Analysis of Observations of the
2018 July 27 Total Lunar Eclipse Reported by Brazilian Observers
During totality the Moon acts as a
sensitive screen that can help us understand the complex dynamics of the many
physical and chemical processes that occur in the middle atmosphere. Thus by
studying such events, we can improve our ability to predict the observed
variations in the size of Earth`s shadow and the effects of stratospheric
volcanic eruptions, that may severely darken the totally eclipsed Moon. Almost
three decades devoted to predicting, observing and analyzing lunar eclipses
have provided us with sufficient knowledge to predict not only contact times
(craters and limb) but also the brightness of eclipses. Such predictions have
been published on Lunissolar prior to the events since 2003.
In response
to our project of observation, 15
observational reports of the 2018 July 27 total lunar eclipse, made by
Brazilian astronomers, were analyzed in order to determine the atmospheric
enlargement of Earth`s shadow and the brightness of the eclipse.
Determining the Size of Earth`s
Umbra
A total of 49 limb and mid-crater
timings of emersions made by 4 experienced observers were received. Based on a
2σ
criterion, 44 of them were selected and analyzed by a program developed by the
author in order to determine the enlargement effect produced by the atmosphere
on the umbra and the corresponding increase in Earth`s figure (expressed as a
percent enlargement in the horizontal parallax of the Moon). The mean
calculated enlargements for each observer are listed in Table 1.
Table 1 - Mean Umbral and Lunar Parallax Enlargements Calculated from
Observed Contact Times |
|||
Observer`s Name |
Number of Selected Timings |
Mean Enlargement of
the Umbra (E%) |
Mean Enlargement of the
Lunar Parallax (π%) |
Antonio Rosa Campos |
14 |
1.478±0.152 |
1.052±0.108 |
Helio de Carvalho Vital |
18 |
1.866±0.035 |
1.328±0.025 |
Robert Magno |
10 |
2.016±0.146 |
1.435±0.104 |
Willian Carlos Souza |
2 |
2.523±0.055 |
1.795±0.040 |
All 4 Observers |
44 |
1.807±0.058 |
1.286±0.041 |
Then the
corresponding mean enlargements obtained by weighing on the number of
observations, expressed with their corresponding uncertainties (±1σ, accounting
for personal bias as well as statistical variations summed in quadrature) are:
<E>= 1.807±0.133 %; <π>=1.286±0.095 %.
These mean
figures for the radius of the umbra are in very good agreement with those
published by the author before the eclipse. They are also slightly lower than
our overall averages (<E>=1.85% and <π>=1.34%). The analysis of mean contact timings is
provided below, expressed both as umbral and parallax
enlargements, respectively. The mean net time difference per timing between
calculated and observed contact times was indeed very small for calculations based
on the author`s predictions using π = 1.286% for this eclipse (calculated from a
correlation still to be published): +0.32s per timing (indicating no
significant advance nor delay), as compared with those based on models adopted
by the two official sources of predictions: -7.8s for NASA (π = 1.00%, a simplified
formula proposed by Danjon a century ago) and +5.7s
for Sky&Tel (a more sophisticated model recently
proposed by Herald-Sinnott based on π=1.36%). Although lower
than the mean uncertainties associated to observed contacts, the comparison
suggests that there is still room for improvements in predictions of this type
of astronomical event, which justifies the painstaking efforts the author has made
in the analyses of many thousand lunar eclipse timings during almost three
decades now.
