Background: An AC-130 is a military aircraft that has a cannon that fires out the side of its fuselage.
If an AC-130 (or similar aircraft) is traveling in straight, level flight at a constant rate of speed calculating gun lead is straightforward. For example if the plane is traveling forward at 100 meters per second, the target is 1000 meters to the side and its cannon shell travels at 1000 meters per second simply fire 1 second or 100 meters early to score a hit.
However what if the AC-130 is traveling in a circular orbit at 100 meters per second around its target instead of beside the target? I'm not sure how to calculate gun lead in that circumstance.
Hopefully the image I attached below will help this make sense. Thanks so much in advance for any input!