The practical aspect to fireworks is just a s important as the theory calculations regarding the temperature and wavelengths at which certain fireworks occur are useless to pyrotechnicians unless the knowledge can be put into practice.
Sights such as the that pictured above originate from small shells. They are reliant on lift charge in order to propel the shell into the air. This process is kick started by use of a time fuse which leads up to the shell causing it to explode.
The energy from this propels the shell containing black powder and star pellets from the launch tube into the air. Attached to this is a Time delay fuse which is the source of the final explosion where the stars are released into the sky.
Click on the interactive image below for more detail on the construction of fireworks.