Mercury

The ecliptic longitude of Mercury can be determined with the aid of Tables 62-64. Table 62 allows the mean longitude, $\bar{\lambda}$, and the mean anomaly, $M$, of Mercury to be calculated as functions of time. Next, Table 63 permits the equation of center, $q$, and the radial anomaly, $\zeta$, to be determined as functions of the mean anomaly. Finally, Table 64 allows the quantities $\delta\theta_-$, $\bar{\theta}$, and $\delta\theta_+$ to be calculated as functions of the epicyclic anomaly, $\mu$. The procedure for using the tables is analogous to the previously described procedure for using the Venus tables. One example of this procedure is given below.

 
Example: May 5, 2005 CE, 00:00 UT:
 
From Cha. 8, $t-t_0=1\,950.5$ JD, $\lambda_S = 44.602^\circ$, and $\zeta_S= -8.56\times 10^{-3}$. Making use of Table 62, we find:

$t$(JD)	$\bar{\lambda}(^\circ)$	$M(^\circ)$
+1000	$132.377$	$132.334$
+900	$83.139$	$83.101$
+50	$204.619$	$204.617$
+.5	$2.046$	$2.046$
Epoch	$252.087$	$174.693$
	$647.268$	$596.791$
Modulus	$314.268$	$236.791$

Given that $M\simeq 237^\circ$, Table 63 yields

$$q(237^\circ)= -16.974^\circ, \mbox{\hspace{0.5cm}}\zeta(237^\circ)=-1.367\times 10^{-1},$$

so

$$\mu=\bar{\lambda}+q-\bar{\lambda}_S = 314.268-16.974-44.602= 252.692\simeq 253^\circ.$$

It follows from Table 64 that

$$\delta\theta_-(253^\circ) = -4.005^\circ,\mbox{\hspace{0.5cm... ...\mbox{\hspace{0.5cm}}\delta\theta_+(253^\circ) = -6.182^\circ.$$

Now,

$$z= (1-\zeta_S)/(1-\zeta) = (1+8.56\times 10^{-3})/(1+1.367\times 10^{-1}) = 0.8873.$$

However, from Table 5, $\bar{z}= 1.04774$ and $\delta z = 0.23216$, so

$$\xi = (\bar{z}-z)/\delta z = (1.04774-0.8873)/0.23216 \simeq 0.69.$$

According to Table 17,

$$\Theta_-(0.69) = 0.107, \mbox{\hspace{0.5cm}}\Theta_+(0.69) = 0.583,$$

so

$$\theta = \Theta_-\,\delta\theta_- + \bar{\theta}+\Theta_+\,\... ... -0.107\times 4.005 -21.609-0.583\times 6.182 = -25.642^\circ.$$

Finally,

$$\lambda=\bar{\lambda}_S + \theta= 44.602-25.642=18.960 \simeq 18^\circ 58'.$$

Thus, the ecliptic longitude of Mercury at 00:00 UT on May 5, 2005 CE was 18AR58.

The conjunctions and elongations of Mercury can be investigated using analogous methods to those employed earlier to examine the conjunctions and elongations of Venus. We find that the mean time period between successive superior, or inferior, conjunctions of Mercury is 116 days. On average, the greatest eastern and western elongations of Mercury occur when the epicyclic anomaly takes the values $\mu=111.7^\circ$ and $248.3^\circ$, respectively. Furthermore, the mean value of the greatest eastern or western elongation is $21.7^\circ$. Finally, the mean time period between a greatest eastern elongation and the following inferior conjunction, or between the inferior conjunction and the following greatest western elongation, is 22 JD. The conjunctions and elongations of Mercury during the years 2000-2002 CE are shown in Table 65.

Table 58: Mean motion of Venus. Here, $\Delta t = t-t_0$, $\Delta\bar{\lambda} = \bar{\lambda}-\bar{\lambda}_0$, $\Delta M = M - M_0$, and $\Delta\bar{F}= \bar{F}-\bar{F}_0$. At epoch ( $t_0= 2\,451\,545.0$ JD), $\bar{\lambda}_0 = 181.973^\circ$, $M_0 = 49.237^\circ$, and $\bar{F}_0 =105.253^\circ$.

