I found the below answer in regards to how one identifies the satellite azimuth from Landsat Images, but am not sure how you translate the path/row into azimuth angle. I have searched for such, but am struggling to find an answer, therefore I repost in the hope that someone might be able to advise...
Alternatively, you could utilize the WRS (Worldwide Reference System) information (metadata fields WRS_PATH and WRS_ROW; for landsat 4 onwards, it is sort of a grid indicating where the satellite is on its orbit). Have a look at the USGS page with has WRS specification documents and shapefile downloads, it is basically straightforward.
However, if you are comparing scenes from the same area, the satellite's azimuth angle is not subject to any change.
(Note that Landsat Metadata has changed a little bit as of August 2012.)
