solve_for_periastron
====================

.. py:function:: 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 :math:`b`, yielding the observer frame coordinates :math:`(b, \alpha)`.

   .. seealso:: :py:meth:`periastron_optimization_function` for the optimization function used.

   .. seealso:: :py:meth:`solve_for_impact_parameter` to also convert periastron distance to impact parameter :math:`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 :math:`0` (direct image).

   :returns: *float* -- periastron distance :math:`P` of the photon