Umbral Enlargement Factors from Midcrater Timings
October 28, 2004 Total Lunar Eclipse
Calculations by Helio C. Vital
Mideclipse Date: 9.0544/11/2003
TD-UTC: 64.8 s ; Umbral Model: Meeus` ;
Oblateness:1/298.257
where:
UTC is the observed time of contact in Universal Time;
F stands for the umbral enlargement percentage (%);
PSI is the umbral angle of contact in degrees and
RC and RO refer to the calculated and observed radii of the umbra,
respectively,
divided by the lunar equatorial parallax
Alexandre Amorim
(Florianópolis, Brazil)
37 timings selected (out of 40 submitted)
Umbral Phase
UTC: 1:14:54 U1
RC= 0.7151 RO=
0.7237 RO-RC= 0.00858
F= 1.200% PSI= -8.81
Proclus
UTC: 2:11:54
IM
RC= 0.7184 RO=
0.7291 RO-RC= 0.01069
F= 1.488% PSI= 6.33
UTC: 4:33:18
EM
RC= 0.7159 RO=
0.7257 RO-RC= 0.00977
F= 1.365% PSI= 57.13
Aristarchus
UTC: 1:27:45
IM
RC= 0.7177 RO=
0.7324 RO-RC= 0.01468
F= 2.046% PSI= 4.90
UTC: 3:51:16
EM
RC= 0.7153 RO=
0.7237 RO-RC= 0.00835
F= 1.168% PSI= 55.96
Langrenus
UTC: 2:12:52
IM
RC= 0.7176 RO=
0.7277 RO-RC= 0.01007
F= 1.403% PSI= -3.38
UTC: 4:47:12
EM
RC= 0.7157 RO=
0.7276 RO-RC= 0.01195
F= 1.670% PSI= 47.25
Tycho
UTC: 1:37:45
IM
RC= 0.7181 RO=
0.7298 RO-RC= 0.01167
F= 1.625% PSI= -18.02
UTC: 4:23: 5
EM
RC= 0.7172 RO=
0.7279 RO-RC= 0.01069
F= 1.490% PSI= 32.61
Aristoteles
UTC: 2: 3:34
IM
RC= 0.7177 RO=
0.7341 RO-RC= 0.01635
F= 2.279% PSI= 17.30
UTC: 4: 5:49
EM
RC= 0.7150 RO=
0.7264 RO-RC= 0.01140
F= 1.595% PSI= 68.50
Eudoxus
UTC: 2: 2:27
IM
RC= 0.7181 RO=
0.7316 RO-RC= 0.01343
F= 1.870% PSI= 15.51
UTC: 4: 8: 5
EM
RC= 0.7154 RO=
0.7259 RO-RC= 0.01047
F= 1.464% PSI= 66.54
Grimaldi
UTC: 1:16:15
IM
RC= 0.7165 RO=
0.7250 RO-RC= 0.00854
F= 1.192% PSI= -7.02
UTC: 3:53:46
EM
RC= 0.7147 RO=
0.7263 RO-RC= 0.01151
F= 1.610% PSI= 43.59
Kepler
UTC: 1:26: 5
IM
RC= 0.7185 RO=
0.7344 RO-RC= 0.01586
F= 2.207% PSI= -1.22
UTC: 3:58:40
EM
RC= 0.7164 RO=
0.7290 RO-RC= 0.01259
F= 1.757% PSI= 49.63
Manilius
UTC: 1:52:11
IM
RC= 0.7196 RO=
0.7312 RO-RC= 0.01159
F= 1.611% PSI= 3.71
UTC: 4:17:55
EM
RC= 0.7172 RO=
0.7280 RO-RC= 0.01079
F= 1.505% PSI= 54.50
Menelaus
UTC: 1:56: 4
IM
RC= 0.7195 RO=
0.7335 RO-RC= 0.01401
F= 1.947% PSI= 4.70
