Area of the planet's atmosphere         2 pi Rp  h
  -----------------------------------  =  ---------------
    Area of entire photosphere               pi  Rs*Rs

                 
                                               Rp     h
                                       =   2  ---- * ---
                                               Rs     Rs


  Here, "h" is something proportional to the scale height
of the planet's atmosphere.  I'll use a very rough value
which is probably on the large side.

  For our (cold) Jupiter, the scale height is about 30 km,
so I'll choose "h" = 300 km for a (hot) Jupiter.

  For a typical hot Jupiter around a Sun-like star, the ratio is
roughly  

             9 x 10^(-5)   ~  10^(-4)


  For our Earth, the scale height is very roughly 8 km, 
so I'll choose "h" = 8 km.

  That means for an Earth-sized planet around a Sun-like star, the ratio is
roughly

             2 x 10^(-7)