Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī[n 1] (Arabic: محمد بن جابر بن سنان البتاني), usually called al-Battānī, a name that was in the past Latinized as Albategnius,[n 2] (before 858 – 929) was an astronomer, astrologer, geographer and mathematician, who lived and worked for most of his life at Raqqa, now in Syria.

His Kitāb az-Zīj aṣ-Ṣābi’ (c. 900), is the earliest extant zīj (astronomical table) made in the Ptolemaic tradition that is hardly influenced by Hindu or Sasanian astronomy.

An annotated version, also in Latin, published in three separate volumes between 1899 and 1907 by the Italian Orientalist Carlo Alfonso Nallino, provided the foundation of the modern study of medieval Islamic astronomy.

Al-Battānī, whose full name was Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī al-Ṣābiʾ al-Battānī, and whose Latinized name was Albategnius, was born before 858 in Harran in Bilād ash-Shām (Islamic Syria), 44 kilometres (27 mi) southeast of the modern Turkish city of Urfa.

[3] The epithet al-Ṣabi’ suggests that his family belonged to the pagan Sabian sect of Harran,[4][5] whose religion featured star worship, and who had inherited the Mesopotamian legacy of an interest in mathematics and astronomy.

According to the Arab biographer Ibn al-Nadīm, the financial problems encountered by al-Battānī in old age forced him to move from Raqqa to Baghdad.

[8] Al-Battānī died in 929 at Qasr al-Jiss,[2] near Samarra, after returning from Baghdad where he had resolved an unfair taxation grievance on behalf of a clan from Raqqa.

He made more accurate observations of the night sky than any of his contemporaries,[3] and was the first of a generation of new Islamic astronomers that followed the founding of the House of Wisdom in the 8th century.

He refined the observations found in Ptolemy's Almagest,[3] and compiled new tables of the Sun and the Moon, previously long accepted as authoritative.

One reason for this is thought to be that al-Battānī's location for his observations at Raqqa was closer to the Earth's equator, so that the ecliptic and the Sun, being higher in the sky, were less susceptible to atmospheric refraction.

[5] The careful construction and alignment of his astronomical instruments enabled him to achieve an accuracy of observations of equinoxes and solstices that had previously been unknown.

[8] Al-Battānī was one of the first astronomers to observe that the distance between the Earth and the Sun varies during the year, which led him to understand the reason why annular solar eclipses occur.

[5] Al-Battānī observed changes in the direction of the Sun's apogee, as recorded by Ptolemy,[21] and that as a result, the equation of time was subject to a slow cyclical variation.

[23] It was impossible for al-Battānī, who adhered to the ideas of a stationary Earth and geocentricism, to understand the underlying scientific reasons for his observations or the importance of his discoveries.

[23] He was aware of the superiority of trigonometry over geometrical chords, and demonstrated awareness of a relation between the sides and angles of a spherical triangle, now given by the expression:[12] Al-Battānī produced a number of trigonometrical relationships:[24] He also solved the equation discovering the formula Al-Battānī used the Iranian astronomer Habash al-Hasib al-Marwazi's idea of tangents to develop equations for calculating and compiling tables of both tangents and cotangents.

[24] Using these trigonometrical relationships, al-Battānī created an equation for finding the qibla, which Muslims face in each of the five prayers they practice every day.

Once attributed to the Iranian astronomer Kushyar Gilani by the German orientalist Carl Brockelmann, it is a fragment of al-Battānī's zīj.

[6] The work, consisting of 57 chapters and additional tables, is extant (in the manuscript árabe 908, held in El Escorial), copied in Al-Andalus during the 12th or 13th century.

[19] A chapter of the Ṣābiʾ Zīj also appeared as a separate work, Kitāb Taḥqīq aqdār al-ittiṣālāt [bi-ḥasab ʿurūḍ al-kawākib] ("On the accurate determination of the quantities of conjunctions [according to the latitudes of the planets]").

[36] Hebrew editions of the al-Zīj al-Ṣābī were produced by the 12th-century Catalan astronomer Abraham bar Hiyya and the 14th-century French mathematician Immanuel Bonfils.

[9] The astronomers Tycho Brahe, Giovanni Battista Riccioli, Johannes Kepler and Galileo Galilei cited Al-Battānī or his observations.

[38] In the 1690s, the English physicist and astronomer Edmund Halley, using Plato Tiburtius's translation of al-Battānī's zīj, discovered that the Moon's speed was possibly increasing.

To interpret his results, Halley was dependent upon on knowing the location of Raqqa, which he was able to do once he had corrected the accepted value for the latitude of Aleppo.

[40] Al-Battānī's observations of eclipses were used by the English astronomer Richard Dunthorne to determine a value for the increasing speed of the Moon in its orbit, he calculated that the lunar longitude was changing at a rate of 10 arcseconds per century.