Al-Battani

Al-Battani

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Early life and work:

     Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī al-Ṣābiʾ al-Battānī (Arabic: محمد بن جابر بن سنان البتاني) (Latinized as Albategnius, Albategni or Albatenius) (c. 858 – 929) was an Arab astronomer, astrologer, and mathematician. He introduced a number of trigonometric relations, and his Kitāb az-Zīj was frequently quoted by many medieval astronomers, including Copernicus.

Works:

1.Astronomy:

    One of al-Battānī's best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds.

     He was able to correct some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative. Some of his measurements were even more accurate than ones taken by Copernicus many centuries later. Researchers have ascribed this phenomenon to al-Battānī being in a geographical location that is closer to the southern latitude, which might have been more favorable for such observations.

     Al-Battānī discovered that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.(In modern heliocentric terms this is due to the changing direction of the eccentricity vector of the Earth's orbit). He also introduced, probably independently of the 5th century Indian astronomer Aryabhata, the use of sines in calculation, and partially that of tangents. He also calculated the values for the precession of the equinoxes (54.5" per year, or 1° in 66 years) and the obliquity of the ecliptic (23° 35').He used a uniform rate for precession in his tables, choosing not to adopt the theory of trepidation attributed to his colleague Thabit ibn Qurra.

     Al-Battānī's work is considered instrumental in the development of science and astronomy.Copernicus quoted him in the book that initiated the Copernican Revolution, the De Revolutionibus Orbium Coelestium. Al-Battānī was frequently quoted by Tycho Brahe, Riccioli, among others. Kepler and Galileo showed interest in some of his observations,and his data continues to be used in geophysics.

2.Mathamatics:

     

In mathamatics, al-Battānī produced a number of trigonometrical relationships:

He also solved the equation sin x = a cos x discovering the formula:

He gives other trigonometric formulae for right angled triangles such as:

Al-Battānī used Al-Marazi's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents, compiling tables of them. He also discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants, which he referred to as a "table of shadows" (in reference to the shadow of a gnomon, for each degree from 1° to 90°.

Honors:

• The crater Albategnius on the Moon is named after him.
• In the fictional Star Trek universe, the  Excelsior-class starship USS Al-Batani NCC-42995, mentioned on Star Trek: Voyager as Kathryn Janeway's first deep space assignment, is named after him.
• The  novel Doctor Who and Night of the Humans,features a solar system called Battani 045.