Although the Moon shows always the same side toward the Earth, because its periodic oscillations
during the rivolution, which are called librations, we can see about 59% of its surface.
3 laws of Cassini  (1721)

1) The Moon rotates in the direct sense with a costant angular velocity and with the sideral period
of rotation equal to the mean sidereal period of revolution.
2) The inclination of the mean plane of the lunar equator respect to the plane of the ecliptic is
constant. I=1°32'32.7''
3) The rotation of the axis of the Moon, the axis of the ecliptic and the axis of the lunar orbit
are in the same plane.

Libration in latitude: similar to the seasons on the Earth, on the Moon too, during its revolution,
we can see the north or the south pole alternatively, with an inclination of 6°41'.

Libration in longitude: because the lunar rotation is constant, but the velocity of the Moon around
the Earth is variable, we can see a variation of 8° on the surface.

Physical libration: a little irregularity in the rotation of the Moon is the cause of a variation of
2-3'.

Data		Times	Libraz.
04/01/2009	2.29	-7.66	°
16/01/2009	11.02	7.41	°
31/01/2009	19.46	-6.59	°
13/02/2009	19.10	6.47	°
27/02/2009	10.46	-5.49	°
13/03/2009	18.27	5.34	°
26/03/2009	0.21	-5.43	°
10/04/2009	1.14	4.64	°
22/04/2009	9.47	-6.19	°
06/05/2009	8.33	4.98	°
20/05/2009	6.26	-7.08	°
02/06/2009	3.28	6.20	°
17/06/2009	8.29	-7.63	°
29/06/2009	23.19	7.24	°
15/07/2009	11.53	-7.53	°
28/07/2009	3.08	7.63	°
12/08/2009	10.38	-6.71	°
25/08/2009	7.33	7.32	°
08/09/2009	16.33	-5.46	°
22/09/2009	7.58	6.50	°
04/10/2009	23.38	-4.71	°
19/10/2009	23.50	5.59	°
15/11/2009	22.37	5.22	°
28/11/2009	16.34	-6.19	°
12/12/2009	5.11	5.98	°
26/12/2009	21.03	-7.25	°
08/01/2010	13.48	7.20	°
24/01/2010	6.07	-7.73	°
05/02/2010	15.48	7.82	°
21/02/2010	13.22	-7.37	°
05/03/2010	21.36	7.55	°
21/03/2010	8.48	-6.26	°
03/04/2010	0.30	6.65	°
16/04/2010	19.24	-5.14	°
30/04/2010	19.00	5.62	°
13/05/2010	5.47	-5.04	°
27/05/2010	22.58	5.06	°
09/06/2010	16.16	-5.72	°
23/06/2010	10.12	5.51	°
07/07/2010	15.19	-6.59	°
20/07/2010	8.12	6.72	°
04/08/2010	21.10	-7.23	°
17/08/2010	1.37	7.74	°
02/09/2010	4.20	-7.28	°
14/09/2010	3.27	8.03	°
30/09/2010	7.57	-6.61	°
12/10/2010	7.09	7.52	°
