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Astronomical Gearing

Al-Biruni's mechanical calendar

Instruments carrying gearings of toothed wheels were used in the Late Antike or Byzantine period as calendrical devices, some of them displaying the phase (age) of the Moon, its position in the zodiac, and the position of the Sun in the zodiac.

A calendrical device was described by the Persian Muslim scholar and polymath al-Biruni (978-1048).

The rotating Moon disc: 59 days rotation period, corresponding to 29.5 days synodic month.

The rotation period of the wheel (39 teeth) for the sidereal month:

The rotation period of blue wheel (60 teeth):

The rotation period of the wheel (49 teeth) for the year:

 average duration gears error synodic month 29.530589 days 29.5 days 0.1 % sidereal month 27.321661 days 27.3 days 0.08 % tropical year 365.24219 days 365.17895 days 0.02 %

 gears average 62 synodic month 62*29.5 d = 1829.0 d 1830.90 d 67 sidereal month 67*27.3 d = 1829.1 d 1830.55 d 5 years 2 d 5 years 4.5 d

 2011 Feb 18, UT 23:00 Full Moon in Leo 2016 Feb 22, UT 23:00 Full Moon in Leo
1830 days later (5 years 4 days) the position of the full Moon is almost the same with respect to the fixed stars.

 Full Moon JD Diff days Long. Moon Diff Long. Long. Sun Diff Long. 1996 Jan 05 UT 22:08 2450088.369 - 104.80° - 284,86° - 2001 Jan 09 UT 20:24 2451919.350 1830.98 109.65° 4.85° 289,65° 4.80° 2006 Jan 14 UT 09:48 2453749.908 1830.56 114.08° 4.44° 294,09° 4.43° 2011 Jan 19 UT 21:21 2455581.390 1831.48 119.45° 5.36° 299,45° 5.37° 2016 Jan 24 UT 01:46 2457411.573 1830.18 123.49° 4.04° 303,49° 4.04° 2021 Jan 28 UT 19:16 2459243.303 1831.73 129,09° 5.60° 309,09° 5.60°

Al-Biruni's Moon Box:
from Wiedemann

 Web Links Abu Arrayhan Muhammad ibn Ahmad al-Biruni (MacTutor History of Mathematics archive) Antikythera Mechanism Sun and Moon Flash Animation The Antikythera Mechanism I: Java-animation of The Sun-Moon Assembly The Antikythera Mechanism The Antikythera Mechanism Books, Articles J.V. Field, D.R. Hill, M.T. Wright: Byzantine and Arabic Mathematical Gearing, Science Museum, London 1985. Jo Marchant: Decoding the Heavens, Solving the Mystery of the World's First Computer; William Heinemann, London 2008. Jo Marchant: Die Entschlüsselung des Himmels, Der erste Computer - ein 2000 Jahre altes Rätsel wird gelöst; Rowohlt 2011. Wiedemann, Eilhard: Ein Instrument, das die Bewegung von Sonne und Mond darstellt; Der Islam; Band 4, Heft 1, 1913; pp 5-13. Hill, D. R.: Al-Biruni's Mechanical Calendar; Annals of Science; Vol 42, Issue 2, 1985; pp 139-163.

Updated: 2014, Sep 02