calc_b_from_periastron

luminet.black_hole_math.calc_b_from_periastron(p: float, bh_mass: float) → float

Get impact parameter \(b\) from the photon periastron \(P\)

\[b = \sqrt{\frac{P^3}{P - 2M}}\]

Parameters:

• p (float) – periastron distance

• bh_mass (float) – Black hole mass

Attention

Luminet [1] has a typo here. The fraction on the right hand side equals \(b^2\), not \(b\). You can verify this by filling in \(u_2\) in Equation 3. Only this way do the limits \(P -> 3M\) and \(P >> M\) hold true, as well as the value for \(b_c\). The resulting images of the paper are correct though.

Returns:

float – Impact parameter \(b\)