Al-Zarqali's moving solar-apogee model

An astronomical model can change in two ways: the calculated body moves, but the elements describing its motion may also change. Historians attribute to al-Zarqali an account of the solar apogee's own motion and a solar model with variable eccentricity, in a lost work summarising twenty-five years of solar observations according to the report presented by Roser Puig ¹.

This is a contribution to modelling, distinct from his universal plate and two-plate equatorium, not a claim that he invented all solar astronomy. The museum presents the work through the scholarship actually read; it has not inspected the lost original or recovered all its calculations ¹.

Apogee means the farthest point from Earth in the Earth-centred description of a body's motion; perigee is the nearest. The accompanying modern image explains that near/far distinction, but it is a generic Earth-centred teaching drawing, not al-Zarqali's solar diagram ².

Puig identifies two linked features: an independent motion of the solar apogee and variable eccentricity in the solar model. These statements do not attribute Kepler's elliptical orbital law or modern gravitational dynamics to the medieval author ¹.

A rate for one changing element is not a complete daily solar ephemeris. Puig separates theoretical works, tables, an almanac and instruments; keeping those categories distinct also prevents counting the same contribution repeatedly under different names ¹.

Astronomical observations and calculations had a long inherited history. MacTutor describes the Toledan Tables as combining material from al-Khwarizmi, al-Battani and Ptolemy with observations by al-Zarqali and his colleagues, in a group containing Muslim and Jewish scholars ³.

That setting makes neither every table entry original nor earlier astronomers dispensable. It also does not establish that every ancient and Arabic model used one identical apogee convention: this account stays with the specific change attributed to al-Zarqali rather than constructing an unsupported universal account of earlier astronomy ¹.

The biography distinguishes years spent observing from the later work summarising the observations. A probable treatise date must therefore not become the beginning of every observation, while an early observation must not automatically become the completion date of the later theory ¹.

Al-Zarqali appears in the historical accounts as an instrument maker and engraver working in Toledo. Puig reports Marrakushi's testimony that he observed there in1061 and Ibn al-Ha'im's attribution of twenty-five years of solar observations; these are reports conveyed by the modern biography, not an observation notebook inspected here ¹.

Puig probably dates the lost solar work to approximately1075–1080 and gives alternative titles, On the Solar Year or A Comprehensive Epistle on the Sun. Its contents are known through Arabic and Latin secondary sources, so the museum does not select a certain title and imply that a surviving original is available ¹.

This is not his separate fixed-star-motion treatise, dated approximately1084–1085 and surviving in Hebrew translation. Similar astronomical subjects do not make the survival history of one text evidence for the survival of the other ¹.

Sunni frame: Individual Muslim identity has a named biographical basis: Bibliotheca Alexandrina includes al-Zarqali in its Muslim-astronomers account, while MacTutor explicitly calls him Muslim. Sunni is the separately declared Andalusian default frame retained in his person record, not a quoted personal legal-school declaration ^{4 5}.

Puig attributes the solar work to him while placing his career within patronage, study and collaborative observation. Recognising a particular contribution need not erase that surrounding work, and mentioning a group does not prove that every member designed this particular solar model ¹.

The central distinction is between calculating a body's changing position and allowing the element defining the apogee's direction to change. Puig gives the apogee its own motion of about one degree in279 Julian years, alongside variable eccentricity; the biography supplies neither the lost treatise's full equations nor an executable reconstruction ¹.

The reported unit can be checked with modern paper arithmetic. One degree contains sixty arcminutes and each arcminute sixty arcseconds, making3600 arcseconds. Dividing3600 by279 gives approximately12.9032 arcseconds per year, or0.00358423 degrees annually: a modern conversion of the reported rate, not a decimal notation attributed to the author ⁶.

Multiplying the unrounded rate by279 returns3600 arcseconds. By contrast, the12.04 arcseconds/year repeated in the museum's older biography corresponds to approximately299.003 years per degree. These quantities are not numerically interchangeable; this check does not resolve the historical discrepancy or establish what the lost text actually said ⁶.

An arcsecond is an angular unit, not one second of elapsed clock time. “Per year” describes how that angle changes with time; confusing the two types of second changes the meaning even when every written numeral is copied correctly ⁶.

Puig describes the variable-eccentricity solar model as influential in the Maghrib and Latin Europe until Copernicus's time. This is a historian's account of prolonged reception, not a list of surviving originals or evidence that everyone in those regions used an unchanged calculation ¹.

MacTutor also discusses the almanac's circulation and adaptation for later dates, but that is another work. Its surviving languages and later revisions cannot simply be reassigned to the lost solar treatise, nor does the tables' popularity establish transmission of every theoretical detail ⁷.

