calc_zeta_r

luminet.black_hole_math.calc_zeta_r(p: float, r: float, bh_mass: float) → float

Calculate \(\zeta_r\)

This is used for the Jacobi incomplete elliptic integral for higher-order images.

\[\zeta_r = \arcsin \left( \sqrt{\frac{Q - P + 2M + \frac{4MP}{r}}{Q - P + 6M}} \right)\]
Parameters:

  • p (float) – periastron distance

  • r (float) – Radius in the black hole frame.

  • bh_mass (float) – Black hole mass

Returns:

float – \(\zeta_r\)