Earth's magnetic field is approximated as a dipole: a field line's distance from the centre follows r = L·cos²(λ), where λ is magnetic latitude and L is the field line's equatorial crossing distance (in Earth radii). Solar-wind particles that cross the magnetopause are captured on field lines and slide toward the poles along this real curve, so the funnel shape you see is the actual dipole geometry, not a decorative cone.
- Landing latitude comes straight from L via λ = arccos(√(1/L)) — lower L-shells (more disturbed, storm-time field) land closer to the equator, which is why the oval expands equatorward as Kp rises.
- Emission color by altitude: atomic oxygen gives the famous green line (~557.7 nm) around 100–150 km and a slower red line (~630 nm) above ~200 km; molecular nitrogen contributes blue/purple below ~100 km where particle energies are highest.
- Magnetopause standoff distance is computed from solar-wind dynamic pressure (∝ density × speed²) using the real pressure-balance scaling R ∝ P-1/6 — faster, denser wind compresses the magnetosphere and pushes the boundary inward.