Energy Conservation in the thin layer approximation: I. The spherical
  classic case for supernovae remnants
  The thin layer approximation applied to the expansion of a supernova remnant
assumes that all the swept mass resides in a thin shell. The law of motion in
the thin layer approximation is therefore found using the conservation of
momentum. Here we instead introduce the conservation of energy in the framework
of the thin layer approximation. The first case to be analysed is that of an
interstellar medium with constant density and the second case is that of 7
profiles of decreasing density with respect to the centre of the explosion. The
analytical and numerical results are applied to 4 supernova remnants: Tycho,
Cas A, Cygnus loop, and SN 1006. The back reaction due to the radiative losses
for the law of motion is evaluated in the case of constant density of the
interstellar medium.