$\Delta t$(JD)	$\Delta\bar{\lambda}(^\circ)$	$\Delta M(^\circ)$	$\Delta \bar{F}(^\circ)$	$\Delta t$(JD)	$\Delta\bar{\lambda}(^\circ)$	$\Delta M(^\circ)$	$\Delta \bar{F}(^\circ)$
10,000	181.687	181.304	181.381	1,000	162.169	162.130	162.138
20,000	3.374	2.608	2.761	2,000	324.337	324.261	324.276
30,000	185.062	183.912	184.142	3,000	126.506	126.391	126.414
40,000	6.749	5.216	5.523	4,000	288.675	288.522	288.552
50,000	188.436	186.520	186.904	5,000	90.844	90.652	90.690
60,000	10.123	7.824	8.284	6,000	253.012	252.782	252.828
70,000	191.810	189.128	189.665	7,000	55.181	54.913	54.966
80,000	13.498	10.432	11.046	8,000	217.350	217.043	217.105
90,000	195.185	191.736	192.426	9,000	19.518	19.174	19.243
100	160.217	160.213	160.214	10	16.022	16.021	16.021
200	320.434	320.426	320.428	20	32.043	32.043	32.043
300	120.651	120.639	120.641	30	48.065	48.064	48.064
400	280.867	280.852	280.855	40	64.087	64.085	64.086
500	81.084	81.065	81.069	50	80.108	80.107	80.107
600	241.301	241.278	241.283	60	96.130	96.128	96.128
700	41.518	41.491	41.497	70	112.152	112.149	112.150
800	201.735	201.704	201.710	80	128.173	128.170	128.171
900	1.952	1.917	1.924	90	144.195	144.192	144.192
1	1.602	1.602	1.602	0.1	0.160	0.160	0.160
2	3.204	3.204	3.204	0.2	0.320	0.320	0.320
3	4.807	4.806	4.806	0.3	0.481	0.481	0.481
4	6.409	6.409	6.409	0.4	0.641	0.641	0.641
5	8.011	8.011	8.011	0.5	0.801	0.801	0.801
6	9.613	9.613	9.613	0.6	0.961	0.961	0.961
7	11.215	11.215	11.215	0.7	1.122	1.121	1.121
8	12.817	12.817	12.817	0.8	1.282	1.282	1.282
9	14.420	14.419	14.419	0.9	1.442	1.442	1.442

Table 59: Deferential anomalies of Venus.

$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$
0	0.000	0.678	90	0.777	-0.005	180	0.000	-0.678	270	-0.777	-0.005
2	0.027	0.677	92	0.776	-0.028	182	-0.027	-0.677	272	-0.776	0.019
4	0.055	0.676	94	0.774	-0.052	184	-0.054	-0.676	274	-0.775	0.043
6	0.082	0.674	96	0.772	-0.075	186	-0.080	-0.674	276	-0.773	0.066
8	0.109	0.671	98	0.768	-0.099	188	-0.107	-0.671	278	-0.770	0.090
10	0.136	0.667	100	0.764	-0.122	190	-0.134	-0.668	280	-0.766	0.113
12	0.163	0.663	102	0.758	-0.145	192	-0.160	-0.663	282	-0.761	0.137
14	0.189	0.657	104	0.752	-0.168	194	-0.186	-0.658	284	-0.755	0.160
16	0.216	0.651	106	0.745	-0.191	196	-0.212	-0.652	286	-0.748	0.183
18	0.242	0.644	108	0.737	-0.214	198	-0.238	-0.645	288	-0.741	0.205
20	0.268	0.636	110	0.728	-0.236	200	-0.263	-0.637	290	-0.732	0.228
