...
running...
How to use
Pick a preset, then change launch speed, fuse time, burst speed, drag and star burn time. The dashed blue circle is where the stars would be without air: it grows at the burst speed while its centre moves like a freely falling body. Real stars lag behind it because of drag and droop because of gravity, which is how willow effects form. A shell bursting before its apex shows the rising centre; after the apex the centre falls.
The science
Shell. A heavy shell launched at speed v0 and angle a follows ballistics with weak quadratic drag a = -g y^ - k |v - w| (v - w), burst when the fuse time runs out. Without air the apex is at t = v0 sin(a)/g.
Burst. At the burst each star gets an extra speed vb in a random direction around the shell's own velocity. For a symmetric burst the centre of mass keeps the shell's velocity, so the star cloud's centre falls freely under gravity: r_c(t) = r_b + v_shell t - g t2/2. The dashed circle of radius vb t around that centre is the drag-free burst.
Star motion. A star feels gravity and drag proportional to its speed squared, dv/dt = -g y^ - k |v - w| (v - w). Terminal speed is sqrt(g/k). With drag only, the distance travelled in a time t is ln(1 + k v0 t)/k, which is why high-drag stars stop short and droop (willow). Small stars have large k.
Simplifications. Two-dimensional cross-section of what is a sphere of stars, stars do not interact, fixed drag coefficient, uniform wind, shell mass constant, burn time randomised by 15 percent, no colour chemistry. Integration is semi-implicit Euler at 1/240 s.