Potential well
The surface warp visualizes scalar gravitational potential. Steeper regions correspond to stronger field gradients and larger acceleration.
Gravitation lab
3D Newtonian gravity, potential wells, and orbit intuition.
This lab turns mass, separation, and probe velocity into a 3D study scene: warped potential surface, gravity vectors, escape-speed behavior, and a live probe path.
Theory
What the scene teaches
Superposition
Two masses create a combined field. The arrows show vector addition, so direction and magnitude both matter.
Probe dynamics
The moving particle responds to the sampled gravity field. Low speed falls inward, tuned speed loops, and high speed escapes.
Caution
This is Newtonian and pedagogical. It does not model relativity, tides on extended bodies, numerical ephemerides, or collision mechanics beyond simple softening.
Mathematical model
Field and potential model
Gravity, magnetic, and electric field scenes are generated from vector-field equations. The vectors and surfaces are sampled from formulas, not sketched.
Newtonian gravity
\[\mathbf{g}(\mathbf{r})=-\frac{GM\,\mathbf{r}}{\lvert \mathbf{r}\rvert^3}\]
The gravity vector points toward the mass and falls as inverse square. Field arrows are samples of this equation.
Potential relation
\[\mathbf{g}=-\nabla \Phi\]
The force field is the negative gradient of the potential surface. This verifies that vector direction and potential shape agree.
Dipole field
\[\mathbf{B}(\mathbf{r}) \propto \left[\frac{3\mathbf{r}(\mathbf{m}\cdot\mathbf{r})}{\lvert \mathbf{r}\rvert^5}-\frac{\mathbf{m}}{\lvert \mathbf{r}\rvert^3}\right]\]
Earth-field lines use a dipole approximation. The visualization is a sampled theoretical field with stated simplifications.
Verification standard: the rendered object must be reproducible from stated equations, catalog parameters, or explicit geometric transforms. Visual reference images may inform presentation only; they are not the source of orbital positions, field vectors, accretion-disk gradients, timing, or engineering layout.
Limitations: browser scenes may use bounded scale, compressed distances, simplified two-body dynamics, schematic transfer curves, or educational approximations where full numerical ephemerides, CFD, finite-element models, or general-relativistic ray tracing are outside the page scope. Those simplifications are part of the model contract, not hidden image-based construction.