The biography connects instrument making, study, observation and the writing of theory and tables. Together these establish a working environment, but they do not prove that the universal plate was the specific measuring instrument used to determine the apogee's rate ¹.

Accordingly, the graph does not invent a dependency between this solar model and each earlier al-Zarqali invention. Shared authorship or subject matter alone is not technical ancestry; inherited calculation and observation remain historical context without a fabricated intermediate manuscript or missing device ¹.

Reception in the Maghrib and Latin Europe is the broad continuation documented by the biography. No named later invention is added as a direct descendant without evidence specific to that relationship ¹.

Modern comparison helps explain changed models and explanations, not fill a missing genealogical link. NASA describes changes in Earth's orbit, its orientation and its axis within modern science; its article does not claim direct derivation from al-Zarqali's lost treatise ⁸.

MacTutor places astronomy in a setting of calendars, timekeeping and directions, but that does not make every theoretical refinement an immediate social transformation. The sources read here give neither a count of the solar model's users nor a measured commercial benefit caused by it ^{9 1}.

The distinction between a need and a particular solution matters. People could need calculated times while an astronomer studied an element changing too slowly to be noticed in ordinary clock reading; general astronomy's importance cannot substitute for evidence of this model's specific everyday adoption ¹.

Its historical significance lies in revising a solar description to include changing elements and in the subsequent reception summarised by Puig. This is a history of adjustment within an inherited calculating tradition, not a scene in which one discovery simply overthrows all earlier knowledge ¹.

This article has not measured the errors of every model prediction against modern observations. One rate, a lost work's possible titles and a reported observing duration are insufficient for that exercise; historical influence must remain distinct from a comprehensive accuracy certificate never produced here ¹.

The narrow answer is that Puig attributes the apogee's own motion and a variable-eccentricity solar model to al-Zarqali. MacTutor repeats the lost-work account and one-degree-in279-years rate; neither contribution needs a headline claiming that he first knew everything about an orbit ^{1 10}.

Writing about the Sun also does not make him the author of Kepler's laws. MacTutor cautions against a comparable exaggeration concerning Mercury, a separate subject; this account keeps solar theory, the equatorium's Mercury geometry and modern orbital explanation distinct ¹¹.

NASA's modern explanation distinguishes Earth's axial precession, the changing orientation of its orbital ellipse and changes in eccentricity. The comparison is useful because “motion” alone does not specify whether a body's position, a path's shape or an axis or path's orientation has changed ¹².

It remains an explicitly modern comparison, not a literal translation of al-Zarqali. NASA's approximate cycles are not used to certify the historical rate or to claim that he supplied gravitational dynamics or predicted Earth's climate; each account has its own questions, vocabulary and evidence ^{13 1}.

The direct witness needed to reconstruct the solar treatise is not available here: Puig calls it lost and describes its contents as indirectly known through Arabic and Latin sources. No manuscript shelfmark or museum visit is invented for that original ¹.

The accompanying image is modern Pearson Scott Foresman educational art declared public domain, adapted into a vector and later revised and translated by Commons contributors. It shows Earth, a path and near/far positions, not apsidal precession, a medieval drawing or eleventh-century hardware ¹⁴.

“The apogee has its own motion” may sound less spectacular than inventing the Sun or anticipating every modern science, but it more accurately represents the modelling contribution attributed to al-Zarqali. The value of the story lies in defining the question whose answer changed, not magnifying every detail of his career ¹.

Unit conversion also gives visitors a modest role in assessing a report. One need not master all astronomical history to notice that a degree in279 years is not12.04 arcseconds annually; the result checks a numerical statement, not the authority of every historical transmitter or a lost text ⁶.

Draw an exaggerated oval on paper, place an Earth point away from its centre, and mark near and far positions. This models what perigee and apogee mean; it is neither a scale drawing nor a reproduction of al-Zarqali's solar model ¹⁵.

Copy the direction joining the positions onto a transparent sheet and turn it a little. Turning that line is different from moving a dot along a fixed path; the activity explains a distinction, not a historical experiment or a real annual amount of precession ⁶.

For a paper calculation, divide3600 by279 and multiply the unrounded answer by279. Returning to3600 checks that the units survived; no telescope or direct view of the Sun is needed, and this is not an observing procedure ⁶.

• Roser Puig, al-Zarqali biography, Biographical Encyclopedia of Astronomers,1258–1260, especially the solar-work paragraph.
• MacTutor, al-Zarqali biography: identity, solar work and limits of the Mercury/Kepler comparison.
• Bibliotheca Alexandrina Antiquities Museum, named Muslim-astronomers account.
• NASA, Milankovitch cycles: modern comparison only.
• Commons, Apogee (PSF).svg: image metadata, history and public-domain declaration.