22	0.293	0.628	112	0.718	-0.258	202	-0.289	-0.629	292	-0.722	0.250
24	0.318	0.618	114	0.707	-0.279	204	-0.313	-0.620	294	-0.712	0.272
26	0.343	0.608	116	0.695	-0.301	206	-0.338	-0.610	296	-0.701	0.293
28	0.367	0.597	118	0.683	-0.322	208	-0.362	-0.599	298	-0.688	0.315
30	0.391	0.586	120	0.670	-0.342	210	-0.385	-0.588	300	-0.675	0.335
32	0.414	0.573	122	0.656	-0.362	212	-0.409	-0.576	302	-0.662	0.356
34	0.437	0.560	124	0.641	-0.382	214	-0.431	-0.563	304	-0.647	0.376
36	0.460	0.547	126	0.625	-0.401	216	-0.453	-0.550	306	-0.631	0.395
38	0.481	0.532	128	0.609	-0.420	218	-0.475	-0.536	308	-0.615	0.414
40	0.502	0.517	130	0.592	-0.438	220	-0.496	-0.521	310	-0.598	0.433
42	0.523	0.502	132	0.574	-0.456	222	-0.516	-0.506	312	-0.580	0.451
44	0.543	0.485	134	0.555	-0.473	224	-0.536	-0.490	314	-0.562	0.468
46	0.562	0.468	136	0.536	-0.490	226	-0.555	-0.473	316	-0.543	0.485
48	0.580	0.451	138	0.516	-0.506	228	-0.574	-0.456	318	-0.523	0.502
50	0.598	0.433	140	0.496	-0.521	230	-0.592	-0.438	320	-0.502	0.517
52	0.615	0.414	142	0.475	-0.536	232	-0.609	-0.420	322	-0.481	0.532
54	0.631	0.395	144	0.453	-0.550	234	-0.625	-0.401	324	-0.460	0.547
56	0.647	0.376	146	0.431	-0.563	236	-0.641	-0.382	326	-0.437	0.560
58	0.662	0.356	148	0.409	-0.576	238	-0.656	-0.362	328	-0.414	0.573
60	0.675	0.335	150	0.385	-0.588	240	-0.670	-0.342	330	-0.391	0.586
62	0.688	0.315	152	0.362	-0.599	242	-0.683	-0.322	332	-0.367	0.597
64	0.701	0.293	154	0.338	-0.610	244	-0.695	-0.301	334	-0.343	0.608
66	0.712	0.272	156	0.313	-0.620	246	-0.707	-0.279	336	-0.318	0.618
68	0.722	0.250	158	0.289	-0.629	248	-0.718	-0.258	338	-0.293	0.628
70	0.732	0.228	160	0.263	-0.637	250	-0.728	-0.236	340	-0.268	0.636
72	0.741	0.205	162	0.238	-0.645	252	-0.737	-0.214	342	-0.242	0.644
74	0.748	0.183	164	0.212	-0.652	254	-0.745	-0.191	344	-0.216	0.651
76	0.755	0.160	166	0.186	-0.658	256	-0.752	-0.168	346	-0.189	0.657
78	0.761	0.137	168	0.160	-0.663	258	-0.758	-0.145	348	-0.163	0.663
80	0.766	0.113	170	0.134	-0.668	260	-0.764	-0.122	350	-0.136	0.667
82	0.770	0.090	172	0.107	-0.671	262	-0.768	-0.099	352	-0.109	0.671
84	0.773	0.066	174	0.080	-0.674	264	-0.772	-0.075	354	-0.082	0.674
86	0.775	0.043	176	0.054	-0.676	266	-0.774	-0.052	356	-0.055	0.676
88	0.776	0.019	178	0.027	-0.677	268	-0.776	-0.028	358	-0.027	0.677
90	0.777	-0.005	180	0.000	-0.678	270	-0.777	-0.005	360	-0.000	0.678

