Two new equations of motion for a supernova remnant (SNR) are derived in the framework of energy conservation for the thin-layer approximation. The first one is based on an inverse square law for the surrounding density and the second one on a non-cubic dependence of the swept mass. Under the assumption that the observed radio-flux scales as the flux of kinetic energy, two scaling laws are derived for the temporal evolution of the surface brightness of SNRs. The astrophysical applications cover two galactic samples of surface brightness and an extragalactic one.
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