F = 2P/c (radiation pressure, ideal mirror)
a = F/m
P_recv = P · min(1, A_sail / (π·r_beam²))
r_beam(d) ≈ 1.22 · λ · d / D_array
- Laser power — total optical power delivered by the ground phased array; more power means more momentum transferred per second, but needs more energy and cooling.
- Mass — a lighter probe accelerates harder for the same force (a = F/m) — this is why Starshot targets gram-scale "starchips", not a full spacecraft.
- Sail area — a bigger sail intercepts more of the beam while it is still narrow, but a wider beam eventually catches up regardless.
- Diffraction limit — even a perfectly focused beam spreads with distance (r ∝ λ·d/D). Past a few million km the spot grows larger than the sail, most photons miss it, and thrust collapses — the probe then coasts at whatever speed it already reached.
- Chemical comparison — a chemical stage carries its own reaction mass, burns out in minutes, and tops out around tens of km/s — orders of magnitude below the light sail's coasting speed.
Model: near-IR laser (λ = 1.06 µm), 1 km ground phased array, ideal reflective sail. Mission clock runs faster than real time so the acceleration and coast phases are visible.