Checking the model against something other than itself

The independent implementations live in a separate module that imports nothing from the engine, restates the physical constants rather than sharing them, and reaches each answer by a different route: closed forms replaced by numerical solutions, composed rotations replaced by explicit matrices, a fixed time grid replaced by random sampling. Where an external fact exists, such as a published orbital period, the check is anchored to that instead.

This is not a comparison against full-fidelity tooling. It shows the arithmetic is right, not that the model is complete. The model still has no J2 drift, no drag, no real ephemerides, no beam patterns and no capacity, andthe method page lists what that costs you.

1. Orbital period, against published values

The engine works in mean motion. This computes the period from Kepler's third law and compares it with the figures published for circular orbits at these altitudes.

2. Coverage half-angle, algebra against arithmetic

The engine uses a closed form. This solves the same question by placing a satellite and a site as three-dimensional vectors, computing the elevation between them directly, and bisecting on the separation until the elevation equals the mask. No half-angle formula is involved.

3. The geometric horizon

With a zero mask the coverage circle reduces to the geometric horizon, where the line of sight is tangent to the sphere. That has its own short closed form, which the general expression has to reproduce exactly.

4. Coverage fraction, fixed steps against random sampling

The engine measures coverage on a fixed grid of times, and a fixed grid can alias against a periodic system. This estimates the same quantity from 20,000 times and longitudes drawn at random, using the independent propagator. Agreement inside the sampling error means the step is not biasing the answer.

5. Satellite positions

The engine composes its rotation inline; the independent version multiplies named matrices in the standard sequence. Across 144 sampled positions spanning three altitudes, four planes and a range of times, the largest disagreement is below one nanometre, which is floating-point noise rather than a difference.

6. How much the time step costs

Not a cross-check but a measurement. The site quotes figures sampled at 20 second steps and states they are stable to roughly one step. This computes a reference at 5 seconds and shows what each coarser step actually does to the answer, so that claim is measured rather than asserted.

What is still missing

The comparison worth having, and the one not here, is against full-fidelity tooling with J2 drift and drag enabled. Two-body propagation in a package like GMAT would agree with this engine almost exactly, because it is the same physics, and would prove only that the arithmetic is right, which the checks above already show. The valuable number is how far the simplification moves the answer once perturbations are switched on. Until that exists, treat everything here as geometry done correctly rather than as coverage predicted accurately.