Astronomical Gearing

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:

sidereal month ration

The rotation period of blue wheel (60 teeth):

ratio

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

tropical
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°