Table 60: Epicyclic anomalies of Venus. All quantities are in degrees. Note that $\bar{\theta}(360^\circ - \mu) =-\bar{\theta}(\mu)$, and $\delta\theta_{\pm}(360^\circ-\mu) = -\delta\theta_{\pm}(\mu)$.

$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$
0	0.000	0.000	0.000	45	0.267	18.694	0.274	90	0.629	35.875	0.649	135	1.344	46.305	1.408
1	0.006	0.420	0.006	46	0.273	19.100	0.281	91	0.640	36.217	0.660	136	1.369	46.320	1.434
2	0.011	0.839	0.012	47	0.280	19.505	0.288	92	0.650	36.557	0.671	137	1.393	46.317	1.461
3	0.017	1.259	0.017	48	0.286	19.910	0.294	93	0.661	36.893	0.682	138	1.418	46.294	1.489
4	0.023	1.679	0.023	49	0.293	20.314	0.301	94	0.672	37.227	0.693	139	1.444	46.252	1.517
5	0.028	2.098	0.029	50	0.300	20.717	0.308	95	0.683	37.558	0.705	140	1.470	46.188	1.546
6	0.034	2.518	0.035	51	0.307	21.119	0.315	96	0.694	37.886	0.717	141	1.496	46.102	1.575
7	0.040	2.937	0.041	52	0.313	21.521	0.322	97	0.706	38.210	0.729	142	1.523	45.992	1.605
8	0.045	3.357	0.046	53	0.320	21.921	0.329	98	0.718	38.531	0.741	143	1.550	45.857	1.636
9	0.051	3.776	0.052	54	0.327	22.321	0.336	99	0.729	38.849	0.753	144	1.577	45.695	1.667
10	0.057	4.195	0.058	55	0.334	22.720	0.344	100	0.742	39.164	0.766	145	1.605	45.505	1.698
11	0.062	4.614	0.064	56	0.341	23.119	0.351	101	0.754	39.474	0.779	146	1.632	45.284	1.730
12	0.068	5.033	0.070	57	0.348	23.516	0.358	102	0.766	39.781	0.792	147	1.660	45.032	1.762
13	0.074	5.452	0.076	58	0.355	23.912	0.366	103	0.779	40.084	0.805	148	1.688	44.745	1.794
14	0.079	5.870	0.082	59	0.363	24.308	0.373	104	0.792	40.383	0.818	149	1.715	44.422	1.827
15	0.085	6.289	0.087	60	0.370	24.702	0.381	105	0.805	40.677	0.832	150	1.742	44.060	1.859
16	0.091	6.707	0.093	61	0.377	25.095	0.388	106	0.818	40.968	0.846	151	1.769	43.657	1.892
17	0.097	7.125	0.099	62	0.385	25.487	0.396	107	0.832	41.253	0.860	152	1.795	43.210	1.924
18	0.102	7.543	0.105	63	0.392	25.879	0.404	108	0.846	41.534	0.875	153	1.820	42.716	1.955
19	0.108	7.960	0.111	64	0.400	26.269	0.411	109	0.860	41.810	0.890	154	1.844	42.173	1.986
20	0.114	8.378	0.117	65	0.407	26.658	0.419	110	0.874	42.081	0.905	155	1.867	41.577	2.015
21	0.120	8.795	0.123	66	0.415	27.045	0.427	111	0.889	42.346	0.920	156	1.888	40.923	2.043
22	0.126	9.212	0.129	67	0.423	27.432	0.435	112	0.904	42.606	0.936	157	1.906	40.210	2.069
23	0.131	9.628	0.135	68	0.431	27.817	0.443	113	0.919	42.860	0.952	158	1.921	39.433	2.092
24	0.137	10.045	0.141	69	0.439	28.201	0.452	114	0.934	43.108	0.968	159	1.933	38.587	2.112
25	0.143	10.461	0.147	70	0.447	28.583	0.460	115	0.950	43.349	0.985	160	1.942	37.669	2.128
26	0.149	10.876	0.153	71	0.455	28.964	0.468	116	0.966	43.585	1.002	161	1.945	36.675	2.140
27	0.155	11.292	0.159	72	0.463	29.344	0.477	117	0.983	43.813	1.019	162	1.943	35.599	2.146
28	0.161	11.707	0.165	73	0.471	29.722	0.485	118	1.000	44.034	1.037	163	1.934	34.437	2.145
29	0.167	12.121	0.172	74	0.480	30.099	0.494	119	1.017	44.248	1.055	164	1.918	33.186	2.137
30	0.173	12.536	0.178	75	0.488	30.474	0.503	120	1.034	44.453	1.074	165	1.893	31.840	2.119
31	0.179	12.950	0.184	76	0.497	30.847	0.512	121	1.052	44.651	1.093	166	1.859	30.396	2.091
32	0.185	13.363	0.190	77	0.506	31.219	0.521	122	1.070	44.840	1.112	167	1.814	28.850	2.050
33	0.191	13.776	0.196	78	0.514	31.589	0.530	123	1.089	45.021	1.132	168	1.758	27.200	1.996
34	0.197	14.189	0.203	79	0.523	31.958	0.539	124	1.108	45.191	1.152	169	1.688	25.442	1.926
35	0.203	14.601	0.209	80	0.532	32.324	0.548	125	1.127	45.353	1.173	170	1.604	23.577	1.840
36	0.209	15.013	0.215	81	0.541	32.689	0.558	126	1.147	45.503	1.194	171	1.505	21.604	1.735
37	0.216	15.424	0.222	82	0.551	33.052	0.567	127	1.167	45.644	1.216	172	1.391	19.526	1.612
38	0.222	15.834	0.228	83	0.560	33.412	0.577	128	1.188	45.772	1.238	173	1.261	17.347	1.468
39	0.228	16.245	0.235	84	0.569	33.771	0.587	129	1.209	45.889	1.260	174	1.116	15.071	1.305
40	0.234	16.654	0.241	85	0.579	34.127	0.597	130	1.230	45.994	1.284	175	0.956	12.707	1.123
41	0.241	17.063	0.248	86	0.589	34.482	0.607	131	1.252	46.085	1.307	176	0.783	10.266	0.922
42	0.247	17.472	0.254	87	0.599	34.834	0.617	132	1.275	46.163	1.331	177	0.598	7.760	0.707
43	0.254	17.880	0.261	88	0.609	35.183	0.628	133	1.297	46.226	1.356	178	0.404	5.202	0.478
44	0.260	18.287	0.267	89	0.619	35.530	0.638	134	1.321	46.274	1.382	179	0.204	2.610	0.242
45	0.267	18.694	0.274	90	0.629	35.875	0.649	135	1.344	46.305	1.408	180	0.000	0.000	0.000

Table 61: The conjunctions and greatest elongations of Venus during the years 2000-2015 CE.

