Days of No shadows at Noon

We have all heard the story on how Eratosthenes measured the circumference of the earth. Eratosthenes observed that during high noon when sun was at Zenith a well at a place called Syene did not cast any shadow on June 21^st; we call this day as summer Solstice. On same day, Solstice, during high noon a shadow was cast when a vertical stick was kept in Alexandria. Based on the angle of shadow cast by the sun he calculated the circumference of the earth, he gave a value of 40233km.

Sun rises in the east and sets in the west, this we notice easily as the duration is very small. The Sun does move in north-south direction too, this we normally notice as seasonal changes more than position of the sun, as the movement of the Sun in north-south direction takes months together.

Sun will be directly overhead at equator on march21/22; the shadow will be at its minimum on that day during high noon. This day is called Equinox and Sun’s angle is taken as Zero degree declination.

As days pass, due to earth’s axis inclination of 23.5degrees, Sun starts moving towards north from March 21st to June 21st. On June 21st Sun would have reached maximum angle of 23.5degrees, this day is called summer Solstice, and after reaching north most angle Sun starts moving back towards equator. The Sun reaches back to zero declination, on September 22nd and this position is called autumn equinox. From this day Sun will move towards south reaching southernmost angle of -23.5 on December 21st, again after reaching this declination sun starts moving towards equator and cycle continues.

Now coming back to shadows, we have seen that there will be minimum or no shadow on equinox day on equator regions like Congo, Uganda and Kenya etc. All other regions not on equator or zero latitude will have shadows on that day. So when will other regions can have minimum or no shadow?

Here is good and easy way to know when the Sun will be directly overhead and there will no shadows in area we live. All we need to know is the declination of the sun and latitude of the place we live, on the day these two match; the Sun will be directly overhead at noon, with minimum or no shadow cast. That means we should live in a region which is less than or equal to 23.5degrees on either side of the equator.

Here is list of declination of the Sun; find out where and when there will be no shadow day based on latitude of your place….Make sure the reference is a vertical  pole or stick and time you check is at exact noon.

Bangalore will have minimum shadow on April 24/25th and again on Aug 19th.

