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We propose simple, explicit, analytical approximations for the kinematics ofan adiabatic blast wave propagating in an exponentially stratified ambientmedium, and for the onset of radiative cooling, which ends the adiabatic era.Our method, based on the Kompaneets implicit solution and the Kahnapproximation for the radiative cooling coefficient, gives straightforwardestimates for the size, expansion velocity, and progression of cooling timesover the surface, when applied to supernova remnants (SNRs). The remnant shapeis remarkably close to spherical for moderate density gradients, but even asmall gradient in ambient density causes the cooling time to vary substantiallyover the remnant's surface, so that for a considerable period there will be acold dense expanding shell covering only a part of the remnant. Ourapproximation provides an effective tool for identifying the approximateparameters when planning 2-dimensional numerical models of SNRs, the example ofW44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with  ecmatex.sty and lscape.sty package

Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling