What to watch for
Raise the mass and the well deepens dramatically. The rings bunch up near the centre, the orbits precess faster, and the light rays whip around through larger angles. Push the mass high enough and the inner rays curve so hard they spiral into the centre rather than escaping. This is the toy version of a photon being captured by a black hole.
Turn on spin and the whole well starts to swirl. This is frame dragging (the Lense-Thirring effect): a rotating mass doesn't just curve spacetime, it drags it around with it, like a spoon stirring honey. Watch how prograde orbits, those going the same way as the spin, get whipped forward, while the sheet itself twists. Around a real spinning black hole this dragging becomes so total inside the ergosphere that nothing can stand still.
The deepest thing to notice is that the marbles and the light rays are doing the same thing: coasting freely, following the local geometry, never pushed. The only difference is their speed through it. Gravity, in this view, isn't a thing that acts on objects: it's the stage they all move across.
Knobs
- Mass M: how heavy the central object is, in geometrised units where . Bigger mass means a deeper well, a larger horizon , sharper light-bending, and faster orbital precession.
- Geodesics: toggle the orbiting test particles. With them on, watch the ellipses slowly rotate: that rosette is the relativistic correction at work.
- Light rays: toggle the incoming light rays (yellow). Each enters straight from the left at a different impact parameter and bends by roughly ; the ones passing closest bend the most.
- Spin a: add rotation to the central mass. The well swirls and prograde paths get dragged forward (Lense–Thirring frame dragging). Set it to zero for the static Schwarzschild case.