X-ray astrophysics provides a great many opportunities to study astronomical structures with large energies or high temperatures. This dissertation will describe two such applications: the use of Swift X-ray Telescope (XRT) data to analyze the interaction between a supernova shock and the circumstellar medium, and the use of a straightforward computer simulation to model the dynamics of intracluster gas in clusters of galaxies and constrain the thermal conduction coefficient.

Stars emit stellar wind at varying rates throughout their lifetimes. This wind populates the circumstellar medium (CSM) with gas. When the supernova explodes, the shock wave propogates outward through this CSM and heats it to X-ray emitting temperatures. By analyzing X-ray observations of the immediate post-supernova environment, we are able to determine whether any significant CSM is present. By stacking a large number of Swift observations of SNe Ia, we increase the sensitivity. We find no X-rays, with an upper limit of 1.7 x 10^38 erg s^-1 and a 3 sigma upper limit on the mass loss rate of progenitor systems 1.1 x 10^-6 solar masses per year x (v_w)/(10 km s^-1). This low upper limit precludes a massive progenitor as the binary companion in the supernova progenitor system, unless that star is in Roche lobe overflow.

The hot Intracluster Medium (ICM) is composed of tenuous gas which is gravitationally-bound to the cluster of galaxies. This gas is not initially of uniform temperature, and experiences thermal conduction while maintaining hydrostatic equilibrium. However, magnetic field lines present in the ionized gas inhibit the full thermal conduction. In this dissertation, we present the results of a new one-dimensional simulation that models this conduction (and includes cooling while maintaining hydrostatic equilibrium). By comparing the results of this model with the observed gas temperature profiles and recent accurate constraints on the scatter of the gas fraction, we are able to constrain the thermal conductivity. Our results suggest that conduction factors are not higher than 10% of full Spitzer conduction for hot, relaxed clusters.