27/10/2010	19.26	-5.38	°
09/11/2010	7.18	6.44	°
22/11/2010	21.04	-4.58	°
06/12/2010	21.11	5.35	°
19/12/2010	16.22	-5.14	°
02/01/2011	11.27	5.06	°
28/01/2011	20.53	6.06	°
13/02/2011	16.12	-7.54	°
25/02/2011	13.01	7.21	°
13/03/2011	23.33	-8.02	°
11/04/2011	3.04	-7.63	°
23/04/2011	0.31	7.24	°
08/05/2011	18.08	-6.51	°
17/06/2011	23.24	5.37	°
30/06/2011	23.00	-5.18	°
15/07/2011	1.24	4.87	°
28/07/2011	6.22	-5.86	°
10/08/2011	6.12	5.38	°
25/08/2011	2.42	-6.82	°
22/09/2011	5.57	-7.54	°
04/10/2011	4.35	7.57	°
20/10/2011	9.49	-7.61	°
17/11/2011	9.29	-6.85	°
29/11/2011	20.30	7.08	°
14/12/2011	13.06	-5.62	°
28/12/2011	0.46	5.94	°
09/01/2012	20.06	-5.09	°
24/01/2012	16.07	4.89	°
05/02/2012	21.52	-5.77	°
20/02/2012	5.20	4.69	°
04/03/2012	16.39	-6.90	°
17/03/2012	11.46	5.74	°
01/04/2012	18.29	-7.79	°
14/04/2012	5.12	6.91	°
12/05/2012	10.27	7.43	°
27/05/2012	23.07	-7.39	°
09/06/2012	17.08	7.25	°
24/06/2012	11.17	-6.20	°
07/07/2012	19.39	6.57	°
21/07/2012	0.44	-5.14	°
04/08/2012	14.56	5.73	°
16/08/2012	16.54	-5.03	°
31/08/2012	20.25	5.21	°
13/09/2012	3.19	-5.75	°
24/10/2012	1.48	6.76	°
08/11/2012	8.00	-7.40	°
20/11/2012	21.53	7.73	°
06/12/2012	16.02	-7.39	°
19/12/2012	2.48	7.88	°
03/01/2013	18.09	-6.56	°
16/01/2013	8.17	7.18	°
30/01/2013	17.08	-5.32	°
13/02/2013	7.59	6.04	°
25/02/2013	19.27	-4.94	°
12/03/2013	19.05	5.10	°
25/03/2013	0.58	-5.60	°
05/05/2013	0.21	6.17	°
20/05/2013	3.03	-7.36	°
01/06/2013	14.05	7.34	°
17/06/2013	10.19	-7.57	°
29/06/2013	14.43	7.88	°
15/07/2013	15.08	-7.05	°
27/07/2013	17.37	7.68	°
12/08/2013	9.26	-5.90	°
24/08/2013	18.12	6.89	°
07/09/2013	22.35	-4.74	°
21/09/2013	11.48	5.89	°
04/10/2013	6.52	-4.66	°
18/10/2013	13.47	5.28	°
31/10/2013	17.34	-5.58	°
13/11/2013	20.51	5.76	°
28/11/2013	19.19	-6.78	°
10/12/2013	22.54	6.99	°
27/12/2013	3.29	-7.64	°
07/01/2014	22.18	7.77	°
05/02/2014	4.27	7.65	°
21/02/2014	10.36	-6.85	°
05/03/2014	11.13	6.76	°
20/03/2014	11.13	-5.62	°
02/04/2014	10.27	5.59	°
15/04/2014	17.17	-5.17	°
29/04/2014	18.19	4.78	°
12/05/2014	19.35	-5.76	°
26/05/2014	2.32	4.98	°
09/06/2014	13.52	-6.73	°
21/06/2014	19.30	6.17	°
19/07/2014	12.41	7.29	°
04/08/2014	18.43	-7.76	°
16/08/2014	17.33	7.75	°
01/09/2014	19.48	-7.25	°
14/09/2014	0.38	7.45	°
29/09/2014	10.09	-6.08	°
12/10/2014	5.47	6.55	°
