The Firework Burst — Every Star Its Own Parabola
A shell bursts over the city and throws its stars out in every direction at once. Seen from the ground each star traces a different parabola; ride the centre of the pattern and those same trails become straight radial lines on a sphere that grows steadily. Gravity gives every star the identical acceleration, so it cannot change how they move relative to each other.
How to use this simulation
- Press Launch firework and then Jump to the burst to catch the moment it opens
- Switch between Ground view and Ride centre to change frame mid-flight
- Load the textbook burst with equal speeds, then Unequal speeds to break the sphere
- Reduce to 12 clear trails to follow individual parabolas one at a time
What to look for
- From the ground every star follows a different parabola, and none of them looks radial
- From the burst centre all the trails straighten into radial lines
- With equal ejection speeds the pattern stays a perfect expanding sphere
- The sphere's radius grows in direct proportion to time, not as time squared
- Unequal speeds distort the sphere immediately, since the radius depends on each star's own u
The physics behind it
Every star leaves the burst with the same speed u in a different direction, and every one of them is then given exactly the same acceleration g. Because the acceleration is common, it cancels completely out of the relative motion: in the frame of the burst centre the stars simply travel outwards in straight lines at constant speed, filling a sphere of radius ut. Meanwhile the centre itself continues along the parabola the shell was already on. The ground view is those two motions added — a growing sphere carried along a parabola.