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The thin layer approximation applied to the expansion of a supernova remnantassumes that all the swept mass resides in a thin shell. The law of motion inthe thin layer approximation is therefore found using the conservation ofmomentum. Here we instead introduce the conservation of energy in the frameworkof the thin layer approximation. The first case to be analysed is that of aninterstellar medium with constant density and the second case is that of 7profiles of decreasing density with respect to the centre of the explosion. Theanalytical and numerical results are applied to 4 supernova remnants: Tycho,Cas A, Cygnus loop, and SN 1006. The back reaction due to the radiative lossesfor the law of motion is evaluated in the case of constant density of theinterstellar medium.

Energy Conservation in the thin layer approximation: I. The spherical classic case for supernovae remnants