21/11/2014	14.05	-5.15	°
01/01/2015	2.35	5.34	°
16/01/2015	2.18	-7.37	°
28/01/2015	8.41	6.59	°
13/02/2015	7.08	-8.01	°
13/03/2015	10.52	-7.79	°
25/03/2015	22.14	7.25	°
10/04/2015	4.10	-6.78	°
23/04/2015	4.52	6.56	°
06/05/2015	23.23	-5.60	°
21/05/2015	3.39	5.64	°
02/06/2015	11.27	-5.25	°
17/06/2015	13.35	4.99	°
29/06/2015	17.06	-5.76	°
27/07/2015	11.51	-6.62	°
09/08/2015	17.00	6.24	°
24/08/2015	13.44	-7.32	°
06/09/2015	7.10	7.41	°
21/09/2015	19.35	-7.49	°
04/10/2015	9.28	7.96	°
19/10/2015	23.21	-6.91	°
01/11/2015	14.54	7.68	°
16/11/2015	13.01	-5.71	°
29/11/2015	17.49	6.74	°
12/12/2015	18.04	-4.79	°
27/12/2015	12.25	5.59	°
08/01/2016	12.23	-5.12	°
18/02/2016	20.16	5.60	°
04/03/2016	8.48	-7.20	°
17/03/2016	1.25	6.83	°
01/04/2016	16.29	-7.69	°
14/04/2016	0.38	7.59	°
29/04/2016	22.49	-7.41	°
27/05/2016	21.04	-6.40	°
09/06/2016	6.00	6.91	°
23/06/2016	17.20	-5.16	°
07/07/2016	1.33	6.01	°
19/07/2016	22.12	-4.71	°
03/08/2016	9.10	5.36	°
16/08/2016	2.26	-5.26	°
29/08/2016	22.31	5.55	°
12/09/2016	23.27	-6.26	°
25/09/2016	15.11	6.67	°
11/10/2016	5.34	-7.18	°
23/10/2016	6.52	7.78	°
08/11/2016	14.34	-7.55	°
20/11/2016	9.56	8.11	°
18/12/2016	15.51	7.54	°
03/01/2017	11.20	-5.92	°
15/01/2017	19.32	6.34	°
29/01/2017	17.39	-4.98	°
12/02/2017	11.56	5.12	°
25/02/2017	9.05	-5.34	°
11/03/2017	4.52	4.70	°
25/03/2017	0.10	-6.41	°
22/04/2017	1.45	-7.41	°
03/05/2017	23.25	6.81	°
01/06/2017	0.46	7.46	°
17/06/2017	7.47	-7.58	°
29/06/2017	7.20	7.37	°
15/07/2017	1.47	-6.56	°
27/07/2017	11.44	6.70	°
11/08/2017	0.13	-5.34	°
24/08/2017	10.15	5.76	°
06/09/2017	9.55	-4.92	°
20/09/2017	18.58	5.05	°
03/10/2017	13.55	-5.58	°
17/10/2017	0.57	5.21	°
31/10/2017	9.25	-6.72	°
12/11/2017	16.00	6.40	°
28/11/2017	13.00	-7.68	°
26/12/2017	19.10	-7.93	°
07/01/2018	23.37	7.63	°
23/01/2018	19.28	-7.27	°
05/02/2018	9.38	7.02	°
20/02/2018	2.02	-6.04	°
05/03/2018	14.18	5.94	°
18/03/2018	10.32	-5.33	°
02/04/2018	7.16	4.94	°
14/04/2018	9.31	-5.71	°
29/04/2018	3.52	4.65	°
12/05/2018	0.53	-6.58	°
25/05/2018	9.39	5.49	°
09/06/2018	0.35	-7.36	°
21/06/2018	17.55	6.74	°
19/07/2018	18.09	7.53	°
04/08/2018	6.17	-7.23	°
16/08/2018	22.57	7.60	°
27/09/2018	16.43	-4.98	°
11/10/2018	23.41	6.08	°
24/10/2018	3.21	-4.77	°
08/11/2018	9.03	5.30	°
20/11/2018	11.59	-5.57	°