UTC: 4:20:50
EM 1/298.26
RC= 0.7171 RO=
0.7304 RO-RC= 0.01335
F= 1.862% PSI= 55.49
Plinius
UTC: 2: 0:24
IM
RC= 0.7193 RO=
0.7307 RO-RC= 0.01140
F= 1.584% PSI= 4.85
UTC: 4:24:45
EM
RC= 0.7169 RO=
0.7303 RO-RC= 0.01342
F= 1.872% PSI= 55.52
Pytheas
UTC: 1:38:12
IM
RC= 0.7191 RO=
0.7290 RO-RC= 0.00996
F= 1.385% PSI= 4.80
Timocharis
UTC: 1:43:40
IM
RC= 0.7190 RO=
0.7310 RO-RC= 0.01194
F= 1.660% PSI= 7.58
UTC: 4: 3:31
EM
RC= 0.7165 RO=
0.7277 RO-RC= 0.01122
F= 1.565% PSI= 58.40
M. Crisium
UTC: 2:16:26
IM
RC= 0.7176 RO=
0.7302 RO-RC= 0.01260
F= 1.757% PSI= 6.29
Plato
UTC: 1:54:31
IM
RC= 0.7177 RO=
0.7305 RO-RC= 0.01288
F= 1.795% PSI= 16.90
Stevinus A
UTC: 4:46:31
EM
RC= 0.7163 RO=
0.7277 RO-RC= 0.01137
F= 1.588% PSI= 38.30
Copernicus
UTC: 1:35:14
IM 1/298.26
RC= 0.7193 RO= 0.7314 RO-RC=
0.01209 F= 1.681% PSI=
0.31
UTC: 4: 5: 9
EM 1/298.26
RC= 0.7171 RO=
0.7248 RO-RC= 0.00765
F= 1.066% PSI= 51.21
Laplace
UTC: 1:46:35
IM
RC= 0.7177 RO=
0.7272 RO-RC= 0.00953
F= 1.328% PSI= 14.64
UTC: 3:53:22
EM
RC= 0.7150 RO=
0.7231 RO-RC= 0.00804
F= 1.124% PSI= 65.57
Euler
UTC: 1:34:30
IM 1/298.26
RC= 0.7187 RO=
0.7342 RO-RC= 0.01549
F= 2.155% PSI= 5.33
UTC: 3:58:12
EM 1/298.26
RC= 0.7162 RO=
0.7291 RO-RC= 0.01282
F= 1.790% PSI= 56.23
Totality
UTC: 2:23:29 U2
RC= 0.7149 RO= 0.7274 RO-RC= 0.01251 F= 1.749%
PSI= 13.36
UTC: 3:45: 0 U3
RC= 0.7124 RO= 0.7294 RO-RC= 0.01707 F= 2.396%
PSI= 63.74
FLATTENING=1/298.26 20 OBS
MEAN FOR IMMERSIONS :
1.6981+-0.0713 % S: 0.32 RD: 0.0419797
A=
0.730314+-0.000861 B=
-0.003693+-0.019786
CORRELATION COEFFICIENT= -0.041700
EXP. FLAT.= 0.0050569+-
0.0270927 (1 sig)
1/(EXP. FLAT.)= 1/
198 (> -20 and < 17) (2 sig=95%)
FLATTENING=1/298.26 17 OBS
MEAN FOR EMERSIONS : 1.5816+-0.0774 % S: 0.32
RD: 0.0489590
A=
0.728825+-0.002174 B=
-0.002451+-0.003255
CORRELATION COEFFICIENT= -0.179630
EXP. FLAT.= 0.0033623+-
0.0044659 (1 sig)
1/(EXP. FLAT.)= 1/
297 (> -180 and < 81) (2
sig=95%)
MEAN ENLARGEMENT WEIGHED ON
ERRORS: 1.645+-0.052
MEAN ENLARGEMENT WEIGHED ON NUMBER
OF OBSERVATIONS: 1.645+-0.052
WEIGHED MEAN FLATTENING: 0.0034071+-0.0050645 (1 sig)
1/(WEIGHED MEAN FLATTENING): 294 (between -149 and 74)(2 sig)
GEOM. FACTOR : 1.40243 AND FLAT.
