# Strip Brightness in a Spherical System

My question concerns the following problem, published in Galactic Dynamics by Binney and Tremaine and based on a work by Schwarzschild.

Specifically, I am having difficulties in deriving the given result in part (c), which I suppose is due to the confusion surrounding the definition of strip brightness. Could someone please explain, with the aid of a diagram if possible, how $$x$$ is related to the projection, $$R$$, of the radius $$r$$ onto the plane of the sky? I am having trouble visualising what $$x$$ is measuring here.

where the center of the strip passes a distance $$x$$ from the center of the circle at closest approach. So starting from the center and moving out, each successive strip would have a progressively larger value of $$x$$, but $$x$$ is a constant for a given strip (with $$x = 0$$ for the center strip).
The only differences from the picture are that (a) the strips have an infinitesimal width $$dx$$, and (b) they are infinite in length rather than the finite circle shown here.
• Which part of the diagram is the strip? I'm still having trouble visualising. How does it relate to $R$? Aug 3, 2020 at 19:14