04/12/2018	21.05	5.40	°
18/12/2018	11.51	-6.73	°
31/12/2018	12.38	6.54	°
15/01/2019	19.03	-7.58	°
28/01/2019	7.30	7.56	°
13/02/2019	4.11	-7.70	°
25/02/2019	12.21	7.78	°
09/04/2019	15.05	-5.70	°
22/04/2019	17.01	6.17	°
05/05/2019	17.41	-4.96	°
20/05/2019	5.48	5.29	°
01/06/2019	15.37	-5.26	°
16/06/2019	1.20	5.14	°
29/06/2019	8.38	-6.09	°
12/07/2019	13.09	6.03	°
08/08/2019	20.37	7.26	°
24/08/2019	18.12	-7.34	°
05/09/2019	19.20	7.98	°
22/09/2019	1.03	-7.09	°
03/10/2019	22.46	7.89	°
19/10/2019	23.39	-6.12	°
01/11/2019	1.56	7.06	°
15/11/2019	19.30	-4.90	°
26/12/2019	3.39	5.02	°
08/01/2020	6.28	-5.71	°
21/01/2020	8.28	5.36	°
05/02/2020	6.57	-7.00	°
17/02/2020	8.52	6.61	°
04/03/2020	13.21	-7.88	°
16/03/2020	8.09	7.47	°
01/04/2020	19.32	-7.97	°
13/04/2020	14.33	7.52	°
29/04/2020	18.13	-7.20	°
11/05/2020	20.44	6.87	°
27/05/2020	0.37	-5.94	°
08/06/2020	21.29	5.89	°
22/06/2020	10.23	-5.14	°
06/07/2020	10.35	5.07	°
19/07/2020	7.08	-5.40	°
02/08/2020	1.43	4.95	°
15/08/2020	21.09	-6.28	°
24/09/2020	20.42	7.12	°
11/10/2020	1.15	-7.69	°
23/10/2020	1.21	7.73	°
08/11/2020	4.28	-7.40	°
20/11/2020	10.19	7.50	°
05/12/2020	21.41	-6.33	°
18/12/2020	17.58	6.56	°
01/01/2021	11.55	-5.25	°
15/01/2021	17.21	5.38	°
28/01/2021	0.49	-5.33	°
11/02/2021	22.54	4.62	°
24/02/2021	11.56	-6.30	°
10/03/2021	0.53	5.03	°
24/03/2021	10.35	-7.37	°
06/04/2021	0.31	6.30	°
21/04/2021	13.59	-7.97	°
04/05/2021	1.10	7.23	°
01/06/2021	7.20	7.45	°
13/07/2021	16.01	-5.63	°
27/07/2021	12.21	6.21	°
09/08/2021	1.38	-4.93	°
19/09/2021	23.59	5.24	°
02/10/2021	19.25	-6.18	°
16/10/2021	7.43	6.06	°
30/10/2021	22.14	-7.11	°
12/11/2021	16.04	7.27	°
28/11/2021	6.04	-7.53	°
10/12/2021	17.27	7.89	°
26/12/2021	12.47	-7.14	°
07/01/2022	23.28	7.63	°
23/01/2022	6.41	-6.02	°
05/02/2022	3.11	6.66	°
18/02/2022	12.32	-5.01	°
04/03/2022	21.59	5.52	°
17/03/2022	2.49	-5.16	°
27/04/2022	9.55	5.49	°
11/05/2022	17.50	-6.97	°
24/05/2022	11.25	6.74	°
09/06/2022	0.22	-7.53	°
21/06/2022	7.12	7.68	°
07/07/2022	6.57	-7.42	°
04/08/2022	9.20	-6.60	°
16/08/2022	11.56	7.39	°
31/08/2022	16.46	-5.32	°
10/10/2022	22.29	5.51	°
23/10/2022	16.23	-5.01	°
06/11/2022	13.56	5.30	°
20/11/2022	11.19	-6.15	°
03/12/2022	0.22	6.27	°
18/12/2022	16.58	-7.29	°
30/12/2022	14.53	7.41	°
16/01/2023	1.49	-7.81	°
