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

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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 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. 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 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.

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.