🌞 Solar Wind & Earth's Magnetosphere — Bow Shock, Magnetopause, Aurora

The shader's magnetopause(phi, r0) function implements a Shue (1997)-style boundary, r = r0·(2/(1+cosφ))^α with α = 0.58, where φ is the angle from the Sun–Earth line and r0 is the subsolar standoff distance. A guard clamps the denominator max(1+cosφ, 0.18) near the tail to avoid a singularity as φ approaches π. The bow shock reuses the same formula with r0 scaled by 1.32, since the shock stands further upstream than the magnetopause itself.

The standoff() function computes a dynamic pressure term press = density × (speed/400)², then sets r0 = 0.42 × (fieldStrength / (press × storm))^1/6, clamped between 0.16 and 0.62 screen units. Because press sits in the denominator under a sixth root, faster or denser wind raises the pressure and shrinks r0 — a soft echo of the real pressure-balance relation that sets Earth's actual magnetopause distance.

Two related formulas run in parallel: the on-screen readout uses kpLevel() = storm×7 + ((speed−300)/500)×2, clamped to 0–9 to mimic the real geomagnetic K_p scale, while the shader itself computes kp = 0.3 + storm×0.9 + ((speed−300)/500)×0.4 to set how strongly the two polar auroral ovals brighten. Both rise with storm/CME activity and solar wind speed, so pushing either slider — or hitting Solar storm! — lights the poles up faster.

No — the entire scene, including the Sun's glow, the plasma stream, the bow shock and magnetopause arcs, the magnetotail, Earth, and the aurora, is painted analytically inside one GLSL fragment shader running on a full-screen quad. Fractal Brownian motion (fbm) noise gives the plasma its turbulent, flowing look, but there are no individual charged particles being integrated through a magnetic field — the boundaries and glow are closed-form functions of position and time.

The tail half-width is tailHalf = r0 × (0.95 + 0.25×fieldStrength), and a night-side mask restricts the tail to the side of Earth away from the Sun (where d.x is negative). Within that wedge, a brighter "plasma sheet" glow is drawn at the tail's centreline, its intensity modulated by the same fbm noise function used for the upstream solar wind, so the tail shimmers rather than appearing as a flat triangle.