This is a top-down 2D view of the sun-orbit plane. Sunlight carries momentum: a sail of area A held at cone angle θ to the local sun-line intercepts effective area A cos θ, and each photon transfers momentum on absorption or specular reflection:
I = S₀ / d² (irradiance, S₀ = 1361 W/m² at d = 1 AU)
F = (I·A·cosθ / c) · [ (1−r)·r̂ + 2r·cosθ·n̂ ]
n̂ = −cosθ·r̂ + sinθ·t̂ (sail normal, θ measured off the sun-line)
Unlike a static force-diagram view, this simulation integrates that force together with solar gravity (leapfrog integrator, GM☉ = 1.327×10²⁰ m³/s²) as the spacecraft actually orbits — r̂ and the tangential axis t̂ are recomputed every step from the spacecraft's current position, so cone angle θ is held fixed relative to the instantaneous sun-line exactly as a real sail's "cone/clock steering law" works on missions like IKAROS or LightSail.
- Cone angle θ — positive θ tilts the sail's reflected-light push to add energy to the orbit (spiral outward over many orbits); negative θ removes energy (spiral inward). θ = 0 gives pure radial thrust with no steering torque.
- 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 while total force scales with sail area, so thrust weakens fast as the spiral carries the craft outward.
- Semi-major axis a — computed each frame from orbital specific energy, a = −GM☉/(2E). It is the reliable spiral indicator: instantaneous distance oscillates around an ellipse, but a only grows when the sail is net adding energy and only shrinks when it is net removing it.
Time speed fast-forwards the simulated clock (hours of orbital motion per real second) — actual solar-sail orbit changes unfold over weeks to months, so this lets you watch a spiral develop in real time without changing the underlying physics.