(Meeus)= 1/ 212.7
DIF. ATM. : 0.72+-1.08
Antonio Rosa Campos (Belo Horizonte, Brazil)
13 timings selected (out of 13 submitted)
Proclus
UTC: 2:11:18
IM
RC= 0.7184 RO=
0.7335 RO-RC= 0.01515
F= 2.109% PSI= 6.11
UTC: 4:33:43
EM
RC= 0.7159 RO=
0.7288 RO-RC= 0.01286
F= 1.796% PSI= 56.98
Taruntius
UTC: 2: 9:48
IM
RC= 0.7185 RO=
0.7312 RO-RC= 0.01268
F= 1.764% PSI= 1.91
Langrenus
UTC: 2:12:42
IM
RC= 0.7176 RO=
0.7291 RO-RC= 0.01142
F= 1.591% PSI= -3.42
Tycho
UTC: 4:22:52
EM
RC= 0.7172 RO=
0.7260 RO-RC= 0.00881
F= 1.228% PSI= 32.63
Aristoteles
UTC: 2: 3:59
IM
RC= 0.7177 RO=
0.7314 RO-RC= 0.01369
F= 1.907% PSI= 17.49
Dionysius
UTC: 4:26: 6
EM
RC= 0.7175 RO=
0.7287 RO-RC= 0.01122
F= 1.564% PSI= 50.14
Eudoxus
UTC: 2: 2:19
IM
RC= 0.7181 RO=
0.7324 RO-RC= 0.01431
F= 1.992% PSI= 15.45
Manilius
UTC: 4:17:58
EM
RC= 0.7172 RO=
0.7284 RO-RC= 0.01117
F= 1.558% PSI= 54.48
Menelaus
UTC: 4:20:13
EM
RC= 0.7171 RO=
0.7258 RO-RC= 0.00871
F= 1.214% PSI= 55.70
Campanus
UTC: 4:13:14
EM
RC= 0.7172 RO=
0.7298 RO-RC= 0.01258
F= 1.754% PSI= 36.44
Plinius
UTC: 2: 0: 0
IM
RC= 0.7193 RO=
0.7337 RO-RC= 0.01442
F= 2.004% PSI= 4.72
UTC: 4:24:20
EM
RC= 0.7169 RO=
0.7272 RO-RC= 0.01028
F= 1.434% PSI= 55.66
FLATTENING=1/298.26 6 OBS
MEAN FOR IMMERSIONS :
1.8947+-0.0768 % S: 0.19 RD: 0.0405171
A=
0.731847+-0.000850 B= 0.001736+-0.017996
CORRELATION COEFFICIENT=
0.039349
EXP. FLAT.=-0.0023719+-
0.0245901 (1 sig)
1/(EXP. FLAT.)= 1/
-422 (> -19 and < 21) (2 sig=95%)
FLATTENING=1/298.26 7 OBS
MEAN FOR EMERSIONS : 1.5069+-0.0871 % S: 0.23
RD: 0.0578232
A=
0.727916+-0.001967 B=
-0.000185+-0.003345
CORRELATION COEFFICIENT= -0.020957
EXP. FLAT.= 0.0002548+-
0.0045948 (1 sig)
1/(EXP. FLAT.)= 1/
3924 (> -112 and < 106) (2
sig=95%)
MEAN ENLARGEMENT WEIGHED ON
ERRORS: 1.725+-0.058
MEAN ENLARGEMENT WEIGHED ON NUMBER
OF OBSERVATIONS: 1.686+-0.059
WEIGHED MEAN FLATTENING: 0.0001662+-0.0052693 (1 sig)
1/(WEIGHED MEAN FLATTENING): 6017 (between -96 and 93)(2 sig)
GEOM. FACTOR : 1.40257 AND FLAT.
