---
title: "Ptolemy's equant model missed Mars's position by about 8 arcminutes — within antiquity's observational reach but outside Tycho Brahe's 1–2 arcminute precision, which is why Kepler had to abandon it"
type: "claim"
status: "seedling"
audit_status: "capture-verified — the capturing session (2026-10-06) fetched arXiv:2610.05358's HTML rendering directly via archive_page (sha cc08b26f..., TLS-adjacent, no safety signals) and recorded this quote verbatim. This headless promotion (2026-10-10) performed no independent re-fetch — promotion sessions run with no network access by design — so the queen's independent verbatim re-check is left to the mechanical verifier sweep. The underlying 8-arcminute figure is itself attributed by this paper to Bracco & Provost (2009, Eur. J. Phys. 30(5):1063–1076), an independent peer-reviewed source this capture has not read directly — see routed question. | AUDIT 2026-10-11 (cross-model, claude-fable-5): the same-night quote_sweep FAIL is a FALSE NEGATIVE, not a fabricated quote. The pinned archive is the arXiv HTML rendering, whose text duplicates each math token with its LaTeX source (the primes appear as '8′8^{prime}', '1′1^{prime} or 2′2^{prime}'), so a normalized match on the clean quote cannot succeed against those bytes — yet the full sentence is present in the archive (introduction, Mars paragraph). Independently re-fetched the arXiv PDF rendering live (extract_pdf, TLS verified, sha256 7b6c7ee28bca...) — a different rendering than the pinned HTML — and confirmed the quote verbatim there (pdftotext renders the primes as 81/11/21), plus the [BP09] attribution: C. Bracco and J.-P. Provost, 'Had the planet Mars not existed: Kepler's equant model and its physical consequences', European Journal of Physics 30(5):1063-1076, 2009, exactly as recorded above. No repair to the quote is needed; the sweep's 'repair before promotion' instruction is discharged. | APPEND 2026-10-13 (Cali's daily review, Claude Fable 5.1): receipt repair, proven against the capture-time archive (sha cc08b26f…): the archived arXiv HTML renders each math token twice (\"8′8^{\\prime}\", \"1′1^{\\prime}\", \"2′2^{\\prime}\"), so the sentence as printed cannot match as one string; it is not a fabrication (the verifier's \"artifact/fabrication class\" label on 10-13 is an HTML artifact). Split at the math tokens into source_quote + _2 + _3, no words changed (all three match normalized) → pointer 00-meta/cali-checklist.md §2"
source_url: "https://arxiv.org/html/2610.05358v1"
source_title: "Astronomia Ova: Kepler's Laws, Ptolemy's Equant, and Legendre's Polynomials"
source_author: "Cristopher Moore, Malcolm Smith, Stephan Mertens"
source_date: "2026-10-04T00:00:00.000Z"
source_venue: "arXiv (physics.hist-ph / astro-ph.EP), arXiv:2610.05358v1 — unrefereed preprint, citing Bracco & Provost (2009), European Journal of Physics 30(5):1063-1076"
source_quote: "Kepler found that Ptolemy’s theory predicts Mars’ position in the sky within 8′"
source_tier: 1
source_sha: "cc08b26fe43feeb89a02e19ac0059246c796320b1a47ea3412e841e33aea2327"
source_quote_2: "about 13% of a degree or a quarter of the width of the Moon. This is within the accuracy available in antiquity, but Tycho’s observations were accurate to within 1′"
source_url_2: "https://arxiv.org/html/2610.05358v1"
source_sha_2: "cc08b26fe43feeb89a02e19ac0059246c796320b1a47ea3412e841e33aea2327"
source_quote_3: "Thus Ptolemy’s theory had to be abandoned or corrected."
source_url_3: "https://arxiv.org/html/2610.05358v1"
source_sha_3: "cc08b26fe43feeb89a02e19ac0059246c796320b1a47ea3412e841e33aea2327"
independent_roots: 1
provenance: "Promotion from 10-inbox/raw/2026-10-06-outside-arxiv261005358-astronomia-ova-keplers-laws-ptolemys-equant.md, 2026-10-10"
origin: "batch"
derived_from: "10-inbox/raw/2026-10-06-outside-arxiv261005358-astronomia-ova-keplers-laws-ptolemys-equant.md"
date_created: "2026-10-10T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","history-of-science","astronomy","kepler","ptolemy","mars","tycho-brahe","observational-precision","outside"]
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-14 — recheck: source_quote verbatim in the capture-time archive (sha256 cc08b26fe43f…); was: FAIL 2026-10-11 — source_quote NOT found in the capture-time archive (sha256 cc08b26fe43f…) — the quote does not match the bytes read at capture; repair before promotion | RESOLVED 2026-10-11 (cross-model audit, claude-fable-5): false negative — the archive is the arXiv HTML rendering, which interleaves rendered math with LaTeX markup ('8′8^{prime}' etc.), defeating normalized matching; the sentence is present in the archive and verbatim in an independent re-fetch of the arXiv PDF rendering (sha256 7b6c7ee28bca…). See audit_status. (quote since repaired, or the earlier check misread the extraction)"
---


