Configure the initial state
The model begins at the chosen altitude on the positive x-axis. Positive radial velocity points away from the body; negative radial velocity points downwards. Positive tangential velocity points prograde around the diagram. The trajectory is then stepped forward using a velocity-Verlet integrator.
The path is generated server-side when you submit the form. For numerical safety, very long runs may use a larger time step than requested so the calculation stays below 18,000 integration steps.
What the controls reveal
Set vₜ to zero
With no tangential component, angular momentum about the body's centre is zero. Even a very large upward speed is just radial motion. Below escape energy the craft rises, stops and returns along a body-intersecting path.
Set vᵣ to zero and vₜ near circular speed
The path becomes almost circular. Gravity is still present at every instant; indeed gravity is precisely what supplies the inward acceleration required to keep turning the velocity vector.
Increase vₜ above circular speed
The current point becomes near periapsis and the opposite side of the orbit rises. Continue increasing tangential speed and the ellipse stretches until the specific orbital energy reaches zero. Beyond that boundary the path is unbound.
Add radial velocity
You change where the spacecraft is on its ellipse. The initial point is no longer necessarily an apsis because part of the velocity points towards or away from the central body.
Why this answers the launch question
A launcher's job is not merely to make the altitude number large. It must manufacture angular momentum. In low Earth orbit that means kilometres per second of velocity that is predominantly tangential. The early vertical climb is therefore a temporary geometric necessity, not the destination of the ascent.