Umbral Enlargement Factors from Mid-Crater Timings
By Helio
C. Vital
MID-ECLIPSE DATE: 27.8484/ 7/2018
DT: 69.120 MOD: 7
TYPE: UMB FLAT: 298.25722
VITAL, CAMPOS, MAGNO, SOUZA - 2018JUL27
UMBRAL ENLARGEMENT (E%)
U4 CONTACT: Partiality Ends Wi: 0.000 We: 2.000
UTC: 22:19:19 EM 1/298.26
RC= 0.63978 RO= 0.65103 RO-RC=
0.01125 E= 1.75810% PSI=
15.010
CRATER: Proclus Wi: 0.000 We: 1.000
UTC: 22:10:20 EM 1/298.26
RC= 0.64225 RO= 0.65881 RO-RC=
0.01656 E= 2.57781% PSI=
21.422
CRATER: Taruntius Wi: 0.000 We: 1.000
UTC: 22:11:14 EM 1/298.26
RC= 0.64248 RO= 0.65715 RO-RC=
0.01467 E= 2.28406% PSI=
17.511
CRATER: Copernicus Wi: 0.000 We: 2.000
UTC: 21:36: 1 EM 1/298.26
RC= 0.64334 RO= 0.65615 RO-RC=
0.01281 E= 1.99096% PSI=
22.022
CRATER: Langrenus Wi: 0.000 We: 2.000
UTC: 22:15:24 EM 1/298.26
RC= 0.64176 RO= 0.65494 RO-RC=
0.01319 E= 2.05464% PSI=
11.749
CRATER: Tycho Wi: 0.000 We: 3.000
UTC: 21:40:46 EM 1/298.26
RC= 0.64284 RO= 0.65468 RO-RC=
0.01183 E= 1.84104% PSI=
3.163
CRATER: Aristoteles Wi: 0.000 We: 1.000
UTC: 21:49: 3 EM 1/298.26
RC= 0.64157 RO= 0.65458 RO-RC
0.01301 E= 2.02732% PSI=
34.103
CRATER: Dionysius Wi: 0.000 We: 2.000
UTC: 21:57: 9 EM 1/298.26
RC= 0.64358 RO= 0.65507 RO-RC=
0.01149 E= 1.78596% PSI=
17.669
CRATER: Eudoxus Wi: 0.000 We: 1.000
UTC: 21:50:22 EM 1/298.26
RC= 0.64196 RO= 0.65602 RO-RC=
0.01406 E= 2.19058% PSI=
32.376
CRATER: Grimaldi Wi: 0.000 We: 1.000
UTC: 21:16:23 EM 1/298.26
RC= 0.64120 RO= 0.65020 RO-RC=
0.00901 E= 1.40469% PSI=
18.017
CRATER: Kepler Wi: 0.000 We: 1.000
UTC: 21:26:28 EM 1/298.26
RC= 0.64274 RO= 0.65150 RO-RC=
0.00876 E= 1.36280% PSI=
22.282
CRATER: Bullialdus Wi: 0.000 We: 1.000
UTC: 21:58:22 EM 1/298.26
RC= 0.64340 RO= 0.65453 RO-RC=
0.01113 E= 1.72952% PSI=
8.918
CRATER: Manilius Wi: 0.000 We: 2.000
UTC: 21:52:10 EM 1/298.26
RC= 0.64344 RO= 0.65720 RO-RC=
0.01375 E= 2.13706% PSI=
22.404
CRATER: Menelaus Wi: 0.000 We: 2.000
UTC: 21:55:43 EM 1/298.26
RC= 0.64330 RO= 0.65708 RO-RC=
0.01379 E= 2.14310% PSI=
22.755
CRATER: Campanus Wi: 0.000 We: 2.000
UTC: 21:33:20 EM 1/298.26
RC= 0.64307 RO= 0.65505 RO-RC=
0.01197 E= 1.86187% PSI=
8.545
CRATER: Billy Wi: 0.000 We: 2.000
UTC: 21:22:19 EM 1/298.26
RC= 0.64233 RO= 0.64963 RO-RC=
0.00731 E= 1.13731% PSI=
14.432
CRATER: Plinius Wi: 0.000 We: 2.000
UTC: 21:59:45 EM 1/298.26
RC= 0.64315 RO= 0.65638 RO-RC=
0.01323 E= 2.05678% PSI=
22.093
PEAK: Pico Wi: 0.000 We: 1.000
UTC: 21:38:25 EM 1/298.26
RC= 0.64190 RO= 0.64755 RO-RC=
0.00565 E= 0.88071% PSI=
34.096
CRATER: Pytheas Wi: 0.000 We: 2.000
UTC: 21:35:18 EM 1/298.26
RC= 0.64300 RO= 0.65537 RO-RC=
0.01236 E= 1.92289% PSI=
26.027
CRATER: Nicolai Wi: 0.000 We: 1.000
UTC: 21:55: 1 EM 1/298.26
RC= 0.64264 RO= 0.65085 RO-RC=
0.00821 E= 1.27699% PSI=
2.130
CRATER: M. Crisium Wi: 0.000 We: 3.000
UTC: 22:13:38 EM 1/298.26
RC= 0.64156 RO= 0.65457 RO-RC=
0.01301 E= 2.02765% PSI=
21.500
CRATER: Plato Wi: 0.000 We: 3.000
UTC: 21:38:13 EM 1/298.26
RC= 0.64152 RO= 0.65028 RO-RC=
0.00876 E= 1.36526% PSI=
35.559
