I've recently met a problem of estimating the density of points on ellipse sampled by focal radii equally dividing the turn around one focus.
For what I mean by equally dividing, here's an example of trisection: Three focal radii trisecting the turn around the right focus ,where A, B and C are the sampled points.
If we increase the number of focal radii equally dividing the turn, what would the density of points be? Can somebody give the result in terms of the length of focal radii?
I'm using this in an astronomical exploration, and the best result I expect is that the density at one point A is approximately proportional to $\text{FA}^{-1}$ with small eccentricity.