  We investigate the hypersonic limit for steady, uniform, and compressible
polytropic gas passing a symmetric straight cone. By considering Radon measure
solutions, we show that as the Mach number of the upstream flow tends to
infinity, the measures associated with the weak entropy solution containing an
attached shock ahead of the cone converge vaguely to the measures associated
with a Radon measure solution to the conical hypersonic-limit flow. This
justifies the Newtonian sine-squared pressure law for cones in hypersonic
aerodynamics. For Chaplygin gas, assuming that the Mach number of the incoming
flow is less than a finite critical value, we demonstrate that the vertex angle
of the leading shock is independent of the conical body's vertex angle and is
totally determined by the incoming flow's Mach number. If the Mach number
exceeds the critical value, we explicitly construct a Radon measure solution
with a concentration boundary layer.