Event	Date	$\lambda$	Elongation
Superior Conjunction	11/06/2000	20GE46
Greatest Elongation	17/01/2001	14PI23	$47.1^\circ$ E
Inferior Conjunction	30/03/2001	09AR36
Greatest Elongation	08/06/2001	01TA39	$45.8^\circ$ W
Superior Conjunction	14/01/2002	23CP59
Greatest Elongation	22/08/2002	15LI08	$46.0^\circ$ E
Inferior Conjunction	31/10/2002	07SC58
Greatest Elongation	11/01/2003	03SG31	$47.0^\circ$ W
Superior Conjunction	18/08/2003	25LE20
Greatest Elongation	29/03/2004	25TA04	$46.0^\circ$ E
Inferior Conjunction	08/06/2004	17GE52
Greatest Elongation	17/08/2004	09CN29	$45.8^\circ$ W
Superior Conjunction	31/03/2005	10AR33
Greatest Elongation	03/11/2005	28SG27	$47.1^\circ$ E
Inferior Conjunction	13/01/2006	23CP36
Greatest Elongation	25/03/2006	18AQ07	$46.5^\circ$ W
Superior Conjunction	27/10/2006	04SC13
Greatest Elongation	09/06/2007	03LE20	$45.4^\circ$ E
Inferior Conjunction	18/08/2007	24LE45
Greatest Elongation	28/10/2007	18VI19	$46.5^\circ$ W
Superior Conjunction	09/06/2008	18GE41
Greatest Elongation	14/01/2009	12PI03	$47.1^\circ$ E
Inferior Conjunction	27/03/2009	07AR19
Greatest Elongation	05/06/2009	29AR25	$45.8^\circ$ W
Superior Conjunction	11/01/2010	21CP24
Greatest Elongation	19/08/2010	12LI49	$46.0^\circ$ E
Inferior Conjunction	29/10/2010	05SC34
Greatest Elongation	08/01/2011	01SG06	$47.0^\circ$ W
Superior Conjunction	16/08/2011	23LE13
Greatest Elongation	27/03/2012	22TA50	$46.0^\circ$ E
Inferior Conjunction	06/06/2012	15GE43
Greatest Elongation	15/08/2012	07CN18	$45.8^\circ$ W
Superior Conjunction	28/03/2013	08AR12
Greatest Elongation	01/11/2013	26SG02	$47.1^\circ$ E
Inferior Conjunction	11/01/2014	21CP08
Greatest Elongation	23/03/2014	15AQ44	$46.5^\circ$ W
Superior Conjunction	25/10/2014	01SC51
Greatest Elongation	06/06/2015	01LE09	$45.4^\circ$ E
Inferior Conjunction	15/08/2015	22LE33
Greatest Elongation	26/10/2015	16VI02	$46.4^\circ$ W

Table 62: Mean motion of Mercury. Here, $\Delta t = t-t_0$, $\Delta\bar{\lambda} = \bar{\lambda}-\bar{\lambda}_0$, $\Delta M = M - M_0$, and $\Delta\bar{F}= \bar{F}-\bar{F}_0$. At epoch ( $t_0= 2\,451\,545.0$ JD), $\bar{\lambda}_0 = 252.087^\circ$, $M_0 = 174.693^\circ$, and $\bar{F}_0 = 204.436^\circ$.

$\Delta t$(JD)	$\Delta\bar{\lambda}(^\circ)$	$\Delta M(^\circ)$	$\Delta \bar{F}(^\circ)$	$\Delta t$(JD)	$\Delta\bar{\lambda}(^\circ)$	$\Delta M(^\circ)$	$\Delta \bar{F}(^\circ)$
10,000	243.770	243.344	243.422	1,000	132.377	132.334	132.342
20,000	127.541	126.688	126.844	2,000	264.754	264.669	264.684
30,000	11.311	10.032	10.266	3,000	37.131	37.003	37.027
40,000	255.081	253.376	253.688	4,000	169.508	169.338	169.369
50,000	138.852	136.720	137.110	5,000	301.885	301.672	301.711
60,000	22.622	20.063	20.533	6,000	74.262	74.006	74.053
70,000	266.392	263.407	263.955	7,000	206.639	206.341	206.395
80,000	150.162	146.751	147.377	8,000	339.016	338.675	338.738
90,000	33.933	30.095	30.799	9,000	111.393	111.010	111.080
100	49.238	49.233	49.234	10	40.924	40.923	40.923
200	98.475	98.467	98.468	20	81.848	81.847	81.847
300	147.713	147.700	147.703	30	122.771	122.770	122.770
400	196.951	196.934	196.937	40	163.695	163.693	163.694
500	246.189	246.167	246.171	50	204.619	204.617	204.617
600	295.426	295.401	295.405	60	245.543	245.540	245.541
700	344.664	344.634	344.640	70	286.466	286.463	286.464
800	33.902	33.868	33.874	80	327.390	327.387	327.387
900	83.139	83.101	83.108	90	8.314	8.310	8.311
1	4.092	4.092	4.092	0.1	0.409	0.409	0.409
2	8.185	8.185	8.185	0.2	0.818	0.818	0.818
3	12.277	12.277	12.277	0.3	1.228	1.228	1.228
4	16.370	16.369	16.369	0.4	1.637	1.637	1.637
5	20.462	20.462	20.462	0.5	2.046	2.046	2.046
6	24.554	24.554	24.554	0.6	2.455	2.455	2.455
7	28.647	28.646	28.646	0.7	2.865	2.865	2.865
8	32.739	32.739	32.739	0.8	3.274	3.274	3.274
9	36.831	36.831	36.831	0.9	3.683	3.683	3.683

Table 63: Deferential anomalies of Mercury.

