Mathematical verification

Every generated model starts from equations.

Exorbit Space separates mathematical models, catalog parameters, visual presentation, and known simplifications. A WebGL object is accepted only when its geometry or animation can be reproduced from equations, units, or explicit scene transforms.

Verification Standard

How generated models are accepted

These rules apply to all generated site models, including solar-system orbits, moon systems, black holes, spacecraft, observatories, field diagrams, scale maps, and engineering models.

Equation first

\[\text{model} \rightarrow \text{parameters} \rightarrow \text{transforms} \rightarrow \text{render}\]

The model definition comes before presentation. Orbits, fields, timing, disks, and engineering assemblies are generated from equations and explicit parameters, not traced from a screenshot or thumbnail.

Unit traceability

\[\mathrm{scene\_value}=\mathrm{scale\_factor}\cdot \mathrm{physical\_value}\]

Where a page shows AU, km, light-years, seconds, periods, masses, radii, or angular values, the rendered value must be connected to a unit conversion or a documented display scale.

Approximation label

\[\mathrm{visual\_model}=\mathrm{physical\_model}+\text{ stated simplification}\]

If the browser view compresses distances, enlarges radii, uses two-body dynamics, or uses schematic geometry, the page must say so. A simplified model is acceptable only when its simplification is explicit.

Core Model Families

Equations used across the website

Two-body orbital mechanics

\[r=\frac{a(1-e^2)}{1+e\cos(\nu)},\qquad M=E-e\sin(E)\]

Solar-system and moon-system positions are calculated from conic sections and Kepler propagation. This proves the paths are generated from orbital elements rather than image placement.

Energy and angular momentum

\[\varepsilon=\frac{v^2}{2}-\frac{\mu}{r},\qquad h=\lvert \mathbf{r}\times\mathbf{v}\rvert\]

Space Dynamics and gravity tools classify trajectories from conserved quantities. Orbit type follows the sign of energy and the angular-momentum vector.

Black-hole scale

\[R_s=\frac{2GM}{c^2}\]

Black-hole silhouettes are scaled from the Schwarzschild relation. Accretion disks use radial thin-disk temperature profiles and Keplerian differential rotation.

Field sampling

\[\mathbf{g}=-\frac{GM\,\mathbf{r}}{\lvert \mathbf{r}\rvert^3},\qquad \mathbf{g}=-\nabla\Phi\]

Gravity and field-lab vectors are sampled from vector equations. The arrows and surfaces must agree by gradient or inverse-square law.

Cosmological scale

\[1+z=\frac{1}{a(t)},\qquad T=T_0(1+z)\]

Big Bang and large-scale astronomy pages use scale-factor, redshift, temperature, and distance conversions as the model source.

Engineering transforms

\[\mathbf{p}_{\mathrm{world}}=TRS\,\mathbf{p}_{\mathrm{local}}\]

Rockets, rovers, landers, telescopes, and stations are built from reproducible scene-graph transforms, dimensional hierarchy, symmetry, and subsystem layout.

What This Does Not Claim

Limits that keep the proof honest

Not full numerical ephemerides everywhere

Some scenes use lightweight two-body propagation or anchored vectors instead of bundled SPICE/Horizons integration. Pages state that limitation where it matters.

Not full GR ray tracing

Black-hole pages use event-horizon scale, photon-ring markers, Keplerian flow, and thin-disk emissivity. They are not full general-relativistic radiative-transfer solvers.

Not manufacturing CAD

Engineering models are educational geometry with correct subsystem logic and transform consistency. They are not certified mechanical drawings or finite-element models.

Not image-derived proof

Images and reference visuals may inform color or composition, but mathematical claims must come from equations, units, data fields, or explicit transformations.