CRATER: Birt Wi: 0.000 We: 2.000
UTC: 21:42:31 EM 1/298.26
RC= 0.64360 RO= 0.65472 RO-RC=
0.01112 E= 1.72791% PSI=
9.673
CRATER: Censorinus Wi: 0.000 We: 1.000
UTC: 22: 5: 7 EM 1/298.26
RC= 0.64316 RO= 0.65505 RO-RC=
0.01189 E= 1.84794% PSI=
15.795
CRATER: Stevinus Wi: 0.000 We: 1.000
UTC: 22: 6:53 EM 1/298.26
RC= 0.64192 RO= 0.64690 RO-RC=
0.00497 E= 0.77468% PSI=
4.051
U3 CONTACT: Totality Ends Wi: 0.000 We: 2.000
UTC: 21:13:49 EM 1/298.26
RC= 0.63950 RO= 0.65316 RO-RC=
0.01366 E= 2.13675% PSI=
23.089
FLATTENING=1/298.25722 44 OBS
MEAN FOR EMERSIONS: 1.8065+-0.0579% S: 0.38430 RD:
0.0320706
PARALLAX ENLARGEMENT (π%)
MID-ECLIPSE DATE: 27.8484/ 7/2018
DT: 69.120 MOD: 7
TYPE: Pi FLAT: 298.25722
VITAL, CAMPOS, MAGNO, SOUZA - 2018JUL27
U4 CONTACT: Partiality Ends Wi: 0.000 We: 2.000
UTC: 22:19:19 EM 1/298.26
RC= 0.63978 RO= 0.65103 RO-RC=
0.01125 Pi=
1.24994% PSI= 15.010
CRATER: Proclus Wi: 0.000 We: 1.000
UTC: 22:10:20 EM 1/298.26
RC= 0.64225 RO= 0.65881 RO-RC=
0.01656 Pi=
1.83476% PSI= 21.422
CRATER: Taruntius
Wi: 0.000 We:
1.000
UTC: 22:11:14 EM 1/298.26
RC= 0.64248 RO= 0.65715 RO-RC=
0.01467 Pi=
1.62585% PSI= 17.511
CRATER: Copernicus Wi: 0.000 We: 2.000
UTC: 21:36: 1 EM
1/298.26
RC= 0.64334 RO= 0.65615 RO-RC=
0.01281 Pi=
1.41777% PSI= 22.022
CRATER: Langrenus Wi: 0.000 We: 2.000
UTC: 22:15:24 EM 1/298.26
RC= 0.64176 RO= 0.65494 RO-RC=
0.01319 Pi=
1.46207% PSI= 11.749
CRATER: Tycho Wi: 0.000 We: 3.000
UTC: 21:40:46 EM 1/298.26
RC= 0.64284 RO= 0.65468 RO-RC=
0.01183 Pi=
1.31071% PSI= 3.163
CRATER: Aristoteles Wi: 0.000 We: 1.000
UTC: 21:49: 3 EM 1/298.26
RC= 0.64157 RO= 0.65458 RO-RC=
0.01301 Pi=
1.44252% PSI= 34.103
CRATER: Dionysius Wi: 0.000 We: 2.000
UTC: 21:57: 9 EM 1/298.26
RC= 0.64358 RO= 0.65507 RO-RC=
0.01149 Pi=
1.27191% PSI= 17.669
CRATER: Eudoxus Wi: 0.000 We: 1.000
UTC: 21:50:22 EM 1/298.26
RC= 0.64196 RO= 0.65602 RO-RC=
0.01406 Pi=
1.55895% PSI= 32.376
CRATER: Grimaldi Wi: 0.000 We: 1.000
UTC: 21:16:23 EM 1/298.26
RC= 0.64120 RO= 0.65020 RO-RC=
0.00901 Pi=
0.99932% PSI= 18.017
CRATER: Kepler Wi: 0.000 We: 1.000
UTC: 21:26:28 EM 1/298.26
RC= 0.64274 RO= 0.65150 RO-RC=
0.00876 Pi=
0.97019% PSI= 22.282
CRATER: Bullialdus Wi: 0.000 We: 1.000
UTC: 21:58:22 EM 1/298.26
RC= 0.64340 RO= 0.65453 RO-RC=
0.01113 Pi=
1.23163% PSI= 8.918
CRATER: Manilius Wi: 0.000 We: 2.000
UTC: 21:52:10 EM 1/298.26
RC= 0.64344 RO= 0.65720 RO-RC=
0.01375 Pi=
1.52187% PSI= 22.404
CRATER: Menelaus Wi: 0.000 We: 2.000
UTC: 21:55:43 EM 1/298.26
RC= 0.64330 RO= 0.65708 RO-RC=
0.01379 Pi=
1.52607% PSI= 22.755
CRATER: Campanus Wi: 0.000 We:
2.000
UTC: 21:33:20 EM 1/298.26
RC= 0.64307 RO= 0.65505 RO-RC=
0.01197 Pi=
1.32568% PSI= 8.545
CRATER: Billy Wi: 0.000 We: 2.000
UTC: 21:22:19 EM 1/298.26
RC= 0.64233 RO= 0.64963 RO-RC=
0.00731 Pi=
0.80951% PSI= 14.432
CRATER: Plinius Wi: 0.000 We: 2.000
UTC: 21:59:45 EM 1/298.26
RC= 0.64315 RO= 0.65638 RO-RC=
0.01323 Pi=
1.46451% PSI= 22.093
PEAK: Pico Wi: 0.000 We: 1.000
UTC: 21:38:25 EM 1/298.26
RC= 0.64190 RO= 0.64755 RO-RC=
0.00565 Pi=
