Tables of Equation of Time and Declination of the Sun

Table Equation of Time (1986*):


00:00 in Universal Time (UT, GMT)

Day January February March April May June July August September October November December
0 -02 48
1 03 16 13 31 12 31 -04 16 +02 51 +02 21 -03 39 -06 19 -00 13 +10 06 +16 23 +11 14
2 03 44 13 39 -12 19 03 48 02 58 02 12 03 50 06 16 +00 06 10 25 16 24 10 51
3 04 12 13 46 12 07 03 30 03 05 02 02 04 02 06 12 00 25 10 44 16 25 10 28
4 04 40 13 53 11 54 03 13 03 11 01 52 04 13 06 07 00 45 11 03 16 25 10 04
5 -05 07 13 59 11 41 02 55 03 17 01 42 04 24 -06 02 +01 05 11 21 +16 24 09 40
6 05 34 14 04 11 28 -02 38 +03 22 +01 31 04 34 +05 56 01 24 +11 39 16 22 +09 15
7 06 01 14 08 -11 14 02 21 03 26 01 20 04 45 05 49 01 45 11 57 16 20 08 50
8 06 27 14 11 -10 59 02 04 03 30 01 09 04 54 05 42 02 05 12 14 16 17 08 24
9 06 52 -14 13 10 45 01 47 03 34 00 58 05 04 05 34 02 26 12 31 16 13 07 58
10 -07 17 14 15 10 30 01 31 03 36 00 46 05 13 -05 26 +02 46 12 47 +16 08 07 31
11 07 41 14 16 10 14 -01 15 +03 39 +00 34 -05 21 05 17 03 07 +13 03 16 02 +07 04
12 08 05 14 16 -09 59 00 59 03 40 00 22 05 29 05 08 03 28 13 19 15 55 06 36
13 08 28 14 16 09 43 00 44 03 41 +00 09 05 37 04 58 03 49 13 34 15 48 06 09
14 08 51 14 14 09 26 00 28 03 42 -00 03 05 44 04 47 04 11 13 48 15 40 05 40
15 -09 13 14 12 09 10 00 13 03 42 00 16 05 51 -04 36 +04 32 14 02 +15 30 05 12
16 09 34 14 09 08 53 +00 01 +03 41 -00 29 -05 57 -04 24 04 53 +14 16 +15 21 +04 43
17 09 55 14 06 -08 36 00 15 +03 40 00 42 06 03 04 12 05 15 14 29 15 10 04 14
18 10 15 14 01 08 19 00 29 03 38 00 54 06 08 03 59 05 36 14 41 14 58 03 45
19 10 34 13 56 08 01 00 43 03 36 01 07 06 12 03 46 05 58 14 53 14 46 03 15
20 -10 52 -13 51 07 44 00 56 03 33 01 20 06 16 03 32 +06 19 15 04 14 32 02 46
21 11 10 13 44 07 26 +01 09 03 30 -01 33 -06 20 -03 17 06 41 +15 15 +14 18 +02 16
22 11 26 13 37 -07 08 01 21 +03 26 01 46 06 23 03 03 07 02 15 24 14 03 01 46
23 11 42 13 29 06 50 01 33 03 22 01 59 06 25 02 47 07 23 15 33 13 48 01 16
24 11 58 13 21 06 32 01 44 03 17 02 12 06 27 02 32 07 44 15 42 13 31 00 47
25 -12 12 -13 12 06 13 01 55 03 12 02 25 -06 28 02 16 +08 05 15 50 13 14 +00 17
26 12 26 13 02 05 55 +02 06 03 06 -02 38 06 28 -01 59 08 26 +15 57 +12 55 -00 13
27 12 39 12 52 -05 37 02 16 +03 00 02 50 06 28 01 42 08 46 16 03 12 37 00 43
28 12 51 12 42 05 19 02 25 02 53 03 03 06 28 01 25 09 07 16 08 12 17 01 12
29 13 02 05 00 02 34 02 46 03 15 06 26 01 07 09 27 16 13 11 57 01 42
30 -13 13 04 42 02 43 02 38 03 27 06 25 00 49 +09 47 16 17 11 35 02 11
31 13 22 04 24 02 30 -06 22 -00 31 +16 20 -02 40
32 -03 09


Table Declination of The Sun (1986*):


00:00 in Universal Time (UT, GMT)