Declination(Dec) is given in Degrees, Minutes and Seconds

			RA			Dec
Year	Month	Date	h	m	s	o	'	"
2013	Apr	1	0	41	20.35	4	26	49.6
2013	Apr	2	0	44	59	4	49	57.3
2013	Apr	3	0	48	37.8	5	12	59.9
2013	Apr	4	0	52	16.77	5	35	57.1
2013	Apr	5	0	55	55.91	5	58	48.5
2013	Apr	6	0	59	35.25	6	21	33.8
2013	Apr	7	1	3	14.8	6	44	12.6
2013	Apr	8	1	6	54.58	7	6	44.6
2013	Apr	9	1	10	34.61	7	29	9.3
2013	Apr	10	1	14	14.89	7	51	26.4
2013	Apr	11	1	17	55.44	8	13	35.6
2013	Apr	12	1	21	36.27	8	35	36.5
2013	Apr	13	1	25	17.4	8	57	28.7
2013	Apr	14	1	28	58.84	9	19	12
2013	Apr	15	1	32	40.6	9	40	45.9
2013	Apr	16	1	36	22.7	10	2	10.1
2013	Apr	17	1	40	5.14	10	23	24.3
2013	Apr	18	1	43	47.95	10	44	28.1
2013	Apr	19	1	47	31.13	11	5	21.2
2013	Apr	20	1	51	14.71	11	26	3.3
2013	Apr	21	1	54	58.68	11	46	34.1
2013	Apr	22	1	58	43.08	12	6	53.1
2013	Apr	23	2	2	27.9	12	27	0.2
2013	Apr	24	2	6	13.17	12	46	55
2013	Apr	25	2	9	58.9	13	6	37.1
2013	Apr	26	2	13	45.1	13	26	6.3
2013	Apr	27	2	17	31.8	13	45	22.2
2013	Apr	28	2	21	19.01	14	4	24.7
2013	Apr	29	2	25	6.73	14	23	13.2
2013	Apr	30	2	28	54.99	14	41	47.6
2013	May	1	2	32	43.79	15	0	7.5
2013	May	2	2	36	33.15	15	18	12.6
2013	May	3	2	40	23.08	15	36	2.5
2013	May	4	2	44	13.57	15	53	37.1
2013	May	5	2	48	4.63	16	10	55.9
2013	May	6	2	51	56.27	16	27	58.6
2013	May	7	2	55	48.49	16	44	44.9
2013	May	8	2	59	41.29	17	1	14.5
2013	May	9	3	3	34.66	17	17	27
2013	May	10	3	7	28.61	17	33	22.3
2013	May	11	3	11	23.13	17	48	59.8
2013	May	12	3	15	18.22	18	4	19.5
2013	May	13	3	19	13.87	18	19	20.9
2013	May	14	3	23	10.09	18	34	3.7
2013	May	15	3	27	6.87	18	48	27.8
2013	May	16	3	31	4.2	19	2	32.7
2013	May	17	3	35	2.08	19	16	18.3
2013	May	18	3	39	0.5	19	29	44.2
2013	May	19	3	42	59.45	19	42	50.3
2013	May	20	3	46	58.94	19	55	36.1
2013	May	21	3	50	58.94	20	8	1.5
2013	May	22	3	54	59.47	20	20	6.3
2013	May	23	3	59	0.51	20	31	50.2
2013	May	24	4	3	2.05	20	43	12.9
2013	May	25	4	7	4.09	20	54	14.2
2013	May	26	4	11	6.63	21	4	54
2013	May	27	4	15	9.66	21	15	12
2013	May	28	4	19	13.18	21	25	7.9
2013	May	29	4	23	17.17	21	34	41.6
2013	May	30	4	27	21.63	21	43	52.9
2013	May	31	4	31	26.54	21	52	41.6
2013	Jun	1	4	35	31.89	22	1	7.4
2013	Jun	2	4	39	37.66	22	9	10.3
2013	Jun	3	4	43	43.83	22	16	50
2013	Jun	4	4	47	50.4	22	24	6.3
2013	Jun	5	4	51	57.33	22	30	59.2
2013	Jun	6	4	56	4.6	22	37	28.3
2013	Jun	7	5	0	12.19	22	43	33.7
2013	Jun	8	5	4	20.08	22	49	15.2
