(a) The radius of Saturn is 60330 km and its rotational period 
is 0.43 days.  At the equator, if differential rotation is minimal,
an object at Saturn's cloudtops travels the entire circumference of
Saturn in one rotational period.  So, its speed is

      2 * 3.14 * 60330 km
  v = ------------------- = 10.2 km/sec.
       0.43 * 86400 sec

(b) Let's say Saturn turns from left to right as we watch it.  Then
at any given moment, the left edge of Saturn's cloudtops is coming
directly toward us, and the right edge is going directly away from 
us.  Since light travelling from objects moving toward us is 
blueshifted, and light travelling from objects moving away from us
is redshifted, there is a shift equal to Saturn's rotational 
velocity both toward the blue and toward the red.  So the shift is
10.2 km/sec in each spectral direction, or 20.4 km/sec total.

(c) The Doppler formula is 

   delta Lambda    v
   ------------ = --- where c = the speed of light, 300000 km/sec.
     Lambda        c

So since the central wavelength is 5200 nm, we can compute the 
shift (delta Lambda) in either direction since we know the shift
is 10.2 km/sec in each direction.  From the center of the line to
either edge,
                 5200 nm * 10.2 km/s
  delta Lambda = ------------------- = 0.177 nm.
                     300000 km/s

So the total width from edge to edge is double that, or 0.354 nm.