This study examines an 8-ja (1,66 m) gnomon built by the Korea Astronomy and Space Science Institute (KASI, 127°22′32″ N, 36°23′57″ E) in 2011. This gnomon is an astronomical instrument with the same function as the Small Gnomon, which was built in 1440 during the reign of King Sejong of the Joseon Dynasty. The length of the column’s (or crossbar’s) shadow cast by the sun at the meridian passage was measured for a total of 303 days out of the 1,492-day observation period, which lasted from December 2015 to December 2019. The shadow lengths showed a measurement error of -0.8 to 1.2 cm compared to modern calculations. Furthermore, this study also estimated the time of the winter solstice using shadow lengths obtained from modern calculations for 50 days before and after the winter solstice. This calculation method was first introduced in the Daming Calendar (462) by Zu Zhongzhi (祖冲之, 429-500) and was applied to the Shushi Calendar (1281) by Guo Shoujing (郭守敬, 1231~1316). The time of the winter solstice did not demonstrate a constant value on the days before and after the winter solstice but showed a decreasing pattern, which had a constant slope each year. The tropical year can be obtained from the time of the winter solstice of two consecutive years. The fractional part of the tropical year (0.242 189 days) was estimated 0.242 789 ± 0.003 570 days in 2015-2016 (using data from 23 days both before and after the winter solstice) and 0.242 480 ± 0.004 616 days in 2016-2017 (using data from 45 days both before and after the winter solstice). Ultimately, the length of the tropical year estimated from the shadow lengths measured by the KASI’s 8-ja gnomon achieved an accuracy of 365.24 days. The observation value of the 8-ja gnomon showed an error of 0.1624 (±0.1229) days. It was found that this actual measurement error could result in an error of 3.9 h in the estimation of the time of the winter solstice or the accuracy of the length of the tropical year.

During the reign of King Sejong in the Joseon Dynasty (1433-1438), the Daegyupyo (large gnomon) was produced. The Daegyupyo, with a crossbar (horizontal bar), was used to observe the length of the gnomon’s shadow cast by the sun passing at the meridian. The shadow of this crossbar can be obtained using a measurable device called the Yeongbu (shadow definer). These Daegyupyo and Yeongbu are described in detail in the “Treatise on Astronomy” of Yuan History or “Celestial Spheres and Globes” of Jega-Yeoksang-Jjp (Collected Discourses on the Astronomy and Calendrical Science of the Chinese Masters). According to Jega-Yeoksang-Jjp, the Yeongbu had a structure similar to a door attached to its frame. A pinhole is located in the center of a copper leaf corresponding to the door of the Yeongbu. The image of the sun’s meridian transit and the shadow of the crossbar through the pinhole are projected onto the surface of the Daegyupyo’s ruler stone. Unlike the width and length of the Yeongbu, the height of the Yeongbu is not recorded. This research analyzed the height of the Yeongbu required to maintain the constant distance from the pinhole to the ruler stone surface. Based on these assumptions, it was estimated that 8 to 13 Yeongbu of different heights would be needed for observations using the Daegyupyo in Seoul. To accommodate the need for Yeongbu of various heights, this study proposed a model for a stackable Yeongbu with an adjustable height.

The armillary sphere, an astronomical observation device embodying the Orbital Heaven Theory of the Later Han Dynasty in China, holds both historical and scientific significance. It has been produced in various forms by many individuals since its inception in the era of King Sejong in the Joseon Dynasty. A prominent figure in this field was Nam Byeong-cheol (南秉哲, 1817-1863), known for his work 'Uigijipseol' (儀器輯說), published in 1859, which detailed the history, production methods, and usage of the armillary sphere. This text particularly highlights 21 applications of the armillary sphere, divided into 33 measurements, covering aspects like installation, time, and positional measurements, supplemented with explanations of spherical trigonometry. Despite numerous records of the armillary sphere's design during the Joseon Dynasty, detailed usage information remains scarce. In this study, the 33 measurements described in 'Uigijipseol' (儀器輯說) were systematically classified into six for installation, nineteen for position measurement, seven for time measurement, and one for other purposes. Additionally, the measurement methods were analyzed and organized by dividing them into the ecliptic ring, moving equatorial ring, and fixed equatorial ring of the armillary sphere. In other words, from a modern astronomical perspective, the results of schematization for each step were presented by analyzing it from the viewpoint of longitude, right ascension, and solar time. Through the analysis of Nam's armillary sphere, this study not only aims to validate the restoration model of the armillary sphere but also suggests the potential for its use in basic astronomical education based on the understanding of the 19th-century Joseon armillary sphere.