How you know it works
The rest of this site says what the engine does and how to call it. This page is the third question — whether the numbers coming back are right — and it is the one that matters for a service whose product is signed computation. Every figure here carries a date, a method, a reference, and a statement of what it does not establish.
Nothing on this page is self-certified. The strongest tests need no external data at all — a conservation law either holds or it does not, and there is no constant in it to tune. Where a reference is required it comes from somebody else, and our work is checked against data and implementations we do not control: ERFA 2.0.1.5, the SOFA-derived library the reference-frame chain is verified against term by term; ILRS Consolidated Prediction Format ephemerides, from the International Laser Ranging Service, for the geodetic spheres; IERS Earth-orientation parameters; and CelesTrak’s public element sets. Each benchmark below names which of them it was computed against, and against what version.
Why these tests, in this order
RANK A BENCHMARK BY HOW LITTLE OF IT CAN BE ARRANGED.
A propagator can be made to agree with almost any reference if you are willing to solve for the initial state that makes it agree. That procedure improves every number on this page and measures nothing, because it absorbs force-model error into the initial conditions. None of the results below is produced that way. The tests are ordered by how much freedom they leave:
A symmetry of the equations. A zonal gravity field is axially symmetric, so the polar component of angular momentum is conserved whatever the coefficients are. There is no number in the test to adjust and no reference to disagree with.
A closed form. The secular nodal rate under J₂ has an analytical expression. The constant it needs is published on this page, so a disagreement is attributable to that constant rather than left ambiguous.
A comparison against somebody else's fitted orbit. Both sides are models, neither is truth, and the residual is bounded below by whichever is worse. Useful as a bound. Not a fidelity figure, and not published as one.
The same reasoning applies to a test that cannot fail. A check written from the same assumption as the code it checks will pass whether or not the assumption is right — internal consistency cannot detect a shared premise. Where a result below rests on an outside implementation, the implementation is named.
Both rules run through the rest of the record. The verification ledger holds only outside anchors — a value somebody else published, or an invariant the mathematics forces — and never a self-comparison. Every entry in the stress tests & bounded mathematics records the trap it is built to avoid, so that it can fail for the right reason.
Named benchmarks
OPEN ANY ENTRY FOR THE METHOD, THE REFERENCE, THE CONFIGURATION AND THE LIMITS.
Called through the live API, the same way a customer calls it: the harmonic propagator inside the enclave. They can only be measured while the engine is running. When it is stopped, the last result is carried forward with its own date, never restamped.
Our own frame-transformation code, run on the measuring host and checked term by term against ERFA. It does not call the physics engine.
Public element sets propagated with the reference SGP4 implementation. They measure the public catalogue and a screening demonstration, not the GDS Physics engine.
Loading measured results…
Beyond the scheduled benchmarks
TWO STANDING RECORDS. OPEN EITHER FOR THE ANCHORS, THE MATHEMATICS AND THE RESULTS.
The benchmarks above are measured on a schedule, against the live service. Two standing records go wider across the engine: one sets its results against anchors somebody else published, the other shows each harness with the mathematics it tests.
Each row sets a result from this engine against an outside anchor: a published value — Mercury’s perihelion advance, the sun-synchronous rate, the inclination drift every geostationary operator budgets for — or a structural invariant the mathematics forces, such as a gravity gradient whose trace must vanish. If the two disagree, ours is wrong.
Each entry is a harness run against the compiled engine — gravity field and relativity, third bodies, the integrator, drag, covariance, conjunction and avoidance, manoeuvre detection — and opens to its formula, its inputs and the measured result against its anchor. Each also names the trap it is built to avoid.
NEITHER IS RE-MEASURED ON THIS PAGE’S SCHEDULE. THEIR RESULTS ARE STATED WHERE THEY ARE PUBLISHED AND NOT COPIED HERE, SO NO FIGURE CAN GO STALE IN TWO PLACES.
What this page does not claim
STATIC. THIS SECTION DOES NOT DEPEND ON THE DATA FILE OR ON SCRIPTING.
A page carrying only successes is marketing and will be read as such. These are the places where a reader could reasonably expect a number and will not find one, with the reason.
Deriving a state from a laser-ranging ephemeris and propagating it gives 35 m at one hour and 2.2 km at a day on LAGEOS-1. That is not published as fidelity. The reference is itself a fitted orbit, and the comparison's floor is our handling of the derived initial state rather than the propagator.
Adding atmospheric drag changed the low-altitude spheres by 1–4 m — they sit at 800–1,490 km, not the regime where drag dominates. Adding third-body gravity improved LAGEOS-1 by 13% and made LAGEOS-2 87% worse. Solar radiation pressure changed nothing at all.
The tell that the third-body term is right rather than broken is that it contributed the same size and direction to both satellites — about −300 to −420 m of in-track. A correct correction added to residuals of opposite sign must improve one and degrade the other. So the term is right and the baseline is wrong: the residual is dominated by something other than the force model.
The fetchable ILRS product is a prediction generated from a fitted orbit — what ranging stations point with. It is not the range measurements, and it is not centimetre truth. Every figure quoted from this page names the product and the provider it was computed against.
The longest arc this engine integrates on this page is thirty hours — eight revolutions, in the nodal-rate test. The frame check spans 1961–2050, which is nutation rather than orbit propagation, and the catalogue benchmark propagates out to about twelve days using the reference SGP4 implementation rather than ours. So no figure here is evidence about a week or a month of continuous integration by this engine.
Each figure is a single run at a single configuration unless a sample count is stated. Spread within a configuration can match spread between configurations, so a difference between two of these numbers is not automatically a difference in the thing being measured.
PG-06 reports how far public element sets sit from a laser-ranging orbit, and how fast that grows. Nothing in that benchmark calls this engine — the propagation is the reference SGP4 implementation. It is published because it establishes the noise floor beneath which no element-set-derived claim can be made, including ours. And the five objects it uses are the easiest in the sky: dead, spherical, laser-ranged, never manoeuvring, and used to define the terrestrial reference frame. It bounds the best case, not the typical one.
Read each residual against the element-set age beside it. The figures span a wide range and most of that spread is the age of the element set rather than anything about the object: two near-identical spheres at near-identical altitudes differ four-fold, and the difference is that nobody had published a new element set for one of them in six days. The current numbers are in PG-06 above — they are not repeated here, because a figure written into this paragraph would go stale the next time the benchmark ran.
How these numbers reach this page
The measuring host runs the benchmarks against the live service, writes a data file, and that file is published with the site. This page never calls the API. It is a static asset like every other page here, and it fetches nothing from another origin — the site's content policy is connect-src 'self' and this page does not relax it.
Fetching live would imply these were computed on page load, which is a stronger claim than the truth: a benchmark result has a date and a configuration attached to it. It would also require opening the gateway to every visitor's browser. The timestamp above is the honest version — it says when, so a stale figure reads as stale.
The reference-frame chain is verified against ERFA, an independent implementation derived from the IAU's Standards of Fundamental Astronomy. Its answers are pinned as fixed values so the check runs on a machine that does not have the library, and those pinned values are only ever replaced from an independent implementation — regenerating them from our own output would make the check circular.