I'm reading Goldstein's Classical Mechanics, the part on "Scattering" in the "Central Force" chapter.
In relation to the figure below, he says that angular momentum, $l$, is given by $$l=mv_0s$$ where $v_0$ is the velocity of the particle and $s$ is the distance from the line of the center of force(as shown in figure).
However, given that $l=\overrightarrow r \times \overrightarrow p=r.mv_0. sin (\theta)$, and $l$ is measured about the center of the sphere shown, it seems as if he has concluded that perpendicular drawn from the center of the sphere to the point of closest approach of the particle is of length $s$, which generally need not be true. To put it simply, how did he get the above expression?