Perhitungan Detail Gerhana matahari Toposentris 26 pebruari 2017

Pak @Taqwa
Perhitungan Detail Gerhana matahari Toposentris
26 pebruari 2017

HISAB GERHANA MATAHARI
"Gerhana Matahari Toposentris 'Aly"
Lokasi pengamatan = Samudera Atlantik   0
LT = -34° 40' 30,93''   BT = -31° 10' 48,67''   TT = 10  Tz = 0

Awamil Kusuf Tanggal 26 Februari 2017 (Awamil kusuf ke46)
X0 = 633.366
X1 = 1891.27692
X2 = -0.02232
Y0 = -1531.998
Y1 = 551.7126
Y2 = 0.28512
D0 = -8.49165
D1 = 0.015261
D2 = 0.000002
M0 = 41.79895
M1 = 15.003085
L10 = 1988.9604
L11 = -0.45252
L12 = -0.0414
L20 = 22.68
L21 = -0.45036
L22 = -0.0414
TanF0 = 0
TanF1 = 16.99884
TanF2 = 16.9128
T0 = 15
DeltaA = 70.1 (DeltaT Dengan Rumus)

Proses Hisab Gerhana Matahari
1. Wasat Kusuf
Dengan Tiga Kali Takdil Wasat Kusuf

a. Takdil Awal Wasat Kusuf
1.  T = 0
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT  = 633.366
6.  Y = Y0 + Y1 x T + Y2 x TxT  = -1531.998
7.  D = D0 + D1 x T + D2 x TxT = -8.49165
8.  M = M0 + M1 x T = 41.79895
9.  L = L10 + L11 x T + L12 x TxT = 1988.9604
10. Q = L20 + L21 x T + L22 x TxT = 22.68
11. E = X1 + 2 x X2 x T  = 1891.27692
12. F = Y1 + 2 x Y2 x T  = 551.7126
13. H = M + BT - 0.00417807 x DeltaT = 10.325881182
14. Z = C Sin H = 0.147570794
15. W = S Cos D - C Cos H Sin D = -0.439926662
16. R = S Sin D + C Cos H Cos D = 0.884609266
17. I = 0.01745329 x M1 x C x Cos H  = 0.212087929
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = -0.005941684
19. U = X/3600 - Z  = 0.028364206
20. V = Y/3600 - W  = 0.014371662
21. A = E/3600 - I  = 0.313266771
22. B = F/3600 - J  = 0.159195184
23. N = AxA + BxB  = 0.123479177
24. P = -(UxA + VxB) / N  = -0.090488637

b. Takdil Tsani Wasat Kusuf
1.  T = -0.090488637
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT  = 462.226746007
6.  Y = Y0 + Y1 x T + Y2 x TxT  = -1581.919386733
7.  D = D0 + D1 x T + D2 x TxT = -8.493030931
8.  M = M0 + M1 x T = 40.441341283
9.  L = L10 + L11 x T + L12 x TxT = 1989.001008927
10. Q = L20 + L21 x T + L22 x TxT = 22.720413471
11. E = X1 + 2 x X2 x T  = 1891.280959413
12. F = Y1 + 2 x Y2 x T  = 551.660999759
13. H = M + BT - 0.00417807 x DeltaT = 8.968272465
14. Z = C Sin H = 0.128339616
15. W = S Cos D - C Cos H Sin D = -0.43942255
16. R = S Sin D + C Cos H Cos D = 0.887852987
17. I = 0.01745329 x M1 x C x Cos H  = 0.212943918
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = -0.005199745
19. U = X/3600 - Z  = 0.000056703
20. V = Y/3600 - W  = 0.000000498
21. A = E /3600- I  = 0.312411904
22. B = F/3600 - J  = 0.158438911
23. N = AxA + BxB  = 0.122704086
24. P = -(UxA + VxB) / N  = -0.000145012