Day January February March April May June July August September October November December
0 -23 07
1 23 03 17 15 07 47 +04 20 +14 55 +21 59 +23 09 +18 09 +08 28 -02 59 14 16 -21 43
2 22 58 16 58 -07 24 +04 44 15 13 22 07 23 05 17 54 08 06 03 22 14 35 21 53
3 22 52 16 40 07 01 05 07 15 31 22 15 23 00 17 39 07 45 03 46 14 54 22 02
4 22 47 -16 23 06 38 05 30 15 49 22 22 22 55 17 23 07 23 04 09 15 13 22 10
5 -22 40 16 05 06 15 05 53 16 06 22 29 22 50 +17 07 +07 00 04 32 -15 31 22 18
6 22 33 15 46 05 52 +06 15 +16 24 +22 36 +22 45 16 51 06 38 -04 55 15 50 -22 26
7 22 26 15 28 -05 29 06 38 16 40 22 42 22 39 16 34 06 16 05 18 16 08 22 33
8 22 19 15 09 05 05 07 01 16 57 22 48 22 32 16 17 05 53 05 41 16 25 22 40
9 22 11 -14 50 04 42 07 23 17 13 22 53 22 25 16 00 05 31 06 04 16 43 22 46
10 -22 02 14 31 04 18 07 45 17 29 22 58 22 18 +15 43 +05 08 06 27 -17 00 22 52
11 21 53 14 11 03 55 +08 08 +17 45 +23 02 +22 11 15 25 04 45 -06 50 17 17 -22 57
12 21 44 13 52 -03 31 08 30 18 00 23 07 22 03 15 08 04 23 07 12 17 33 23 02
13 21 34 13 32 03 08 08 52 18 15 23 11 21 54 14 50 04 00 07 35 17 50 23 07
14 21 24 -13 12 02 44 09 13 18 30 23 14 21 46 14 31 03 37 07 57 18 06 23 11
15 -21 13 -12 51 02 20 09 35 18 45 23 17 21 37 +14 13 +03 14 08 20 -18 21 23 15
16 21 02 12 31 01 57 +09 56 +18 59 +23 20 +21 27 +13 54 02 51 -08 42 -18 36 -23 18
17 20 51 12 10 -01 33 10 18 +19 13 23 22 21 17 13 35 02 27 09 04 18 51 23 20
18 20 39 11 49 01 09 10 39 19 26 23 24 21 07 13 16 02 04 09 26 19 06 23 22
19 20 27 11 28 00 46 11 00 19 40 23 25 20 57 12 57 01 41 09 48 19 20 23 24
20 -20 14 -11 06 -00 22 11 21 19 52 23 26 20 46 12 37 +01 18 10 09 19 34 23 25
21 20 01 10 45 +00 02 +11 41 20 05 +23 26 +20 34 +12 17 00 54 -10 31 -19 48 -23 26
22 19 48 10 23 +00 26 12 01 +20 17 23 27 20 23 11 57 00 31 10 52 20 01 23 27
23 19 34 10 01 00 49 12 22 20 29 23 26 20 11 11 37 +00 08 11 13 20 14 23 26
24 19 20 09 39 01 13 12 42 20 40 23 25 19 59 11 17 -00 16 11 34 20 27 23 26
25 -19 05 - 09 17 01 37 13 01 20 51 23 24 19 46 10 56 -00 39 11 55 20 39 23 25
26 18 51 08 55 02 00 +13 21 21 02 +23 23 +19 33 +10 36 01 02 -12 16 -20 51 -23 23
27 18 35 08 32 +02 24 13 40 +21 13 23 21 19 20 10 15 01 26 12 36 21 02 23 21
28 18 20 08 10 02 47 13 59 21 23 23 18 19 06 09 54 01 49 12 57 21 13 23 19
29 18 04 03 11 14 18 21 32 23 16 18 53 09 33 02 12 13 17 21 23 23 16
30 -17 48   03 34 14 37 21 42 23 12 18 38 09 11 -02 36 13 37 21 34 23 12
31 17 32   03 57   21 51   +18 24 +08 50   -13 56   -23 08
32                       -23 04

E: equation of time, δ: declination of the Sun, min: minutes, sec: seconds.

* These values are for solar years 1986+4n (n=0,1,2,3,...). For 1987+4n, values corresponding to 6 hours earlier; for 1988+4n, values corresponding to 12 hours earlier (prior to March) and to 12 hours later (from March on); for 1989+4n, values corresponding to 6 hours later are used. For example, for 0 Jan. 1989 (31 Dec. 1988) the declination is determined as follows;

Declination (δ) = -23º 27' - [-23º 27' - (-23º 03')] x 6 / 24 = -23º 06'. Ibrâhîm Fezârî Baghdâdî was the earliest Muslim to devise the quadrant and use it to measure the Sun's altitude. Among the very valuable books that he wrotre are Zeyj-i-Fezârî, Amal-i-bi-l-usturlâb and Kitâb-ul-mikyâs-uz-zawâl. He passed away in 188 [A.D. 803]. Two other extremely valuable books are Kitâb-ul-usturlâb, by Usbu' Ghirnâtî (of Granada), who passed away in 426 (hijrî), and Ridâyat-ul-mubtadî by Alî bin Ahmad Baghdâdî (of Baghdâd) who passed away in 801 [A.D. 1389] in Egypt.

E = (true time) - (mean time).

The above values are determined when it was 00:00 in London i.e. at 24:00 (the previous midnight). They are used after correction in direct proportion to a given longtitude. The time t in standart time is calculated from δ = δ2 + (δ2 - δ1) x (t - (S/15)) / 24 where δ1 and δ2 are the values on that day and on the following, respectively; S is the degree of the meridian determining standart time; all used with their algebraic signs.