Physics Reference
Brachistochrone (flip & brake)
t = 2 × √(d / a)
v_max = √(a × d / 2)
Δv = 2 × v_max
Δτ ≈ Δt (non-rel) | ∫dt/γ (rel)
Dart (full acceleration)
t = √(2d / a)
v_final = a × t
Δv = v_final
Rocket Equation
Δv = Isp × g₀ × ln(m₀/m₁)
v_e = Isp × 9.81 m/s²
prop % = 1 − 1/mass_ratio
Special Relativity
dv/dt = a_proper / γ³
γ = 1 / √(1 − v²/c²)
dτ = dt / γ (proper time)
Auto-applied when v > 0.1c
Laser Sail (Photon Thrust)
F = (1+R)·P / c
a = F / m
P_req = m·a·c / (1+R)
d_cutoff = r_sail / θ_div
P_eff = P·(d_cutoff/x)² beyond cutoff
recoil = P / c (on laser platform)