solve_for_periastron

luminet.black_hole_math.solve_for_periastron(radius: float, incl: float, alpha: float, bh_mass: float, order: int = 0) → float

Calculate the periastron of a photon trajectory, when the black hole coordinates are known.

This photon periastron can be converted to an impact parameter \(b\), yielding the observer frame coordinates \((b, \alpha)\).

See also

periastron_optimization_function() for the optimization function used.

See also

solve_for_impact_parameter() to also convert periastron distance to impact parameter \(b\) (observer frame).

Parameters:

• radius (float) – radius on the accretion disk (BH frame)

• incl (float) – inclination of the black hole

• alpha – angle along the accretion disk (BH frame and observer frame)

• bh_mass (float) – mass of the black hole

• order (int) – Order of the image. Default is \(0\) (direct image).

Returns:

float – periastron distance \(P\) of the photon