(Meeus)= 1/ 212.7
DIF. ATM. : 0.04+-1.12
Raquel Yumi Shida
(São Paulo, Brazil)
1 timing selected (out of 2 submitted)
Manilius
UTC: 1:51:35 IM
1/298.26
RC= 0.7196 RO=
0.7358 RO-RC= 0.01618
F= 2.248% PSI= 3.51
Observational Astronomy Network (REA/Brazil)
Alexandre Amorim; Antonio Rosa Campos; Raquel Yumi Shida
51 Timings selected (out of 55
submitted)
Umbral Phase Wi:
1.000 We: 0.000
UTC: 1:14:54 U1
RC= 0.7151 RO= 0.7237 RO-RC= 0.00858 F= 1.200%
PSI= -8.81
Proclus Wi: 2.000
We: 2.000
UTC: 2:11:36 IM
RC= 0.7184 RO=
0.7313 RO-RC= 0.01292
F= 1.798% PSI= 6.22
UTC: 4:33:31
EM
RC= 0.7159 RO=
0.7272 RO-RC= 0.01132
F= 1.581% PSI= 57.06
Taruntius Wi:
1.000 We: 0.000
UTC: 2: 9:48 IM
RC= 0.7185 RO=
0.7312 RO-RC= 0.01268
F= 1.764% PSI= 1.91
Aristarchus Wi:
1.000 We: 1.000
UTC: 1:27:45 IM
RC= 0.7177 RO=
0.7324 RO-RC= 0.01468
F= 2.046% PSI= 4.90
UTC: 3:51:16
EM
RC= 0.7153 RO=
0.7237 RO-RC= 0.00835
F= 1.168% PSI= 55.96
Langrenus Wi:
2.000 We: 1.000
UTC: 2:12:47 IM
RC= 0.7176 RO=
0.7284 RO-RC= 0.01074
F= 1.497% PSI= -3.40
UTC: 4:47:12
EM
RC= 0.7157 RO=
0.7276 RO-RC= 0.01195
F= 1.670% PSI= 47.25
Tycho Wi: 1.000 We:
2.000
UTC: 1:37:45 IM
RC= 0.7181 RO=
0.7298 RO-RC= 0.01167
F= 1.625% PSI= -18.02
UTC: 4:23:29
EM
RC= 0.7172 RO=
0.7313 RO-RC= 0.01408
F= 1.964% PSI= 32.57
Aristoteles Wi:
2.000 We: 1.000
UTC: 2: 3:47 IM
RC= 0.7177 RO=
0.7327 RO-RC= 0.01502
F= 2.093% PSI= 17.39
UTC: 4: 5:49
EM
RC= 0.7150 RO=
0.7264 RO-RC= 0.01140
F= 1.595% PSI= 68.50
Dionysius Wi:
0.000 We: 1.000
UTC: 4:26: 6 EM
RC= 0.7175 RO=
0.7287 RO-RC= 0.01122
F= 1.564% PSI= 50.14
Eudoxus Wi:
2.000 We: 1.000
UTC: 2: 2:23 IM
RC= 0.7181 RO=
0.7320 RO-RC= 0.01387
F= 1.931% PSI= 15.48
UTC: 4: 8: 5
EM
RC= 0.7154 RO= 0.7259
RO-RC= 0.01047 F= 1.464%
PSI= 66.54
Grimaldi Wi:
1.000 We: 1.000
UTC: 1:16:15 IM
RC= 0.7165 RO=
0.7250 RO-RC= 0.00854
F= 1.192% PSI= -7.02
UTC: 3:53:46
EM
RC= 0.7147 RO=
0.7263 RO-RC= 0.01151
F= 1.610% PSI= 43.59
Kepler Wi: 1.000 We:
1.000
UTC: 1:26: 5 IM
RC= 0.7185 RO=
0.7344 RO-RC= 0.01586
F= 2.207% PSI= -1.22
UTC: 3:58:40
EM
RC= 0.7164 RO=
0.7290 RO-RC= 0.01259
F= 1.757% PSI= 49.63
Manilius Wi:
2.000 We: 2.000
UTC: 1:51:53 IM
RC= 0.7196 RO=
0.7335 RO-RC= 0.01388
F= 1.929% PSI= 3.61
UTC: 4:17:57
EM
RC= 0.7172 RO=
0.7282 RO-RC= 0.01098
F= 1.531% PSI= 54.49
Menelaus Wi:
1.000 We: 2.000
UTC: 1:56: 4 IM
RC= 0.7195 RO=
0.7335 RO-RC= 0.01401
F= 1.947% PSI= 4.70
UTC: 4:20:31
EM
RC= 0.7171 RO=
0.7281 RO-RC= 0.01103
F= 1.538% PSI= 55.59
Campanus Wi:
0.000 We: 1.000
UTC: 4:13:14 EM