2013	Jun	9	5	8	28.25	22	54	32.6
2013	Jun	10	5	12	36.67	22	59	25.8
2013	Jun	11	5	16	45.31	23	3	54.7
2013	Jun	12	5	20	54.16	23	7	59.3
2013	Jun	13	5	25	3.18	23	11	39.4
2013	Jun	14	5	29	12.35	23	14	55
2013	Jun	15	5	33	21.64	23	17	46
2013	Jun	16	5	37	31.04	23	20	12.4
2013	Jun	17	5	41	40.52	23	22	14
2013	Jun	18	5	45	50.04	23	23	51
2013	Jun	19	5	49	59.6	23	25	3.1
2013	Jun	20	5	54	9.16	23	25	50.5
2013	Jun	21	5	58	18.7	23	26	13.1
2013	Jun	22	6	2	28.21	23	26	10.9
2013	Jun	23	6	6	37.66	23	25	44
2013	Jun	24	6	10	47.05	23	24	52.2
2013	Jun	25	6	14	56.34	23	23	35.7
2013	Jun	26	6	19	5.52	23	21	54.5
2013	Jun	27	6	23	14.58	23	19	48.6
2013	Jun	28	6	27	23.5	23	17	18
2013	Jun	29	6	31	32.25	23	14	22.9
2013	Jun	30	6	35	40.81	23	11	3.4
2013	Jul	1	6	39	49.17	23	7	19.4
2013	Jul	2	6	43	57.29	23	3	11.1
2013	Jul	3	6	48	5.15	22	58	38.7
2013	Jul	4	6	52	12.74	22	53	42.1
2013	Jul	5	6	56	20.03	22	48	21.7
2013	Jul	6	7	0	26.99	22	42	37.4
2013	Jul	7	7	4	33.61	22	36	29.4
2013	Jul	8	7	8	39.86	22	29	58
2013	Jul	9	7	12	45.72	22	23	3.2
2013	Jul	10	7	16	51.16	22	15	45.2
2013	Jul	11	7	20	56.18	22	8	4.3
2013	Jul	12	7	25	0.75	22	0	0.6
2013	Jul	13	7	29	4.84	21	51	34.2
2013	Jul	14	7	33	8.45	21	42	45.5
2013	Jul	15	7	37	11.55	21	33	34.6
2013	Jul	16	7	41	14.13	21	24	1.7
2013	Jul	17	7	45	16.18	21	14	7
2013	Jul	18	7	49	17.69	21	3	50.8
2013	Jul	19	7	53	18.64	20	53	13.3
2013	Jul	20	7	57	19.02	20	42	14.7
2013	Jul	21	8	1	18.84	20	30	55.3
2013	Jul	22	8	5	18.08	20	19	15.2
2013	Jul	23	8	9	16.74	20	7	14.6
2013	Jul	24	8	13	14.83	19	54	53.9
2013	Jul	25	8	17	12.34	19	42	13.3
2013	Jul	26	8	21	9.27	19	29	13
2013	Jul	27	8	25	5.61	19	15	53.2
2013	Jul	28	8	29	1.38	19	2	14.2
2013	Jul	29	8	32	56.56	18	48	16.4
2013	Jul	30	8	36	51.15	18	33	59.9
2013	Jul	31	8	40	45.16	18	19	25.1
2013	Aug	1	8	44	38.57	18	4	32.2
2013	Aug	2	8	48	31.4	17	49	21.6
2013	Aug	3	8	52	23.63	17	33	53.5
2013	Aug	4	8	56	15.26	17	18	8.3
2013	Aug	5	9	0	6.31	17	2	6.1
2013	Aug	6	9	3	56.75	16	45	47.5
2013	Aug	7	9	7	46.61	16	29	12.6
2013	Aug	8	9	11	35.87	16	12	21.8
2013	Aug	9	9	15	24.55	15	55	15.5
2013	Aug	10	9	19	12.63	15	37	53.8
2013	Aug	11	9	23	0.13	15	20	17.2
2013	Aug	12	9	26	47.04	15	2	25.9
2013	Aug	13	9	30	33.38	14	44	20.4
2013	Aug	14	9	34	19.15	14	26	0.8
2013	Aug	15	9	38	4.36	14	7	27.6
2013	Aug	16	9	41	49.01	13	48	41
2013	Aug	17	9	45	33.12	13	29	41.3
2013	Aug	18	9	49	16.69	13	10	28.9