0.62675% PSI= 34.096
CRATER: Pytheas Wi: 0.000 We: 2.000
UTC: 21:35:18 EM 1/298.26
RC= 0.64300 RO= 0.65537 RO-RC=
0.01236 Pi=
1.36908% PSI= 26.027
CRATER: Nicolai Wi: 0.000 We: 1.000
UTC: 21:55: 1 EM 1/298.26
RC= 0.64264 RO= 0.65085 RO-RC=
0.00821 Pi=
0.90906% PSI= 2.130
CRATER: M. Crisium Wi: 0.000 We: 3.000
UTC: 22:13:38 EM 1/298.26
RC= 0.64156 RO= 0.65457 RO-RC=
0.01301 Pi=
1.44274% PSI= 21.500
CRATER: Plato Wi: 0.000 We: 3.000
UTC: 21:38:13 EM 1/298.26
RC= 0.64152 RO= 0.65028 RO-RC=
0.00876 Pi=
0.97141% PSI= 35.559
CRATER: Birt Wi: 0.000 We: 2.000
UTC: 21:42:31 EM 1/298.26
RC= 0.64360 RO= 0.65472 RO-RC=
0.01112 Pi=
1.23059% PSI= 9.673
CRATER: Censorinus Wi: 0.000 We: 1.000
UTC: 22: 5: 7 EM 1/298.26
RC= 0.64316 RO= 0.65505 RO-RC=
0.01189 Pi=
1.31581% PSI= 15.795
CRATER: Stevinus Wi: 0.000 We: 1.000
UTC: 22: 6:53 EM 1/298.26
RC= 0.64192 RO= 0.64692 RO-RC=
0.00500 Pi=
0.55382% PSI= 4.051
U3: Totality Ends Wi: 0.000 We: 2.000
UTC: 21:13:49 EM 1/298.26
RC= 0.63950 RO= 0.65316 RO-RC=
0.01366 Pi=
1.51896% PSI= 23.089
FLATTENING=1/298.25722 44 OBS
MEAN FOR EMERSIONS
: 1.2858+-0.0412 % S:
0.27356 RD: 0.0320729
Determining the Brightness of the
Eclipse
The totally eclipsed Moon was very
low when attempts of estimating its brightness had to be made about half an
hour after sunset. However, in spite of the challenging
observational conditions and the very poor contrast, a few observers bravely
succeeded in the task, which allowed us to use 3 different approaches in order
to determine the brightness of the eclipse. Five
observers reported Danjon estimates: Antonio Rosa Campos
(L=0.5), Willian Carlos Souza (L=0.5), Helio de Carvalho Vital
(L=2), Saulo Machado Filho (L=3) and Audemário Prazeres (L=3). The arithmetic mean is
L=1.8±0.5 and can be converted into the visual magnitude of the Moon by using a
correlation derived by the author (Eq.1). Thus m= 4.2 – 3 (1.8)
+ (1.8/2)2 = -0.4±1.0. It is
interesting to note that the Moon was seen lower (and consequently darker and
colorless due to atmospheric extinction) by observers situated further to the
west. Consequently, they assigned to the eclipse L=0.5. In contrast, those that
observed the event past midtotality, from the
Northeastern Region of Brazil, saw the Moon higher, brighter and colorful, thus assigning to
it L=3.
In addition, photographs of the
Moon at mideclipse taken by observers in Europe and Africa, consistently showed a dark red Moon almost
homogeneously illuminated at its center with a slightly brighter rim. Also, an
amazing "out-of-focus yellow ring" was the first image of the totally
eclipsed Moon seen through the author`s camera 27 minutes after its rise time
(in agreement with his own prediction). Then,
remembering that the Danjon Scale for Lunar Eclipse
Brightness assigns L=2 to a "Deep red or rust-colored eclipse with a very
dark central shadow, while the outer edge of umbra is relatively bright" (which
corresponds to m=-0.8±0.4), we can indeed confirm that the eclipse was dark.
