UNIFIED STATE · TOOLS · TECHNICAL
UNIFIED GRAVITY · THE EQUATIONS, RUN IN THE SKY

The Unified Orrery

THE SOLAR SYSTEM, COUNTED · NO T IN THE MACHINE

An orrery is a machine for pretending the sky runs on clockwork. This one removes the clock. Every quantity on this page is a count compared to a count: orbits that close, rates that thin near the mass, an ellipse whose long axis leans forward a measured sliver per closing — and a stone you can drop into the counting, to watch one line of calculus with no t in it close the fall into an ellipse that leans exactly the measured sliver. The planets below move because your screen refreshes — that pace is presentation. The physics is the ratios, and the ratios carry no t.

The rate, the fall, the seam. Gravity is not a force pulling things through time — it is the counting itself, thinning toward the mass. Whatever falls is following the gradient of its own count; whatever orbits is falling forever past the mark.

UNIFIED GRAVITY — THE EQUATIONS · THE READING THIS ORRERY RUNS
§ 01 · THE EQUATIONS — FIVE LINES, NO T
NOTHING PROPOSED · EVERYTHING RE-READ

Five lines run the whole page. Each is established physics; none contains t. Where the textbook writes a time, these write a count — turns of a clock, closings of an orbit — and compare it to another count. The four benches below use nothing else.

E · 01
ν = mc²∕h
The clock
Every figure of mass m is a metronome: mc²/h turns per turn of the standard. Mass is a tempo, and all rates are ratios of counts.
ESTABLISHED · DE BROGLIE 1924
E · 02
ν(r) = ν√(1−rs∕r)
The rate
Near mass — and at speed, √(1−v²/c²) — the counting runs thin. rs = 2GM∕c² is the seam where it would stop.
ESTABLISHED · POUND–REBKA 1959 · GPS DAILY
E · 03
g = −c²∇ln ν
The fall
The fall is the gradient of the count. Read where the thinning is weak, this line hands back Newton's GM∕r² — and § 03 below runs it raw.
ESTABLISHED · WEAK-FIELD EQUIVALENCE
E · 04
(N₁∕N₂)² = (a₂∕a₁)³
The ledger
Kepler's third law with the times cancelled: while orbit 1 closes N₁ times, orbit 2 closes N₂. Counts against counts — the ledger balances.
ESTABLISHED · KEPLER 1619
E · 05
δφ = 3πrs∕a(1−e²)
The lean of the ellipse
Per closing, the long axis leans forward by this angle — pure geometry, per orbit, not per second. Mercury's 43″ lives here.
ESTABLISHED · EINSTEIN 1915 · LE VERRIER'S GAP
§ 02 · THE ORRERY — EIGHT COUNTS, ONE LEDGER
E·01 · E·04 · DRAG TO TURN · SCROLL TO APPROACH

Eight orbits, drawn from the real elements — sizes, stretches, tilts, to the JPL J2000 books. No planet is "at" a time; each is somewhere in its own closing, and the only honest statement connecting them is the ledger: while Earth closes once, Mercury closes 4.15 times, Neptune a 165th. Pick a body and check E·04 yourself — the square of the count ratio against the cube of the orbit, two numbers, one balance. Then run THE AUDIT and read all eight rows at once: the residuals are not errors. They are masses.

THE ORBIT · a
THE STRETCH · e
COUNT AGAINST COUNT · PER EARTH CLOSING
THE LEDGER · (N⊕∕N)² ≟ a³
THE WALK NOW · v∕c
THE RECORD — THE LEDGER, AUDITED
Run THE AUDIT: eight rows, balanced to parts per thousand — and the residuals themselves speak. Jupiter's −1.0‰ is, almost entirely, Jupiter itself: the exact ledger reads a³∕(N⊕∕N)² = 1 + m∕M☉, and Jupiter weighs 0.95‰ of the Sun. The books even run backward: in 1846 Uranus's count would not balance, and Le Verrier resolved them with mass, not repeal — Neptune, found within a degree of where the arithmetic said to look.
HELIOCENTRIC · RADIAL SCALE COMPRESSED (r0.45) — THE CHART, NOT THE TERRITORY · ELEMENTS TO JPL J2000 · DOTS ON THE CHOSEN ORBIT: EQUAL COUNTS — CROWDED WHERE THE WALK IS SLOW · DRAG TO TURN · SCROLL TO APPROACH
EARTH · CLOSINGS SINCE YOU ARRIVED
MERCURY · CLOSINGS
§ 03 · THE FALL — THE CALCULUS, RUN RAW
E·02 ∘ E·03 → E·05 · THE STONE WALKS ITS OWN COUNT

