Chapter 15.6, Problem 7P

(a) Repeat Problem 6 where the "circular" area is now on the curved surface of the earth, say all points at distance $s$ from Chicago (measured along a great circle on the earth’s surface) with $s\le \pi R/3$ where $R=$ radius of the earth. The seeds could be replaced by, say, radioactive fallout particles (assuming these to be uniformly distributed over the surface of the earth). Find $F(s)$ and $f(s)$.

(b) Also find $F(s)$ and $f(s)$ if $s\le 1\ll R$ (say $s\le 1$ mile where $R=4000$ miles). Do your answers then reduce to those in Problem 6?