27/01/2023	18.50	7.79	°
13/02/2023	6.48	-7.44	°
25/02/2023	2.13	7.28	°
08/04/2023	9.27	-5.28	°
21/04/2023	23.40	5.14	°
04/05/2023	22.48	-5.35	°
18/05/2023	21.15	4.72	°
01/06/2023	9.33	-6.17	°
29/06/2023	7.39	-7.12	°
11/07/2023	8.31	6.73	°
27/07/2023	10.04	-7.71	°
08/08/2023	8.12	7.60	°
24/08/2023	13.26	-7.62	°
05/09/2023	14.31	7.72	°
21/09/2023	11.20	-6.79	°
03/10/2023	21.24	7.11	°
18/10/2023	15.35	-5.52	°
01/11/2023	0.07	6.04	°
13/11/2023	23.25	-4.93	°
11/12/2023	0.23	-5.58	°
25/12/2023	1.59	4.83	°
07/01/2024	19.09	-6.78	°
20/01/2024	7.52	5.89	°
04/02/2024	22.19	-7.77	°
17/02/2024	4.00	6.99	°
04/03/2024	2.52	-8.02	°
16/03/2024	11.39	7.37	°
01/04/2024	3.12	-7.40	°
13/04/2024	19.59	7.00	°
28/04/2024	12.12	-6.20	°
11/05/2024	23.08	6.17	°
20/06/2024	18.39	-5.37	°
05/07/2024	19.10	4.97	°
18/07/2024	7.02	-6.09	°
01/08/2024	3.48	5.58	°
15/08/2024	5.27	-6.95	°
28/08/2024	3.57	6.83	°
12/09/2024	9.48	-7.46	°
25/09/2024	1.05	7.78	°
10/10/2024	15.54	-7.33	°
23/10/2024	5.35	7.95	°
07/11/2024	16.21	-6.42	°
20/11/2024	10.44	7.31	°
04/12/2024	15.06	-5.17	°
18/12/2024	10.39	6.19	°
30/12/2024	18.51	-4.81	°
10/02/2025	12.52	5.09	°
24/02/2025	0.01	-6.67	°
09/03/2025	2.06	6.16	°
24/03/2025	5.52	-7.50	°
05/04/2025	17.35	7.26	°
21/04/2025	13.42	-7.65	°
03/05/2025	19.49	7.68	°
19/05/2025	17.26	-7.01	°
31/05/2025	23.02	7.35	°
16/06/2025	7.03	-5.81	°
28/06/2025	22.38	6.54	°
12/07/2025	14.37	-4.79	°
26/07/2025	13.45	5.68	°
08/08/2025	4.39	-4.84	°
22/08/2025	13.28	5.32	°
04/09/2025	17.36	-5.67	°
17/09/2025	23.01	5.98	°
02/10/2025	19.25	-6.71	°
15/10/2025	2.36	7.23	°
31/10/2025	3.28	-7.46	°
12/11/2025	1.06	8.03	°
28/11/2025	12.31	-7.48	°
26/12/2025	13.53	-6.65	°
07/01/2026	12.43	7.01	°
22/01/2026	14.06	-5.40	°
17/02/2026	17.08	-5.03	°
03/03/2026	19.37	4.76	°
16/03/2026	21.15	-5.80	°
30/03/2026	1.45	4.96	°
13/04/2026	17.54	-6.90	°
11/05/2026	21.11	-7.69	°
23/05/2026	17.08	7.19	°
09/06/2026	0.32	-7.82	°
20/06/2026	21.40	7.52	°
06/07/2026	23.59	-7.18	°
19/07/2026	3.35	7.16	°
03/08/2026	11.07	-5.97	°
16/08/2026	6.18	6.31	°
29/08/2026	23.40	-4.99	°
13/09/2026	0.04	5.40	°
25/09/2026	16.00	-5.11	°
09/10/2026	22.22	4.96	°
23/10/2026	4.02	-6.08	°
04/11/2026	23.04	5.66	°
02/12/2026	6.35	6.92	°
30/12/2026	11.49	7.61	°
