Sunlight carries momentum. A flat sail of area A at distance r from the star intercepts flux
S(r) = S₀·(r₀/r)². Tilting the sail's normal by pitch angle α away from the star-line
spreads that flux over a larger effective area and redirects the reflected photons, giving a thrust
F = (S(r)/c) · A · (1+ρ) · cos²(α)
Fᵣ = F·cos(α) (radial component)
Fₜ = F·sin(α) (tangential component)
The radial part fights or adds to gravity; the tangential part changes orbital angular momentum. A
positive tangential thrust in the direction of motion raises the orbit (outward spiral); a negative one
brakes the craft and lowers it — the same "tacking" trick a sailboat uses against the wind, just with
photons instead of air. Reflectivity ρ (0.5 = absorptive, 1.0 = perfect mirror) sets how much momentum
each photon transfers.