Sunlight carries momentum. A sail of area A tilted at cone angle θ to the sun-line intercepts an effective area A cos θ, and each incoming photon transfers momentum on absorption or reflection:
I = S₀ / d² (solar irradiance, S₀ = 1361 W/m² at d = 1 AU)
F = (I·A·cosθ / c) · [ (1−r)·ŝ + 2r·cosθ·n̂ ]
Here ŝ is the unit vector along the incoming sunlight, n̂ is the sail's outward normal, r is the fraction of photons specularly reflected (1 − r is absorbed), and c is the speed of light. The absorbed fraction pushes the sail straight along the sunlight direction (photon recoil); the reflected fraction pushes it along the sail's own normal with double the momentum transfer (mirror recoil), scaled by cos θ because reflection off a tilted mirror only returns a component of the incoming momentum to the normal.
- Cone angle θ — tilting the sail steers the net thrust vector off the sun-line: at θ = 0 it points straight away from the sun (fastest radial push); at larger θ a growing sideways (tangential) component appears, letting real missions like IKAROS or the Planetary Society's LightSail raise or lower their orbit by steering.
- Reflectivity r — a perfect mirror (r = 1) delivers up to twice the thrust of a perfect absorber (r = 0) at the same irradiance, because a reflected photon reverses momentum instead of just depositing it.
- Distance / radius — irradiance falls off as 1/d² (inverse-square law) while total force scales linearly with sail area, which is why real solar sails are built as large, ultra-thin membranes.
Thrust efficiency compares the current force to the theoretical maximum for the same irradiance and area — a perfect mirror at normal incidence (θ = 0, r = 1).