Everything above places the planets; this bench earns them. Drop a stone into the counting and nothing pulls it: it takes the path along which its own count is extremal — the geodesic rule, which is general relativity's whole instruction, run as a calculus of variations on the census. Written per turn of the orbit, with u = 1∕r, the instruction is the one line on the bench below, and no t appears in it: radius as a function of its own turning. The machine integrates that line step by step in φ — second difference on the left, the rule on the right, equal at every step and sampled live — and out of the arithmetic an ellipse closes, leans, and pays Mercury's 43″ a century without ever being told about Mercury. The count itself is read back from the sweep, because equal areas are equal counts: Kepler's second law is not a law on this page. It is the definition.

u″ + u = 1∕p + (3rs∕2)u²
E·02 ∘ E·03, WRITTEN PER TURN · u = 1∕r · p = a(1−e²) · NO T — ONLY THE TURNING · ESTABLISHED — EINSTEIN 1915, FIRST ORDER
THE RULE AT THE STONE · u″+u ⇄ 1∕p+(3rs′∕2)u²
THE LEAN PER CLOSING · MEASURED BY THE MACHINE
THE LEAN PER CLOSING · CLOSED FORM E·05
AT THE TRUE SEAM ×1 · MEASURED
THE CLOSING · FROM THE SWEPT AREA ⇄ LEDGER a³ᐟ²
THE RECORD — WHAT THE MACHINE PAYS
THE ORBITAL PLANE, TILTED — DRAG TO TURN · THE STONE WALKS AT ITS OWN COUNT — EQUAL AREAS PER FRAME, SO IT WHIPS THE PERIHELION · COPPER DOTS: PERIHELION, WALKING FORWARD · WHEN THE ORBIT OUTGROWS THE FRAME THE RADIUS IS COMPRESSED (√r) · THE MAGNIFIER IS ON THE DIAL — THE ×1 ROW IS ALWAYS THE TRUE SEAM
CLOSINGS WALKED
THE COUNT, READ FROM THE AREA
§ 04 · THE RATE — THE COUNT, THINNED ACROSS THE SYSTEM
E·02 · EVERY PLANET IS A CLOCK

The Sun thins the counting around it — by gravity's term GM∕c²r, and for anything orbiting, by its own speed, v²∕2c². Every planet is a clock set at a different depth. Slide along the system and read the ledger against Earth's clock: Mercury's runs two milliseconds a day slow; Neptune's, a fraction fast. No clock has stood on Mercury — but the same lapse, tested at Earth to parts in a hundred thousand, leaves no room for it to differ.

GRAVITY'S TERM · GM∕c²r
SPEED'S TERM · v²∕2c² IN ORBIT
TOTAL THINNING · 3GM∕2c²r
DRIFT AGAINST EARTH'S CLOCK
THE RECORD — THE LAPSE, TESTED
The rule itself: Pound–Rebka 1959, Gravity Probe A 1976 (70 parts per million), NIST 2022 across one millimetre, and the GPS correction running four decades. The Sun's own thinning: Cassini 2003 timed its radio waves through the thinned count at the Sun's limb and confirmed the lapse to 2.3 × 10⁻⁵. At Earth's station the solar account reads 1.48 × 10⁻⁸ — a clock far from the Sun gains 1.28 ms on us every day, and the planetary ephemerides carry exactly this bookkeeping.
TOTAL THINNING VS DISTANCE · PARTS IN 10⁸ · LOG DISTANCE, 0.15 → 40 AU · THE CURVE DIES AS 1∕r — THE COUNT CROWDS TOWARD THE MASS
§ 05 · THE LEAN OF THE ELLIPSE — PER CLOSING, NOT PER SECOND
E·05 · LE VERRIER'S 43″, YOURS

A Newtonian ellipse repeats itself exactly; the counted one leans. Each closing carries the long axis forward by δφ = 3πrs∕a(1−e²) — an angle per orbit, no time anywhere in it. The century below is not a duration; it is a count of closings, 415 of them for Mercury. Le Verrier weighed the books in 1859 and found 43″ a century missing; Vulcan was invented to pay the debt and never found. The counting pays it exactly — § 03 above paid it the hard way, by integrating the fall; this bench is the closed form, fast enough to sweep the roster.