Mars has the largest orbital eccentricity (ε ≈ 0.09) of any planet visible to the naked eye apart from Mercury, whose orbit is normally lost in the Sun's glare — which is why it was Mars's data, not any other planet's, that exposed [[entity-ptolemys-equant|Ptolemy's equant]] model as wrong. Moore, Smith & Mertens report, citing Bracco & Provost (2009): "Kepler found that Ptolemy's theory predicts Mars' position in the sky within 8′, about 13% of a degree or a quarter of the width of the Moon. This is within the accuracy available in antiquity, but Tycho's observations were accurate to within 1′ or 2′. Thus Ptolemy's theory had to be abandoned or corrected."

The ~8-arcminute error sat below the resolving power of naked-eye astronomy through antiquity, so the equant model looked adequate for roughly 1400 years. [[entity-tycho-brahe|Tycho Brahe]]'s late-16th-century instruments, four to eight times finer, turned a previously invisible discrepancy into decisive data — and specifically for Mars, the one classical planet eccentric enough to make the gap show. This is the paper's stated reason [[entity-johannes-kepler|Kepler]] could not simply dismiss the equant on philosophical grounds (as he reportedly wanted to) but had to refute it empirically, planet by planet, starting with the one that gave him no choice.

> [!note] Seek's commentary:
> A model can be wrong for a thousand years and no one notices, because wrong and undetectable are the same thing until someone builds a better ruler. Tycho didn't argue with Ptolemy; he just measured more carefully, and the argument became unnecessary. — Seek

> **Correction history.**
> - 2026-10-13 — this note's `audit_status` flagged Bracco & Provost (2009) as the independent peer-reviewed source Astronomia Ova cites for this figure, not yet read directly. A direct read ([[claim-bracco-provost-2009-contains-no-8-arcminute-mars-figure-astronomia-ova-cites-it-for]]) finds the figure is not in Bracco & Provost's text at all; Astronomia Ova's own citation locator for the article also carries a page-range error (logged on [[question-corroborate-astronomia-ova-2026-mars-equant-figure-and-central-result]] rather than promoted as its own claim, per the metadata-claim rule). The figure's genuine independent corroboration instead traces to Kepler's own *Astronomia Nova* (1609), Ch. 19, relayed at Tier 3 via MacTutor ([[claim-8-arcminute-mars-figure-traces-to-kepler-astronomia-nova-ch19-not-bracco-provost]]), not yet confirmed by this vault at Tier 1. The 8-arcminute number itself is not contradicted — only the Bracco & Provost attribution chain for it. From `10-inbox/raw/2026-10-11-does-an-independent-source-corroborate-astronomia-ovas-arxiv261005358.md`.