# The Design and Simulation of an Astronomical Clock
## 10 Discussion  
Analyzing the data collected in Table 7 and regarding the features of the modeled astronomical clock, the following remarks and conclusions can be drawn:  
1. Throughout the duration of 44 days, the differences for the Sun longitudes between the ephemeris data and the data obtained by the motion study of the clock mechanism operation gradually grow from 0\({}^{\circ}\) to +1.23\({}^{\circ}\). This divergence occurs because the clock mechanism neglects the equation of time and tracks only the mean motion of the Sun. This error induces the difference between the true and the mean local time. 2. During the 44 days, the differences for the Moon longitudes between the ephemeris data and the data obtained by the simulation have positive and negative signs and their absolute values are larger than those calculated for the Sun. These errors are expected since the orbit and the motion of the Moon have many irregularities and the Moon gear train of the clock mechanism displays only its uniform motion and determines its mean positions. Moreover, since the clock is adjusted for the date on which the Moon is located in its orbital apogee, the Moon mean positions obtained by the simulation \"oscillate\" around the correct positions on both sides, between \(-4.36^{\circ}\) and +7.35\({}^{\circ}\). 3. The mean longitudes of the lunar node N determined by the mechanism motion study are identical to those given in ephemeris tables. This means that the lunar nodes gear train generates good approximation for the mean precession of the lunar nodes. 4. During June 2020, two significant and interesting astronomical events occurred, the first of which was the lunar eclipse and the second one was the solar eclipse. The eclipse of the Moon was penumbral and took place on 5-6 June 2020 [17] and the solar eclipse was annular and occurred on 21 June 2020 [18]. Since it is equipped with the lunar node pointer, the astronomical clock presented in this work was able to predict these events with acceptable accuracy. In Belgrade, the lunar eclipse began on 5 June at 19:45:51 CET, reached its maximum at 21:24:55 CET and ended at 23:04:03 CET. The astronomical clock predicted the beginning of the lunar eclipse on 5 June2020 at approximately 16:42 when the Moon pointer entered the eclipse sector and the maximum at 23:16 when the Moon pointer overlapped the Sun pointer inside the eclipse sector, as is shown on Figure 15. (The clock tells local mean solar time for Belgrade.) The end of the eclipse could not be determined by the positions of the Sun, the Moon and the lunar node pointers of the clock. The error of the clock prediction was visible but it was not too large. In Belgrade, the annular solar eclipse reached its maximum on 21 June 2020 at 8:40:04 CET and, as is shown in Figure 16, the astronomical clock predicted that this maximum would occur on 20 June 2020 at 17:58 when the Moon icon overlapped the Sun icon inside the eclipse sector and almost overlapped the nodal pointer. The error was quite large, more than 12 h ahead, but this was expected since the error range for the Moon longitude was also large (\(-4.36^{\circ}\), \(+7.35^{\circ}\)). Predictions of the lunar and solar eclipses with similar values of error are obtained by an entirely different mechanical device described and explained in [19]. Figure 15: Full Moon and penumbral lunar eclipse of 5–6 June 2020. It will be interesting to compare the design of the astronomical clock presented in this paper with the design of the famous Prague astronomical clock. Both clocks have similar dials, designed as the stereographic projection of the celestial sphere, and both of them display the motions and the mean positions of the Sun, Moon, zodiac circle and the Moon phases. As for the difference, the presented clock has the lunar node pointer which enables the prediction of lunar and solar eclipses. Moreover, this clock displays lunar phases in a more vivid way on a separate dial equipped with a rotational sphere which is painted half white and half dark blue.