Example Eclipse Calculations

Let us use our model to examine the lunar-solar syzygies of the year 1992 CE, in order to see whether any of them were associated with solar or lunar eclipses. The table below shows the dates and times of the new moons of 1992 CE, calculated using the method described at the beginning of this section. Also shown is the magnitude of the moon's ecliptic latitude at each syzygy, $\vert\beta_{syz}\vert$, calculated from Eqs. (125) and (144), as well as the critical values of this parameter for a general, total, and annular solar eclipse. The latter are calculated from Eqs. (152)-(154). It can be seen that the criterion for a total solar eclipse (i.e., $\vert\beta_{syz}\vert<\beta_{St}$ and $\beta_{St}>\beta_{Sa}$) is satisfied for the syzygy marked with a T, the criterion for an annular solar eclipse (i.e., $\vert\beta_{syz}\vert<\beta_{Sa}$ and $\beta_{Sa}>\beta_{St}$) for the syzygy marked with an A, and the criterion for a partial solar eclipse (i.e., $\beta_{St},\beta_{Sa}<\vert\beta_{syz}\vert< \beta_{S}$) for the syzygy marked with a P. It is easily verified that a total solar eclipse, an annular solar eclipse, and a partial solar eclipse did indeed take place in 1992 CE at the dates and times indicated.

Date	Time (UT)	$\beta_{S}(')$	$\beta_{St}(')$	$\beta_{Sa}(')$	$\vert\beta_{syz}\vert(')$
04/01/1992	23:00	85.0	52.5	55.5	22.8	A
03/02/1992	16:00	84.9	52.5	55.4	177.9
04/03/1992	09:00	85.7	53.4	55.8	282.7
03/04/1992	00:00	87.1	55.1	56.5	307.5
02/05/1992	14:00	88.7	57.0	57.4	245.8
01/06/1992	01:00	90.3	58.8	58.3	115.6
30/06/1992	12:00	91.5	60.1	59.0	46.3	T
29/07/1992	21:00	92.2	60.7	59.4	195.3
28/08/1992	05:00	92.3	60.7	59.5	290.2
26/09/1992	14:00	91.8	59.9	59.2	304.8
26/10/1992	00:00	90.7	58.5	58.7	234.8
24/11/1992	11:00	89.2	56.8	57.8	99.3
24/12/1992	01:00	87.4	54.9	56.9	64.3	P

The table below shows the dates and times of the full moons of 1992 CE. Also shown is the magnitude of the moon's ecliptic latitude at each syzygy, as well as the critical values of this parameter for a general and a total lunar eclipse. The latter are calculated from Eqs. (151) and (150), respectively. It can be seen that the criterion for a total lunar eclipse (i.e., $\vert\beta_{syz}\vert< \beta_{Mt}$) is satisfied for the syzygy marked with a T, whereas the criterion for a partial lunar eclipse (i.e., $\beta_{Mt}<\vert\beta_{syz}\vert< \beta_{M}$) is satisfied for the syzygy marked with a P. It is easily verified that a total lunar eclipse, and a partial lunar eclipse did indeed take place in 1992 CE at the dates and times indicated.

Date	Time (UT)	$\beta_{M}(')$	$\beta_{Mt}(')$	$\vert\beta_{syz}\vert(')$
19/01/1992	20:00	60.3	27.4	104.2
18/02/1992	05:00	60.1	27.3	237.8
18/03/1992	14:00	59.3	26.9	305.6
17/04/1992	01:00	57.9	26.2	288.5
16/05/1992	13:00	56.3	25.3	190.8
15/06/1992	03:00	54.7	24.4	39.4	P
14/07/1992	20:00	53.4	23.7	123.4
13/08/1992	13:00	52.8	23.3	251.6
12/09/1992	05:00	53.1	23.5	308.6
11/10/1992	21:00	54.3	24.1	278.2
10/11/1992	12:00	55.8	24.9	169.6
10/12/1992	01:00	57.5	25.8	13.8	T
08/01/1993	12:00	59.0	26.7	145.4