c. Takdil Tsalis Wasat Kusuf
1.  T = -0.090633649
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT  = 461.952487416
6.  Y = Y0 + Y1 x T + Y2 x TxT  = -1581.999384238
7.  D = D0 + D1 x T + D2 x TxT = -8.493033144
8.  M = M0 + M1 x T = 40.439165655
9.  L = L10 + L11 x T + L12 x TxT = 1989.00107346
10. Q = L20 + L21 x T + L22 x TxT = 22.720477692
11. E = X1 + 2 x X2 x T  = 1891.280965886
12. F = Y1 + 2 x Y2 x T  = 551.660917068
13. H = M + BT - 0.00417807 x DeltaT = 8.966096836
14. Z = C Sin H = 0.128308736
15. W = S Cos D - C Cos H Sin D = -0.439421796
16. R = S Sin D + C Cos H Cos D = 0.887857823
17. I = 0.01745329 x M1 x C x Cos H  = 0.212945194
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = -0.005198553
19. U = X/3600 - Z  = 0.000011399
20. V = Y/3600 - W  = -0.000022477
21. A = E/3600 - I  = 0.31241063
22. B = F/3600 - J  = 0.158437697
23. N = AxA + BxB  = 0.122702905
24. P = -(UxA + VxB) / N  = 0

1.1. Jam Wasat Kusuf / Puncak Gerhana
Data :
a. Dari Awamil Kusuf
T0 = 15    TZ = 0    DeltaT = 70.1
Tanf1 = 16.99884    Tanf2 = 16.9128
b. Dari Takdil Tsalis Wasat Kusuf
T = -0.090633649   P = 0
U = 0.000011399    V = -0.000022477    R = 0.887857823
A = 0.31241063    B = 0.158437697    N = 0.122702905
L = 1989.00107346    Q = 22.720477692
1. Waktu puncak Gerhana
      a. t = T + P  = -0.09063365
      b. Puncak Gerhana (K) = T0 + t + TZ - DeltaT / 3600 = 14.889838572 = 14 : 53 : 23.42 UT
2. Magnitudo dan Jenis Gerhana
      m = Sqrt (UxU + VxV) = 0.000025203
      L' = L/3600 - R x Tanf1/3600 = 0.548307922
      Q' = Q/3600 - R x Tanf2/3600 = 0.002140088
      e = Sqrt(N) = 0.350289745
     z = ( AxV - UxB ) / ( e x L' ) = -0.000045964
    Tau = (L' / e)  x  Sqrt(1- z x z) = 1.565298242
     Magnitudo = (L'- m) / (L'+ Q') = 0.996066313

Ketentuan Jenis Gerhana :
Tidak terjadi Gerhana bila Magnitudo lebih kecil dari Nol
Gerhana sebagian bila magnitudo lebih besar dari nol dan nilai m lebih besar dari nilai mutlak Q'
Gerhana Total bila magnitudo lebih besar dari nol dan nilai m lebih kecil dari nilai mutlak Q'dan Q' Negatif
Gerhana Cincin  bila magnitudo lebih besar dari nol dan nilai m lebih kecil dari nilai mutlak Q'dan Q' Positif

2. Awal dan Akir Kulli (Total)/Awal dan akir khalqi (Cincin)
a. Dari Takdil Tsalis Wasat Kusuf
U = 0.000011399    V = -0.000022477    R = 0.887857823
A = 0.31241063    B = 0.158437697    N = 0.122702905
b. Dari Puncak Gerhana Dan Magnitudo
1. Puncak Gerhana (K) = 14 : 53 : 23.42 UT
2. Q' = 0.002140088
3. e  = 0.350289745
c. Takdil Awal dan Akir Total/Cincin
   w = ( AxV - UxB ) / ( e x Q' ) = -0.011776464
   d = Abs((Q' / e)  x  Sqrt(1- w x w)) = 0.006109055

2.1. Awal Kulli (Total)/Awal khalqi (Cincin)
     Awal Total/Cincin = Puncak Gerhana (k) - d
     = 14.883729517
     = 14 : 53 : 01.426 UT