15/01/2027	14.00	-7.76	°
27/01/2027	22.43	7.43	°
12/02/2027	8.46	-6.74	°
25/02/2027	7.05	6.56	°
25/03/2027	7.05	5.45	°
06/04/2027	14.20	-5.39	°
21/04/2027	16.00	4.71	°
03/05/2027	21.54	-6.05	°
18/05/2027	2.25	4.93	°
31/05/2027	17.43	-6.93	°
13/06/2027	17.36	6.09	°
28/06/2027	19.06	-7.52	°
26/07/2027	23.02	-7.52	°
08/08/2027	13.57	7.69	°
23/08/2027	23.12	-6.79	°
05/09/2027	18.29	7.44	°
20/09/2027	8.32	-5.56	°
03/10/2027	19.40	6.64	°
31/10/2027	13.09	5.68	°
10/12/2027	4.38	-6.10	°
23/12/2027	20.13	5.83	°
07/01/2028	8.51	-7.19	°
20/01/2028	2.11	7.07	°
04/02/2028	17.40	-7.75	°
17/02/2028	3.11	7.76	°
16/03/2028	8.25	7.59	°
31/03/2028	22.36	-6.41	°
13/04/2028	11.37	6.76	°
23/05/2028	20.53	-4.96	°
07/06/2028	13.01	5.13	°
20/06/2028	4.57	-5.56	°
04/07/2028	1.26	5.45	°
18/07/2028	2.46	-6.45	°
30/07/2028	20.45	6.62	°
15/08/2028	8.15	-7.15	°
27/08/2028	12.33	7.70	°
12/09/2028	15.39	-7.32	°
24/09/2028	14.06	8.07	°
07/11/2028	10.54	-5.55	°
19/11/2028	19.38	6.52	°
03/12/2028	14.36	-4.65	°
17/12/2028	11.07	5.37	°
30/12/2028	6.29	-5.11	°
13/01/2029	3.38	4.96	°
26/01/2029	23.45	-6.33	°
08/02/2029	10.59	5.88	°
24/02/2029	3.43	-7.49	°
08/03/2029	0.56	7.07	°
24/03/2029	10.21	-8.03	°
21/04/2029	14.06	-7.71	°
03/05/2029	11.33	7.31	°
19/05/2029	6.42	-6.64	°
31/05/2029	15.44	6.48	°
15/06/2029	2.24	-5.44	°
28/06/2029	12.24	5.51	°
11/07/2029	13.15	-5.11	°
25/07/2029	17.26	4.92	°
07/08/2029	18.31	-5.72	°
20/08/2029	23.08	5.28	°
04/09/2029	13.57	-6.71	°
16/09/2029	18.37	6.50	°
02/10/2029	16.20	-7.50	°
14/10/2029	15.57	7.50	°
30/10/2029	21.02	-7.67	°
11/11/2029	23.21	7.73	°
27/11/2029	21.20	-7.00	°
10/12/2029	8.21	7.14	°
25/12/2029	3.50	-5.77	°
07/01/2030	13.26	6.02	°
20/01/2030	10.58	-5.14	°
04/02/2030	6.24	4.94	°
16/02/2030	10.44	-5.71	°
16/03/2030	4.14	-6.80	°
29/03/2030	3.35	5.59	°
13/04/2030	5.16	-7.69	°
25/04/2030	17.39	6.81	°
11/05/2030	9.06	-7.96	°
23/05/2030	21.47	7.44	°
08/06/2030	10.25	-7.44	°
21/06/2030	3.58	7.37	°
06/07/2030	1.00	-6.29	°
19/07/2030	6.50	6.74	°
01/08/2030	16.36	-5.15	°
16/08/2030	3.15	5.88	°
12/09/2030	11.16	5.28	°
24/09/2030	15.16	-5.61	°
08/10/2030	22.54	5.50	°
22/10/2030	13.41	-6.62	°
04/11/2030	15.06	6.64	°
19/11/2030	19.23	-7.38	°
02/12/2030	9.24	7.66	°
18/12/2030	3.56	-7.47	°
30/12/2030	14.03	7.88	°