$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$	$M(^\circ)$	$q(^\circ)$	$100\,\zeta$
0	0.000	20.564	90	22.900	-4.229	180	0.000	-20.564	270	-22.900	-4.229
2	1.086	20.544	92	22.677	-4.896	182	-0.663	-20.555	272	-23.100	-3.551
4	2.169	20.487	94	22.433	-5.552	184	-1.326	-20.528	274	-23.276	-2.864
6	3.247	20.391	96	22.168	-6.197	186	-1.987	-20.483	276	-23.428	-2.168
8	4.316	20.257	98	21.884	-6.831	188	-2.647	-20.420	278	-23.553	-1.463
10	5.376	20.085	100	21.580	-7.452	190	-3.304	-20.340	280	-23.652	-0.750
12	6.422	19.876	102	21.259	-8.062	192	-3.959	-20.242	282	-23.723	-0.030
14	7.454	19.631	104	20.920	-8.659	194	-4.610	-20.126	284	-23.764	0.697
16	8.467	19.350	106	20.566	-9.243	196	-5.257	-19.993	286	-23.775	1.429
18	9.460	19.035	108	20.195	-9.815	198	-5.900	-19.842	288	-23.755	2.165
20	10.431	18.685	110	19.809	-10.373	200	-6.538	-19.675	290	-23.703	2.905
22	11.377	18.303	112	19.409	-10.918	202	-7.170	-19.490	292	-23.617	3.648
24	12.298	17.889	114	18.996	-11.450	204	-7.796	-19.288	294	-23.497	4.392
26	13.190	17.445	116	18.569	-11.969	206	-8.417	-19.070	296	-23.342	5.137
28	14.052	16.971	118	18.129	-12.473	208	-9.030	-18.835	298	-23.150	5.880
30	14.882	16.469	120	17.677	-12.964	210	-9.637	-18.583	300	-22.922	6.621
32	15.680	15.941	122	17.212	-13.441	212	-10.236	-18.316	302	-22.656	7.359
34	16.443	15.388	124	16.737	-13.904	214	-10.827	-18.032	304	-22.353	8.091
36	17.171	14.811	126	16.250	-14.353	216	-11.410	-17.733	306	-22.010	8.818
38	17.862	14.212	128	15.752	-14.787	218	-11.985	-17.418	308	-21.629	9.536
40	18.517	13.593	130	15.243	-15.207	220	-12.552	-17.087	310	-21.208	10.245
42	19.133	12.954	132	14.724	-15.613	222	-13.109	-16.741	312	-20.748	10.942
44	19.710	12.299	134	14.196	-16.004	224	-13.657	-16.380	314	-20.249	11.628
46	20.249	11.628	136	13.657	-16.380	226	-14.196	-16.004	316	-19.710	12.299
48	20.748	10.942	138	13.109	-16.741	228	-14.724	-15.613	318	-19.133	12.954
50	21.208	10.245	140	12.552	-17.087	230	-15.243	-15.207	320	-18.517	13.593
52	21.629	9.536	142	11.985	-17.418	232	-15.752	-14.787	322	-17.862	14.212
54	22.010	8.818	144	11.410	-17.733	234	-16.250	-14.353	324	-17.171	14.811
56	22.353	8.091	146	10.827	-18.032	236	-16.737	-13.904	326	-16.443	15.388
58	22.656	7.359	148	10.236	-18.316	238	-17.212	-13.441	328	-15.680	15.941
60	22.922	6.621	150	9.637	-18.583	240	-17.677	-12.964	330	-14.882	16.469
62	23.150	5.880	152	9.030	-18.835	242	-18.129	-12.473	332	-14.052	16.971
64	23.342	5.137	154	8.417	-19.070	244	-18.569	-11.969	334	-13.190	17.445
66	23.497	4.392	156	7.796	-19.288	246	-18.996	-11.450	336	-12.298	17.889
68	23.617	3.648	158	7.170	-19.490	248	-19.409	-10.918	338	-11.377	18.303
70	23.703	2.905	160	6.538	-19.675	250	-19.809	-10.373	340	-10.431	18.685
72	23.755	2.165	162	5.900	-19.842	252	-20.195	-9.815	342	-9.460	19.035
74	23.775	1.429	164	5.257	-19.993	254	-20.566	-9.243	344	-8.467	19.350
76	23.764	0.697	166	4.610	-20.126	256	-20.920	-8.659	346	-7.454	19.631
78	23.723	-0.030	168	3.959	-20.242	258	-21.259	-8.062	348	-6.422	19.876
80	23.652	-0.750	170	3.304	-20.340	260	-21.580	-7.452	350	-5.376	20.085
82	23.553	-1.463	172	2.647	-20.420	262	-21.884	-6.831	352	-4.316	20.257
84	23.428	-2.168	174	1.987	-20.483	264	-22.168	-6.197	354	-3.247	20.391
86	23.276	-2.864	176	1.326	-20.528	266	-22.433	-5.552	356	-2.169	20.487
88	23.100	-3.551	178	0.663	-20.555	268	-22.677	-4.896	358	-1.086	20.544
90	22.900	-4.229	180	0.000	-20.564	270	-22.900	-4.229	360	-0.000	20.564

Table 64: Epicyclic anomalies of Mercury. All quantities are in degrees. Note that $\bar{\theta}(360^\circ - \mu) =-\bar{\theta}(\mu)$, and $\delta\theta_{\pm}(360^\circ-\mu) = -\delta\theta_{\pm}(\mu)$.

