 t, $3.5M

Formulas used throughout Rocket equation: Δv = I_sp · g · ln(m₀/m_f) Radiative heat rejection: q = ε σ (T⁴ − T_sink⁴) Plane change cost: Δv = 2 v sin(Δi/2) Drag deceleration: a = ½ ρ v² C_d (A/m) Beam divergence: θ ≈ λ / D


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