3. Awal Kusuf  / Awal Gerhana Matahari
Terlebih dahulu hitung perkiraan Waktu (Pw) awal dan akir gerhana
Pw Awal Gerhana Pw AwalG = t - Tau = -1.655931892
Pw Akir Gerhana Pw AkirG = t + Tau = 1.474664592

a. Takdil Awal Li Awal Kusuf
1.  T = Pw AwalG = -1.655931892
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT = -2498.520972517
6.  Y = Y0 + Y1 x T + Y2 x TxT = -2444.814659085
7.  D = D0 + D1 x T + D2 x TxT = -8.516915692
8.  M = M0 + M1 x T = 16.954863069
9.  L = L10 + L11 x T + L12 x TxT = 1989.596218928
10. Q = L20 + L21 x T + L22 x TxT = 23.312242115
11. E = X1 + 2 x X2 x T = 1891.3508408
12. F = Y1 + 2 x Y2 x T = 550.768321398
13. H = M + BT - 0.00417807 x DeltaT = -14.518205749
14. Z = C Sin H = -0.206386984
15. W = S Cos D - C Cos H Sin D = -0.441455231
16. R = S Sin D + C Cos H Cos D = 0.871990741
17. I = 0.01745329 x M1 x C x Cos H  = 0.208695542
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = 0.007771598
19. U = X/3600 - Z  = -0.487646619
20. V = Y/3600 - W  = -0.237659952
21. A = E/3600- I  = 0.316679692
22. B = F/3600 - J  = 0.145219602
23. K = AxA + BxB  = 0.12137476
24. n = Sqrt (K)  = 0.348388806
25. e = L/3600 - R x TanF1/3600  = 0.548548163
26. m =(AxV- UxB)/(nxe)   = -0.023265543
27. P =-(UxA + VxB)/k-(e/n) x Sqrt(1- mxm)  = -0.017430691
j
b. Takdil Tsani Li Awal Kusuf
1.  T = T + P = -1.673362583
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT = -2531.488531001
6.  Y = Y0 + Y1 x T + Y2 x TxT = -2454.414844771
7.  D = D0 + D1 x T + D2 x TxT = -8.517181586
8.  M = M0 + M1 x T = 16.693348933
9.  L = L10 + L11 x T + L12 x TxT = 1989.601704143
10. Q = L20 + L21 x T + L22 x TxT = 23.31768968
11. E = X1 + 2 x X2 x T = 1891.351618906
12. F = Y1 + 2 x Y2 x T = 550.758381721
13. H = M + BT - 0.00417807 x DeltaT = -14.779719885
14. Z = C Sin H = -0.21002253
15. W = S Cos D - C Cos H Sin D = -0.441591931
16. R = S Sin D + C Cos H Cos D = 0.871052963
17. I = 0.01745329 x M1 x C x Cos H  = 0.208446701
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = 0.00791309
19. U = X/3600 - Z  = -0.493168729
20. V = Y/3600 - W  = -0.24018997
21. A = E/3600- I  = 0.316928749
22. B = F/3600 - J  = 0.145075349
23. K = AxA + BxB  = 0.121490689
24. n = Sqrt (K)  = 0.348555145
25. e = L/3600 - R x TanF1/3600  = 0.548554115
26. m =(AxV- UxB)/(nxe)   = -0.023935401
27. P =-(UxA + VxB)/k-(e/n) x Sqrt(1- mxm)  = -0.00001308

3.1. Jam Awal Kusuf / Awal Gerhana Matahari
Data :
a. Dari Awamil Kusuf
T0 = 15    TZ = 0    DeltaT = 70.1
b. Dari Takdil Tsani Li Awal Kusuf
T = -1.673362583   P = -0.00001308

3.2. Waktu Awal Gerhana Matahari
   a. t = T + P  = -1.673375663
   b. Awal Gerhana Matahari = T0 + t + TZ - DeltaT / 3600 = 13.30683267 = 13 : 18 : 24.60 UT