$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$	$\mu$	$\delta\theta_-$	$\bar{\theta}~~~~$	$\delta\theta_+$
0	0.000	0.000	0.000	45	1.711	11.702	2.403	90	3.450	20.277	5.113	135	4.257	19.475	7.325
1	0.038	0.270	0.052	46	1.749	11.941	2.459	91	3.486	20.395	5.177	136	4.237	19.267	7.327
2	0.075	0.540	0.104	47	1.788	12.179	2.515	92	3.522	20.509	5.241	137	4.214	19.048	7.324
3	0.113	0.809	0.156	48	1.827	12.415	2.572	93	3.557	20.618	5.305	138	4.188	18.818	7.317
4	0.150	1.079	0.208	49	1.866	12.650	2.628	94	3.592	20.722	5.368	139	4.159	18.578	7.304
5	0.188	1.348	0.260	50	1.905	12.882	2.685	95	3.627	20.822	5.432	140	4.127	18.326	7.286
6	0.225	1.618	0.313	51	1.944	13.114	2.742	96	3.662	20.917	5.496	141	4.092	18.064	7.262
7	0.263	1.887	0.365	52	1.983	13.343	2.799	97	3.696	21.007	5.559	142	4.053	17.791	7.233
8	0.301	2.156	0.417	53	2.022	13.571	2.857	98	3.729	21.091	5.623	143	4.011	17.506	7.197
9	0.338	2.425	0.469	54	2.061	13.797	2.914	99	3.762	21.171	5.686	144	3.966	17.210	7.155
10	0.376	2.693	0.521	55	2.100	14.021	2.972	100	3.795	21.246	5.749	145	3.917	16.903	7.106
11	0.414	2.961	0.574	56	2.139	14.244	3.030	101	3.827	21.315	5.812	146	3.865	16.585	7.050
12	0.451	3.229	0.626	57	2.178	14.464	3.088	102	3.858	21.378	5.874	147	3.809	16.255	6.986
13	0.489	3.497	0.678	58	2.217	14.683	3.146	103	3.889	21.436	5.937	148	3.749	15.914	6.915
14	0.527	3.764	0.731	59	2.257	14.899	3.205	104	3.919	21.488	5.999	149	3.686	15.561	6.836
15	0.564	4.031	0.783	60	2.296	15.113	3.263	105	3.949	21.534	6.060	150	3.619	15.197	6.749
16	0.602	4.298	0.836	61	2.335	15.326	3.322	106	3.977	21.575	6.121	151	3.548	14.822	6.654
17	0.640	4.564	0.889	62	2.374	15.536	3.381	107	4.005	21.609	6.182	152	3.473	14.436	6.549
18	0.678	4.829	0.941	63	2.413	15.743	3.441	108	4.032	21.636	6.242	153	3.394	14.039	6.436
19	0.716	5.094	0.994	64	2.453	15.949	3.500	109	4.059	21.658	6.301	154	3.311	13.630	6.314
20	0.753	5.359	1.047	65	2.492	16.152	3.560	110	4.084	21.673	6.360	155	3.224	13.211	6.182
21	0.791	5.622	1.100	66	2.531	16.353	3.620	111	4.109	21.681	6.418	156	3.133	12.780	6.041
22	0.829	5.886	1.153	67	2.570	16.551	3.680	112	4.132	21.682	6.475	157	3.039	12.339	5.890
23	0.867	6.148	1.206	68	2.609	16.747	3.740	113	4.155	21.676	6.532	158	2.940	11.888	5.729
24	0.905	6.410	1.259	69	2.649	16.940	3.801	114	4.176	21.663	6.587	159	2.838	11.426	5.558
25	0.943	6.672	1.312	70	2.688	17.131	3.862	115	4.197	21.643	6.641	160	2.732	10.955	5.377
26	0.981	6.932	1.366	71	2.727	17.319	3.923	116	4.216	21.616	6.695	161	2.622	10.474	5.186
27	1.019	7.192	1.419	72	2.766	17.504	3.984	117	4.233	21.580	6.747	162	2.508	9.983	4.985
28	1.057	7.451	1.473	73	2.805	17.686	4.045	118	4.250	21.538	6.797	163	2.391	9.483	4.774
29	1.095	7.709	1.526	74	2.844	17.865	4.107	119	4.265	21.487	6.846	164	2.271	8.974	4.554
30	1.133	7.967	1.580	75	2.882	18.042	4.169	120	4.278	21.428	6.894	165	2.147	8.457	4.324
31	1.172	8.223	1.634	76	2.921	18.215	4.231	121	4.291	21.361	6.940	166	2.019	7.932	4.084
32	1.210	8.479	1.688	77	2.960	18.385	4.293	122	4.301	21.286	6.984	167	1.889	7.399	3.835
33	1.248	8.734	1.742	78	2.999	18.552	4.355	123	4.310	21.202	7.026	168	1.756	6.859	3.578
34	1.286	8.987	1.796	79	3.037	18.716	4.417	124	4.317	21.109	7.067	169	1.620	6.312	3.312
35	1.325	9.240	1.851	80	3.075	18.876	4.480	125	4.322	21.008	7.105	170	1.481	5.759	3.038
36	1.363	9.491	1.905	81	3.114	19.033	4.543	126	4.326	20.898	7.140	171	1.340	5.200	2.757
37	1.402	9.742	1.960	82	3.152	19.186	4.606	127	4.327	20.778	7.173	172	1.197	4.636	2.469
38	1.440	9.991	2.015	83	3.190	19.336	4.669	128	4.326	20.649	7.204	173	1.052	4.067	2.174
39	1.479	10.240	2.070	84	3.227	19.482	4.732	129	4.323	20.511	7.231	174	0.905	3.494	1.875
40	1.517	10.487	2.125	85	3.265	19.625	4.795	130	4.318	20.363	7.256	175	0.756	2.917	1.570
41	1.556	10.732	2.180	86	3.302	19.763	4.859	131	4.311	20.206	7.277	176	0.607	2.337	1.261
42	1.594	10.977	2.236	87	3.340	19.898	4.922	132	4.301	20.038	7.295	177	0.456	1.755	0.949
43	1.633	11.220	2.291	88	3.377	20.029	4.986	133	4.289	19.861	7.309	178	0.304	1.171	0.634
44	1.672	11.462	2.347	89	3.413	20.155	5.049	134	4.274	19.673	7.319	179	0.152	0.586	0.317
45	1.711	11.702	2.403	90	3.450	20.277	5.113	135	4.257	19.475	7.325	180	0.000	0.000	0.000