THE SEAM OF THE SUN · rs = 2GM∕c²2.95 km
THE LEAN PER CLOSING · δφ
CLOSINGS PER CENTURY · FROM THE LEDGER
THE LEAN PER CENTURY
THE RECORD — WHAT WAS MEASURED
THE ROSETTE — THIRTEEN CLOSINGS, LEAN EXAGGERATED × TO BE VISIBLE · DOTS MARK PERIHELION, WALKING FORWARD
§ 06 · THE OPEN FLAGS — FALSIFIABILITY ANNEX
AN INSTRUMENT, NEVER AN ORACLE

ESTABLISHED

Kepler's harmonic law, 1619, holding across eight planets and every spacecraft since; Neptune from Uranus's imbalance, 1846; Mercury's anomalous 43.0″ per century, isolated by Le Verrier 1859, derived by Einstein 1915 with no free parameter, standing today at 42.98 ± 0.04 in the MESSENGER-era ephemerides; the geodesic as extremal aging, and the first-order orbit line u″ + u = 1∕p + (3rs∕2)u² — Einstein 1915, the very line § 03 integrates raw; the gravitational lapse from 22.5 m (Pound–Rebka 1959) to one millimetre (NIST 2022); Cassini's 2.3 × 10⁻⁵ through the Sun's thinned count; the GPS ledger, balanced daily in production.

THE READING — UNIFIED GRAVITY

The thread alone: no t anywhere in the machine. Orbits close; counts compare. The rate is the count thinned near mass, the fall is its gradient — the stone in § 03 walks the path on which its own count is extremal, and the integrator's parameter is the orbit's own turning, never a clock. The ledger is Kepler with the times cancelled; the lean is geometry per closing. The pace of every drawing is presentation — turn it to zero and no physics changes, because nothing on this page happens in time.

No equation is altered by the reading. That is the point, and the price: the sky carries the same load by a different grip.

OPEN QUESTIONS & LIMITS

Everything here is weak-field and first order: the orbit line and δφ = 3πrs∕a(1−e²) are the leading lean, and the full account is Einstein's equation, which no one line abbreviates. § 03's magnifier scales the seam for the eye — the dial states it, and the ×1 row is recomputed at the true seam on every run; where the magnifier is high, the closed form and the integration part company, and the parting measures the second order, not a mistake. § 04 takes circular speed for the orbital term. The audit's residuals are the planets' own masses and the ice giants' still-settling mean books — stated in the table. The chart compresses radius so Mercury and Neptune share a frame; the Sun's oblateness contributes a measured, subtracted sliver to Mercury's lean; frame-dragging is real and far below this page's line width.

HOW THIS PAGE FAILS — THE CONDITIONS, STATED

FLAG · 01

The rate. One clock, at any station, whose rate departs from the lapse √(1−rs∕r) — at any height a lattice clock can resolve, in any potential a spacecraft can carry one through. One verified case, and E·02 falls, and § 04 with it.

FLAG · 02

The lean. One weak-field perihelion departing from 3πrs∕a(1−e²) beyond the ephemeris budget — Mercury's is watched to ±0.04″ a century. One verified case, and E·05 falls, and § 03 and § 05 with it.

FLAG · 03

The ledger. One solar-system orbit whose count ratio breaks (N₁∕N₂)² = (a₂∕a₁)³ with no unseen mass to balance the books — the Uranus test, run in reverse and left unresolved. One verified case, and E·04 falls, and the orrery with it.

FLAG · 04

The standing flag — re-derivation is not discovery. Every number this page produces, the standard account produces; removing t from the ink changes no prediction, by construction. The reading becomes a theory only on the day the counting demands a number the textbook does not — and the measurement takes the counting's side. No such case is known. This flag stays raised, in the open, at the same volume as the claims it tests.