There are either a near kinematic distance of 5.5 kpc or a far distance of 8.8 kpc for a Galactic supernova remnant (SNR) G32.8$-$0.1 derived by using the rotation curve of the Galaxy. Here we make sure that the remnant distance is the farther one 8.
8 kpc through solving a group of equations for the shell-type remnants separately at the adiabatic-phase and the radiative-phase. For SNR G346.6$-$0.2 we determine its distance also the farther one 11 kpc rather than the nearer one 5.5 kpc.
There are several different methods to determine the individual supernovae (SNe) initial explosion energy, here we derive the average or typical explosion energy of shell-type supernova remnants (SNRs) in a particular way. By solving a group of equat
ions pertaining to shell-type SNRs at the same stage we obtained some physical parameters, e.g. the distance ($d$), evolved age ($t$), etc.. Assuming series of different SN initial explosion energies ranging from $10^{48}$ ergs to $10^{53}$ ergs, we derived series of distance and age parameters with which compared already known ones. Thus the most likely value of the SNe initial explosion energy is obtained when the deviation is least, which equals to about $10^{51}$ ergs, in good agreement with the undertook value.
We derive the $Sigma$-$D$ relation of Galactic supernova remnants of shell-type separately at adiabatic-phase and at radiative-phase through two sets of different formulas, considering the different physical processes of shell-type remnants at both s
tages. Also statistics on Galactic shell-type remnants about 57 was made. Then we do some comparison with other results obtained before. It shows that all the best fit lines in the $Sigma$-$D$ relation plots newly are to some extent flatter than those derived by some authors at early time. Our theoretical and statistical outcomes are in somewhat good consistency.
