a, b, c D f constants, Eq. (9) diameter of the sphere function of d function of r Poo/ps p = pressure r — radial coordinate, distance from center of sphere R = shock radius, radial coordinate of shock u = radial component of velocity £7 oo = free-stream velocity v = circumferential component of velocity 8 = (2/D)V'Q _ Q , stagnation-point surface velocity gradient 8 = r — (D/2), radial distance from sphere surface 7 = ratio of specific heats X = Ps/pt p = mass density 6 = polar coordinate angle, measured from stagnation point