2013	Aug	19	9	52	59.75	12	51	4
2013	Aug	20	9	56	42.31	12	31	26.9
2013	Aug	21	10	0	24.38	12	11	38
2013	Aug	22	10	4	5.98	11	51	37.5
2013	Aug	23	10	7	47.14	11	31	25.6
2013	Aug	24	10	11	27.86	11	11	2.8
2013	Aug	25	10	15	8.17	10	50	29.3
2013	Aug	26	10	18	48.08	10	29	45.4
2013	Aug	27	10	22	27.6	10	8	51.4
2013	Aug	28	10	26	6.77	9	47	47.7
2013	Aug	29	10	29	45.58	9	26	34.6
2013	Aug	30	10	33	24.05	9	5	12.3
2013	Aug	31	10	37	2.21	8	43	41.3
2013	Sep	1	10	40	40.06	8	22	1.9
2013	Sep	2	10	44	17.63	8	0	14.3
2013	Sep	3	10	47	54.92	7	38	19
2013	Sep	4	10	51	31.95	7	16	16.2
2013	Sep	5	10	55	8.73	6	54	6.4
2013	Sep	6	10	58	45.29	6	31	49.7
2013	Sep	7	11	2	21.62	6	9	26.7
2013	Sep	8	11	5	57.76	5	46	57.7
2013	Sep	9	11	9	33.71	5	24	22.9
2013	Sep	10	11	13	9.49	5	1	42.7
2013	Sep	11	11	16	45.11	4	38	57.5
2013	Sep	12	11	20	20.6	4	16	7.6
2013	Sep	13	11	23	55.96	3	53	13.3
2013	Sep	14	11	27	31.23	3	30	15
2013	Sep	15	11	31	6.41	3	7	13
2013	Sep	16	11	34	41.53	2	44	7.5
2013	Sep	17	11	38	16.61	2	20	59
2013	Sep	18	11	41	51.68	1	57	47.7
2013	Sep	19	11	45	26.76	1	34	33.9
2013	Sep	20	11	49	1.87	1	11	18
2013	Sep	21	11	52	37.04	0	48	0.2
2013	Sep	22	11	56	12.3	0	24	40.9
2013	Sep	23	11	59	47.67	0	1	20.4
2013	Sep	24	12	3	23.16	0	22	1
2013	Sep	25	12	6	58.81	0	45	23
2013	Sep	26	12	10	34.64	-1	8	45.1
2013	Sep	27	12	14	10.66	-1	32	7.1
2013	Sep	28	12	17	46.9	-1	55	28.6
2013	Sep	29	12	21	23.38	-2	18	49.3
2013	Sep	30	12	25	0.11	-2	42	8.7
2013	Oct	1	12	28	37.13	-3	5	26.6
2013	Oct	2	12	32	14.43	-3	28	42.6
2013	Oct	3	12	35	52.06	-3	51	56.4
2013	Oct	4	12	39	30.01	-4	15	7.4
2013	Oct	5	12	43	8.31	-4	38	15.4
2013	Oct	6	12	46	46.98	-5	1	20
2013	Oct	7	12	50	26.03	-5	24	20.9
2013	Oct	8	12	54	5.47	-5	47	17.5
2013	Oct	9	12	57	45.32	-6	10	9.6
2013	Oct	10	13	1	25.6	-6	32	56.7
2013	Oct	11	13	5	6.32	-6	55	38.6
2013	Oct	12	13	8	47.5	-7	18	14.7
2013	Oct	13	13	12	29.16	-7	40	44.8
2013	Oct	14	13	16	11.32	-8	3	8.4
2013	Oct	15	13	19	54	-8	25	25.3
2013	Oct	16	13	23	37.21	-8	47	35
2013	Oct	17	13	27	20.99	-9	9	37.2
2013	Oct	18	13	31	5.34	-9	31	31.5
2013	Oct	19	13	34	50.3	-9	53	17.5
2013	Oct	20	13	38	35.87	-10	14	54.9
2013	Oct	21	13	42	22.1	-10	36	23.3
2013	Oct	22	13	46	8.98	-10	57	42.3
2013	Oct	23	13	49	56.54	-11	18	51.6
2013	Oct	24	13	53	44.8	-11	39	50.7
2013	Oct	25	13	57	33.78	-12	0	39.3
2013	Oct	26	14	1	23.48	-12	21	17
2013	Oct	27	14	5	13.93	-12	41	43.3
