The Unified Orrery — The Solar System, Counted
An orrery is a machine for pretending the sky runs on clockwork. This one removes the clock. Eight orbits as counts against counts, the rate thinned toward the Sun, a stone dropped raw into the calculus — and out of one line with no t in it, an ellipse that closes, leans, and pays Mercury’s 43″ a century without ever being told about Mercury.
Five lines run the whole page, each established physics, none containing t: the clock ν = mc²∕h, the rate ν(r) = ν∞√(1−rs∕r), the fall g = −c²∇ln ν, Kepler’s third law with the times cancelled, and the lean of the ellipse, δφ = 3πrs∕a(1−e²). Where the textbook writes a time, these write a count — turns of a clock, closings of an orbit — and compare it to another count. Four benches use nothing else.
The orrery itself draws all eight orbits from the JPL J2000 books — sizes, stretches, tilts — in a 3D frame you drag to turn and scroll to approach. No planet is “at” a time; each is somewhere in its own closing, and the ledger connects them: while Earth closes once, Mercury closes 4.15 times, Neptune a 165th. Run THE AUDIT and the ledger opens in full — eight rows balanced to parts per thousand, and the residuals are not errors. They are masses: Jupiter’s −1.0‰ is, almost entirely, Jupiter itself, weighing 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.
The deepest bench drops a stone into the counting and pulls nothing: the machine integrates u″ + u = 1∕p + (3rs∕2)u² step by step in the orbit’s own turning — no clock as parameter — and the count is read back from the swept area, because on this page Kepler’s second law is not a law. It is the definition. An ellipse closes, leans, and lands on 42.98″ a century at the true seam; the MESSENGER-era books hold 42.98 ± 0.04.
The page separates its claims: established — Kepler 1619 across eight planets and every spacecraft since; Neptune from Uranus’s imbalance, 1846; Mercury’s 43.0″ isolated by Le Verrier 1859, derived by Einstein 1915 with no free parameter; the orbit line the machine integrates, Einstein 1915 at first order; the lapse from 22.5 m down to one millimetre; Cassini’s 2.3 × 10⁻⁵; the GPS ledger, balanced daily; interpretation — no t anywhere in the machine: orbits close, counts compare, the fall is the gradient of the count, no equation altered by the reading, which is the point and the price; open — weak-field and first order throughout, the seam magnifier stated on its dial with the ×1 row always recomputed at the true seam, and the standing flag: re-derivation is not discovery.