ellipse

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 \(P \approx b\)) 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 \(3M\), 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 \(3M\).

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 \(b\) of the photon trajectory in the observer frame, which is in this case identical to the radius in the black hole frame \(r\)