2013	Oct	28	14	9	5.14	-13	1	57.8
2013	Oct	29	14	12	57.12	-13	22	0.3
2013	Oct	30	14	16	49.88	-13	41	50.1
2013	Oct	31	14	20	43.43	-14	1	27.1
2013	Nov	1	14	24	37.78	-14	20	50.6
2013	Nov	2	14	28	32.93	-14	40	0.4
2013	Nov	3	14	32	28.9	-14	58	55.9
2013	Nov	4	14	36	25.69	-15	17	36.8
2013	Nov	5	14	40	23.29	-15	36	2.7
2013	Nov	6	14	44	21.72	-15	54	13.1
2013	Nov	7	14	48	20.96	-16	12	7.5
2013	Nov	8	14	52	21.03	-16	29	45.7
2013	Nov	9	14	56	21.92	-16	47	7.2
2013	Nov	10	15	0	23.63	-17	4	11.6
2013	Nov	11	15	4	26.17	-17	20	58.4
2013	Nov	12	15	8	29.54	-17	37	27.3
2013	Nov	13	15	12	33.74	-17	53	38
2013	Nov	14	15	16	38.77	-18	9	29.9
2013	Nov	15	15	20	44.63	-18	25	2.8
2013	Nov	16	15	24	51.33	-18	40	16.2
2013	Nov	17	15	28	58.86	-18	55	9.8
2013	Nov	18	15	33	7.23	-19	9	43.2
2013	Nov	19	15	37	16.42	-19	23	56.1
2013	Nov	20	15	41	26.45	-19	37	48
2013	Nov	21	15	45	37.29	-19	51	18.6
2013	Nov	22	15	49	48.96	-20	4	27.5
2013	Nov	23	15	54	1.43	-20	17	14.4
2013	Nov	24	15	58	14.71	-20	29	39
2013	Nov	25	16	2	28.77	-20	41	40.8
2013	Nov	26	16	6	43.61	-20	53	19.6
2013	Nov	27	16	10	59.21	-21	4	34.9
2013	Nov	28	16	15	15.56	-21	15	26.6
2013	Nov	29	16	19	32.64	-21	25	54.2
2013	Nov	30	16	23	50.42	-21	35	57.5
2013	Dec	1	16	28	8.9	-21	45	36.2
2013	Dec	2	16	32	28.03	-21	54	49.8
2013	Dec	3	16	36	47.8	-22	3	38.3
2013	Dec	4	16	41	8.18	-22	12	1.3
2013	Dec	5	16	45	29.14	-22	19	58.4
2013	Dec	6	16	49	50.64	-22	27	29.6
2013	Dec	7	16	54	12.67	-22	34	34.5
2013	Dec	8	16	58	35.18	-22	41	13
2013	Dec	9	17	2	58.15	-22	47	24.7
2013	Dec	10	17	7	21.54	-22	53	9.6
2013	Dec	11	17	11	45.34	-22	58	27.3
2013	Dec	12	17	16	9.51	-23	3	17.8
2013	Dec	13	17	20	34.02	-23	7	40.9
2013	Dec	14	17	24	58.85	-23	11	36.5
2013	Dec	15	17	29	23.97	-23	15	4.3
2013	Dec	16	17	33	49.34	-23	18	4.4
2013	Dec	17	17	38	14.95	-23	20	36.5
2013	Dec	18	17	42	40.75	-23	22	40.6
2013	Dec	19	17	47	6.73	-23	24	16.6
2013	Dec	20	17	51	32.84	-23	25	24.5
2013	Dec	21	17	55	59.06	-23	26	4.1
2013	Dec	22	18	0	25.36	-23	26	15.5
2013	Dec	23	18	4	51.71	-23	25	58.7
2013	Dec	24	18	9	18.07	-23	25	13.5
2013	Dec	25	18	13	44.42	-23	24	0.2
2013	Dec	26	18	18	10.71	-23	22	18.6
2013	Dec	27	18	22	36.92	-23	20	8.8
2013	Dec	28	18	27	3.01	-23	17	30.8
2013	Dec	29	18	31	28.94	-23	14	24.8
2013	Dec	30	18	35	54.69	-23	10	50.8
2013	Dec	31	18	40	20.21	-23	6	49

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