Mathematical model
Planet rotation and scale model
Planet meshes are procedural study models: radius, axial tilt, and rotation come from catalog fields, while surface textures are visual aids. The mathematical model does not infer planet shape from a picture.
Rotation phase
\[\theta(t)=\theta_0+\frac{2\pi t}{P_{\mathrm{rot}}}\]
The displayed spin angle advances from the body's rotation period P_rot. Retrograde rotation is represented by the sign of P_rot.
Axial tilt
\[\mathbf{r}_{\mathrm{tilted}}=R_z(\varepsilon)\,\mathbf{r}_{\mathrm{body}}\]
The spin axis is tilted by an explicit obliquity epsilon. The proof is a rigid-body rotation matrix, not an artist-drawn axis.
Scale contract
\[R_{\mathrm{scene}}=k\,R_{\mathrm{catalog}}\]
Scene radius is a scalar multiple of catalog radius unless the user chooses a readability mode. The page states when visual radius is bounded so the model is not mistaken for exact visual scale.
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.
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