Table 65: The conjunctions and greatest elongations of Mercury during the years 2000-2002 CE.

Event	Date	$\lambda$	Elongation
Superior Conjunction	15/01/2000	25CP08
Greatest Elongation	15/02/2000	13PI44	$18.1^\circ$ E
Inferior Conjunction	01/03/2000	11PI23
Greatest Elongation	28/03/2000	10PI35	$27.9^\circ$ W
Superior Conjunction	09/05/2000	18TA59
Greatest Elongation	09/06/2000	13CN27	$24.2^\circ$ E
Inferior Conjunction	06/07/2000	14CN39
Greatest Elongation	27/07/2000	15CN03	$19.7^\circ$ W
Superior Conjunction	22/08/2000	29LE16
Greatest Elongation	06/10/2000	09SC17	$25.6^\circ$ E
Inferior Conjunction	30/10/2000	06SC58
Greatest Elongation	15/11/2000	04SC02	$19.3^\circ$ W
Superior Conjunction	25/12/2000	04CP18
Greatest Elongation	28/01/2001	27AQ07	$18.4^\circ$ E
Inferior Conjunction	13/02/2001	24AQ23
Greatest Elongation	11/03/2001	23AQ05	$27.5^\circ$ W
Superior Conjunction	23/04/2001	03TA22
Greatest Elongation	22/05/2001	24GE13	$22.6^\circ$ E
Inferior Conjunction	16/06/2001	25GE26
Greatest Elongation	09/07/2001	26GE18	$21.1^\circ$ W
Superior Conjunction	05/08/2001	13LE32
Greatest Elongation	19/09/2001	22LI50	$26.6^\circ$ E
Inferior Conjunction	14/10/2001	20LI51
Greatest Elongation	29/10/2001	17LI50	$18.5^\circ$ W
Superior Conjunction	04/12/2001	12SG45
Greatest Elongation	12/01/2002	10AQ33	$18.9^\circ$ E
Inferior Conjunction	27/01/2002	07AQ42
Greatest Elongation	21/02/2002	05AQ55	$26.6^\circ$ W
Superior Conjunction	07/04/2002	17AR27
Greatest Elongation	04/05/2002	04GE54	$21.0^\circ$ E
Inferior Conjunction	27/05/2002	05GE48
Greatest Elongation	21/06/2002	07GE04	$22.8^\circ$ W
Superior Conjunction	21/07/2002	28CN06
Greatest Elongation	01/09/2002	06LI10	$27.3^\circ$ E
Inferior Conjunction	27/09/2002	04LI35
Greatest Elongation	13/10/2002	01LI44	$18.0^\circ$ W
Superior Conjunction	14/11/2002	21SC39
Greatest Elongation	26/12/2002	24CP01	$19.8^\circ$ E