The vertical epicyclic frequency's cross term is a√M/r^1.5 (radius to the
−1.5), following Okazaki 1987. The spec previously wrote a·Ω_φ/r, which makes
Ω_θ too large and breaks monotonic growth of precession with spin. Caught
during Task 1 implementation by the grows_with_spin test; syncing the spec
to the corrected formula that shipped in 891eadf.
Spec for 5-8 planets on Kerr circular orbits with strong-field Lense-Thirring
nodal precession. Path A: CPU computes position each frame, uploads to the
existing storage buffer; shader unchanged.
Physics: closed-form Ω_φ (Bardeen 1972 eqn 2.16) and Ω_θ (Caltech Ph236
epicyclic vertical frequency), giving exact nodal precession Ω_φ - Ω_θ.
χ=0 degenerates exactly to Schwarzschild (Ω_LT = 0, Newtonian Ω_φ).
Explicitly rejects Mino-time analytic geodesics (Fujita-Hikida): circular
orbits collapse the three-frequency decomposition to Ω_φ alone, elliptic
functions have no WGSL/std backing, and it would break physics.rs's
single-testable-mirror design. Closed-form Kerr frequencies are the right
tool for circular orbits.
Orbit radius bound to k·kerr_isco(χ), so planets track the disk inner edge
as spin changes and span the strong-field region (k=2.5 → r ∈ [1.25, 7.5]).
Random initial attitudes (ChaCha8Rng + UI seed) so the three orbital planes
precess at different Ω_LT rates — the visible Kerr signature.
Decomposes Planet into OrbitParams (immutable elements) + Planet (derived
center), keeps SphereData GPU layout untouched. Adds time_scale UI knob
because Ω_LT at r=8 needs ~25 min per revolution otherwise.