Estimates of the visual magnitude
of the totally eclipsed Moon were also reported. They were made by using as a
reference bright Mars in opposition, as it was shining at m=-2.8 only 7o
from the Moon and 2.8o higher than it. Initially expressed as
fractions of the brightness of Mars (FI=I/Io), they were
converted into magnitude differences (Δm=2.5log(FI)),
which were then corrected for differential atmospheric extinction before
being expressed as visual magnitudes as listed in Table 2. Apparently, the Moon
was several times dimmer than Mars though it quickly recovered to surpass it
just a couple of minutes before the end of totality (U3).
Table 2 - Estimates of the Visual
Magnitude of the Totally Eclipsed Moon by Helio C.
Vital |
|||||||||
Time (UTC-3h) |
Fraction of hour
after Midecl. (x) |
Fraction of
Brightness of Mars (Fi) |
Magnitude Difference |
Altitude of Mars (o) |
Atmospheric
Extinction of Mars |
Altitude of the Moon
(o) |
Atmospheric
Extinction of the Moon |
Differential
Atmospheric Extinction |
Corrected Visual
Magnitude of the Moon (m) |
17:52 |
0.500 |
1/6 |
1.9 |
8.2 |
1.9 |
5.4 |
2.7 |
-0.8
(=1.9-2.7) |
-2,8+1,9-0,8=-1,7 |
17:57 |
0.583 |
1/3.5 |
1.4 |
9.2 |
1.6 |
6.4 |
2.3 |
-0.7 |
-2,1 |
18:03 |
0.683 |
1/2 |
0.7 |
10.5 |
1.5 |
7.7 |
2.0 |
-0.5 |
-2,6 |
18:07 |
0.750 |
2/3 |
0.4 |
11.3 |
1.4 |
8.5 |
1.8 |
-0.4 |
-2,8 |
18:09 |
0.783 |
1 |
0.0 |
11.7 |
1.4 |
9.0 |
1.7 |
-0.3 |
-3,1 |
18:12 |
0.833 |
4/3 |
-0.3 |
12.3 |
1.3 |
9.6 |
1.6 |
-0.3 |
-3,4 |
A fitting function in
the form m=-0.72-3.9x2
can than then be used to smoothly describe the light curve of the totally
eclipsed Moon throughout the observation. It indicates that m=-0.7±0.3 (corresponding
to L=1.9) was the
minimum brightness of the totally eclipsed Moon. Such figure closely agrees not only with our
predictions, but also with the previous estimates explained above.
The result indicates that there was no additional darkening due to recent
volcanic eruptions (because they did not inject significant amounts of aerosols
into the stratosphere). Then the reason this eclipse seemed darker than most
eclipses observed in the last decades was because the Moon crossed the center
of Earth`s shadow where the amount of sunlight reaching the Moon was 12
magnitudes lower than usual. Then at maximum eclipse, Earth`s atmosphere,
backlit by the occulted Sun, would have appeared to an observer on the Moon as
a very thin dark red ring of light shining at m=-14.7, a fascinating refracted
image produced by the sum of all sunrises and sunsets in progress on Earth at
that moment.
Acknowledgments
The author wishes to
thank all observers that have contributed by sending reports and thus making
this work possible. Namely, their contributions and names can be listed as
follows:
(1) Contact timings: Antonio Rosa Campos, Robert Magno, Willian Carlos Souza, Helio
de Carvalho Vital
(2) Estimates of Eclipse Brightness
(Danjon Numbers): Saulo Machado Filho, Antonio Rosa Campos, Willian Carlos
Souza, Audemário Prazeres, Helio de Carvalho Vital
(3) Estimates of
Eclipse Brightness (Visual Magnitudes and Light Curve): Helio de Carvalho Vital
(4) Photos: Ricardo Vaz
Tolentino, Audemário
Prazeres, José Guilherme Aguiar, Marcelo Oliveira, Márcio Rodrigues Mendes, Willian Carlos
Souza, Beatriz Felicidade, Helio de Carvalho
Vital
(5) Negative
Observations from Clouded out Observers: Alexandre Amorim, Antonio Padilla Filho,
Rodolfo Langhi, Marcos Jerônimo
Barreto
Thanks also go to the
excellent site http://www.mondfinsternis.net/ that through many years now has supported
our work (briefly described elsewhere by Sinnott and Herald-Sinnott among
others) by posting citations and links to our Lunissolar.
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