4. Akir Kusuf  / Akir Gerhana Matahari
a. Takdil Awal Li Akir Kusuf
1.  T = Pw AkirG = 1.474664592
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT = 3422.316570509
6.  Y = Y0 + Y1 x T + Y2 x TxT = -717.786931471
7.  D = D0 + D1 x T + D2 x TxT = -8.469140794
8.  M = M0 + M1 x T = 63.923468227
9.  L = L10 + L11 x T + L12 x TxT = 1988.203054862
10. Q = L20 + L21 x T + L22 x TxT = 21.925840138
11. E = X1 + 2 x X2 x T = 1891.211090973
12. F = Y1 + 2 x Y2 x T = 552.553512737
13. H = M + BT - 0.00417807 x DeltaT = 32.450399408
14. Z = C Sin H = 0.441748648
15. W = S Cos D - C Cos H Sin D = -0.457242907
16. R = S Sin D + C Cos H Cos D = 0.770475968
17. I = 0.01745329 x M1 x C x Cos H  = 0.181918042
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = -0.017241202
19. U = X/3600 - Z  = 0.508894844
20. V = Y/3600 - W  = 0.257857648
21. A = E/3600 - I  = 0.343418373
22. B = F/3600 - J  = 0.170728289
23. K = AxA + BxB  = 0.147084327
24. n = Sqrt (K)  = 0.383515746
25. e = L/3600 - R x TanF1/3600 = 0.548640516
26. m =(AxV- UxB)/(nxe)   = 0.007938262
27. P =-(UxA + VxB)/k-(e/n) x Sqrt(1- mxm)  = -0.056986271

b. Takdil Tsani Li Akir Kusuf
1.  T = P + T = 1.417678322
2.  G = Tan-1 (0.99664719 Tan LT) = -34.585280592
3.  S = 0.99664719 Sin G + (TT/6378140) Sin LT = -0.56572999
4.  C = Cos G + (TT/6378140) Cos LT = 0.823283511
5.  X = X0 + X1 x T + X2 x TxT = 3314.543430459
6.  Y = Y0 + Y1 x T + Y2 x TxT = -749.273969728
7.  D = D0 + D1 x T + D2 x TxT = -8.470010792
8.  M = M0 + M1 x T = 63.06849836
9.  L = L10 + L11 x T + L12 x TxT = 1988.235665996
10. Q = L20 + L21 x T + L22 x TxT = 21.958328182
11. E = X1 + 2 x X2 x T = 1891.21363484
12. F = Y1 + 2 x Y2 x T = 552.521016886
13. H = M + BT - 0.00417807 x DeltaT = 31.595429542
14. Z = C Sin H = 0.43133302
15. W = S Cos D - C Cos H Sin D = -0.45627172
16. R = S Sin D + C Cos H Cos D = 0.776926061
17. I = 0.01745329 x M1 x C x Cos H  = 0.183623806
18. J = 0.01745329 x (M1 x Z x Sin D - R x D1)  = -0.016842939
19. U = X/3600 - Z  = 0.489373489
20. V = Y/3600 - W  = 0.248140061
21. A = E/3600 - I  = 0.341713315
22. B = F/3600 - J  = 0.170320999
23. K = AxA + BxB  = 0.145777233
24. n = Sqrt (K)  = 0.381807848
25. e = L/3600 - R x TanF1/3600 = 0.548619118
26. m =(AxV- UxB)/(nxe)   = 0.006885002
27. P =-(UxA + VxB)/k-(e/n) x Sqrt(1- mxm)  = -0.000183709

3.1. Jam Awal Kusuf / Awal Gerhana Matahari
Data :
a. Dari Awamil Kusuf
T0 = 15    TZ = 0    DeltaT = 70.1
b. Dari Takdil Tsani Li Awal Kusuf
T = -1.673362583   P = -0.00001308

3.2. Waktu Awal Gerhana Matahari
   a. t = T + P  = -1.673375663
   b. Awal Gerhana Matahari = T0 + t + TZ - DeltaT / 3600 = 13.30683267 = 13 : 18 : 24.60 UT


KESIMPULAN :
Gerhana Di Lokasi Pengamatan : Samudera Atlantik   0
LT = -34° 40' 30,93''   BT = -31° 10' 48,67''   TT = 10  Tz = 0
Hari Ahad Pahing 26 Februari 2017
Jenis Gerhana = Cincin
Terlihat di lokasi sebagai Gerhana Matahari Cincin
"Gerhana Matahari Toposentris 1.0"
Sirkumulasi Gerhana
Awal Gerhana = 13 : 18 : 24.598
  Awal  Cincin = 14 : 53 : 01.426
Puncak Gerhana = 14 : 53 : 23.419
  Akhir  Cincin = 14 : 53 : 45.411
Akir Gerhana = 16 : 23 : 53.081
  Durasi  Cincin = 00 : 00 : 43.985
Durasi Gerhana = 03 : 05 : 28.483
Magnitudo = 0.996066313