Geometric Astronomy and Time

Astrolabes

The astrolabe is an ancient astronomical device with many uses. A longer explanation of the usage and design of my astrolabe can be found on the website of the Prague Planetarium, written by Dr J. Rozehnal: https://www.planetum.cz/astrolab/.

Ilustrations from the article https://www.planetum.cz/astrolab/.

My astrolabe being cut out of balsa wood. Video: laser cutting.

Prototypes (3D printed half-sized versions), wooden without final markings.

3D printed model of the astrolabe

My STL model for 3D printing is available upon request.

The back side of the astrolabe

The back side contains the Equation of Time in polar form, and can be used to determine the time very precisely.

The mater of the astrolabe

Contains circles of equal altitude (almucantara), circles of equal azimuth, twilight lines (civil, nautical and astronomical), and meridian lines.

3D printed astrolabe

The mater and the alhidade are in black, the rete is in white.

The rete of the astrolabe

Contains the positions of selected stars, the celestial equator, the ecliptic and markings of right ascension.

My article about the construction of astrolabes for the Czechoslovak Journal for Physics, 2023

ccf_4-23_A.pdf

Current version of the Astrolabe

Front view

Rete + mater + alhidade.

Back view

Equation of time in a polar form. Conversion between the day of the year and the position of the Sun on the ecliptic with "traditional" boundaries (i.e. not the current official IAU constellation boundaries).

My lecture on spherical geometry for the Astronomy Olympiad

SphericalGeometry.pdf

Timekeeping and the Equation of Time

The Equation of Time (EOT) is the discrepancy between sundials and watches.

I try to measure the time of the Sun crossing my local meridian (visually or photoelectrically).

My local meridian, in my room. A photoresistor measures the decrease of flux due to the Sun going behind a stable stucture.

The equation of time, as measured on my meridian. The effect of the obliquity and eccentricity is plotted here as a first-degree approximation - i.e. a harmonic function.

Midday measurements

2021-01-11 12:10:20 o
2021-01-18 12:12:50 o
2021-01-21 12:13:30 o
2021-01-27 12:15:06 o
2021-02-01 12:16:30 o
2021-02-14 12:17:00 o
2021-02-15 12:16:58 o
2021-02-18 12:16:30 o
2021-02-25 12:15:30 o
2021-02-26 12:15:25 o
2021-02-28 12:15:01 o
2021-12-18 11:59:25 o
2022-01-14 12:11:00 o
2022-01-20 12:13:49 o
2022-01-21 12:13:40 o
2022-02-22 12:14:08 o
2022-02-27 12:15:00 o
2022-10-23 11:46:55 o
2022-10-25 11:46:10 photoelectric, bad weather
2022-10-28 11:46:15 photoelectric
2022-10-28 11:46:40 o
2022-10-29 11:46:29 o (photoelectric ignored due to atm.cond.)
2022-11-08 11:47:04 photoelectric, good weather, with polarizer
2022-12-08 11:56:37 o
2022-12-17 11:58:16 o
2023-01-05 12:07:21 o, not best weather
2023-01-10 12:09:24 o, bad weather
2023-01-14 12:10:52 o, ok weather. from camera 12:10:54 cca
2023-01-16 12:11:55 o, perfect weather, from camera 12:11:56

Doing simple geometric observations near GranTeCan telescope,

which is the largest single aperture telescope (10,4 meter).

Roque de los Muchachos: from left to right: Carlsberg meridian telescope (decomissioned), Willian Herschel telescope (large dome to the right of the gnomon), the Dutch Open Telescope, Mercator telescope, Sweedish solar telescope, Isaac Newton telescope, Jacobus Kapteyn telescope (far right)

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