Analysis of Observations of the 2018 July 27 Total Lunar Eclipse Reported by Brazilian Observers

Helio C. Vital

 

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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