ellipse
=======

.. py:function:: luminet.black_hole_math.ellipse(r, a, incl) -> float

   Equation of an ellipse

   This equation can be used for calculations in the Newtonian limit (large :math:`P \approx b`)
   It is also used to interpolate photons that originate from close to the black hole, and the front of the accretion disk.
   In this case, their periastron theoretically lies below :math:`3M`, but they are not absorbed by the black hole, as
   they travel away from the black hole, and never actually reach the part of their orbit that lies below :math:`3M`.

   :Parameters: * **r** (*float*) -- radius on the accretion disk (BH frame)
                * **a** (*float*) -- angle along the accretion disk (BH frame and observer frame)
                * **incl** (*float*) -- inclination of the black hole

   :returns: *float* -- Impact parameter :math:`b` of the photon trajectory in the observer frame, which is in this case identical to the radius in the black hole frame :math:`r`