calc_b_from_periastron
======================

.. py:function:: luminet.black_hole_math.calc_b_from_periastron(p: float, bh_mass: float) -> float

   Get impact parameter :math:`b` from the photon periastron :math:`P`


   .. math::

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

   :Parameters: * **p** (*float*) -- periastron distance
                * **bh_mass** (*float*) -- Black hole mass

   .. attention::

      :cite:t:`Luminet_1979` has a typo here.
      The fraction on the right hand side equals :math:`b^2`, not :math:`b`.
      You can verify this by filling in :math:`u_2` in Equation 3.
      Only this way do the limits :math:`P -> 3M` and :math:`P >> M` hold true,
      as well as the value for :math:`b_c`.  The resulting images of the paper are correct though.

   :returns: *float* -- Impact parameter :math:`b`