RC= 0.7172 RO=
0.7298 RO-RC= 0.01258
F= 1.754% PSI= 36.44
Plinius Wi:
2.000 We: 2.000
UTC: 2: 0:12 IM
RC= 0.7193 RO=
0.7322 RO-RC= 0.01291
F= 1.794% PSI= 4.79
UTC: 4:24:32
EM
RC= 0.7169 RO=
0.7288 RO-RC= 0.01185
F= 1.653% PSI= 55.59
Pytheas Wi:
1.000 We: 0.000
UTC: 1:38:12 IM
RC= 0.7191 RO=
0.7290 RO-RC= 0.00996
F= 1.385% PSI= 4.80
Timocharis Wi:
1.000 We: 1.000
UTC: 1:43:40 IM
RC= 0.7190 RO=
0.7310 RO-RC= 0.01194
F= 1.660% PSI= 7.58
UTC: 4: 3:31
EM
RC= 0.7165 RO=
0.7277 RO-RC= 0.01122
F= 1.565% PSI= 58.40
M. Crisium Wi:
1.000 We: 0.000
UTC: 2:16:26 IM
RC= 0.7176 RO=
0.7302 RO-RC= 0.01260
F= 1.757% PSI= 6.29
Plato Wi: 1.000 We:
0.000
UTC: 1:54:31 IM
RC= 0.7177 RO=
0.7305 RO-RC= 0.01288
F= 1.795% PSI= 16.90
Stevinus A Wi:
0.000 We: 1.000
UTC: 4:46:31 EM
RC= 0.7163 RO=
0.7277 RO-RC= 0.01137
F= 1.588% PSI= 38.30
Copernicus Wi:
1.000 We: 1.000
UTC: 1:35:14 IM
RC= 0.7193 RO=
0.7314 RO-RC= 0.01209
F= 1.681% PSI= 0.31
UTC: 4: 5: 9
EM
RC= 0.7171 RO=
0.7248 RO-RC= 0.00765
F= 1.066% PSI= 51.21
Laplace Wi:
1.000 We: 1.000
UTC: 1:46:35 IM
RC= 0.7177 RO=
0.7272 RO-RC= 0.00953
F= 1.328% PSI= 14.64
UTC: 3:53:22
EM
RC= 0.7150 RO=
0.7231 RO-RC= 0.00804
F= 1.124% PSI= 65.57
Euler Wi: 1.000 We:
1.000
UTC: 1:34:30 IM 1/298.26
RC= 0.7187 RO=
0.7342 RO-RC= 0.01549
F= 2.155% PSI= 5.33
UTC: 3:58:12
EM 1/298.26
RC= 0.7162 RO=
0.7291 RO-RC= 0.01282
F= 1.790% PSI= 56.23
Totality Wi:
1.000 We: 1.000
UTC: 2:23:29 U2
RC= 0.7149 RO= 0.7274 RO-RC= 0.01251 F= 1.749%
PSI= 13.36
UTC: 3:45: 0 U3
RC= 0.7124 RO= 0.7294 RO-RC= 0.01707 F= 2.396%
PSI= 63.74
FLATTENING=1/298.26 27 OBS
MEAN FOR IMMERSIONS :
1.7621+-0.0530 % S: 0.28 RD: 0.0300963
A=
0.730958+-0.000670 B=
-0.005934+-0.015380
CORRELATION COEFFICIENT= -0.074049
EXP. FLAT.= 0.0081184+-
0.0210415 (1 sig)
1/(EXP. FLAT.)= 1/
123 (> -29 and < 20) (2 sig=95%)
FLATTENING=1/298.26 24 OBS
MEAN FOR EMERSIONS : 1.6101+-0.0563 % S: 0.28
RD: 0.0349509
A=
0.731986+-0.001372 B=
-0.006754+-0.002126
CORRELATION COEFFICIENT= -0.544064
EXP. FLAT.= 0.0092269+-
0.0029047 (1 sig)
1/(EXP. FLAT.)= 1/
108 (> 293 and < 67) (2 sig=95%)
MEAN ENLARGEMENT WEIGHED ON
ERRORS: 1.691+-0.039
MEAN ENLARGEMENT WEIGHED ON NUMBER
OF OBSERVATIONS: 1.691+-0.039
WEIGHED MEAN FLATTENING: 0.0092062+-0.0032438 (1 sig)
1/(WEIGHED MEAN FLATTENING): 109 (between 368 and 64)(2 sig)
GEOM. FACTOR : 1.40243 AND FLAT.
(Meeus)= 1/ 212.7
DIF. ATM. : 1.96+-0.69
Report on the Oct. 28 Lunar Eclipse
Possible Effect of Mount Reventador`s Eruption on Eclipses
in 2003 and 2004