domingo, 1 de novembro de 2015

Analysis of Observations of the 2015 Sep. 28 Total Lunar Eclipse

Helio C. Vital
lunissolar@gmail.com 
REA/Brasil - Lunissolar

Unfavorable Weather Conditions for Most Brazilian Observers

Unfortunately, a huge storm system caused 90% of the potential Brazilian observers, mostly located in São Paulo, Rio de Janeiro and Florianópolis, to be clouded out during the eclipse. However, we were still able to gather 8 Danjon estimates (L) and 2 series (curves) of L. We also got an extensive sequence of contact timings made in Belo Horizonte by the CEAMIG/REA team in addition to many photos of the totally eclipsed moon. Based on such data, we were able to determine how dark the eclipse was as well as how large the contribution of Earth`s atmosphere to the umbra currently is.

How Dark Was the Eclipse?

The total lunar eclipse of September 27-28, 2015 was moderately dark as we had already predicted in our Observation Project. It was not very dark as many observers claimed, even though the brightness of the eclipsed Moon was found to be dimmer by approximately 50 thousand times at mid-totality in comparison with the Full Moon.

Danjon Number Estimates

A very easy way to estimate the brightness of an eclipse is to find the prevailing coloration of the Moon. This very simple and practical method was proposed by Danjon and, although it is not as accurate as direct estimates of magnitude, it is also informative.

Danjon Estimates (L) Made Easier

When considering how we could help beginners make Danjon estimates, we elaborated the following procedures, also suggesting that extreme values (like L=0) should be avoided:

Alex`s Danjonmeter

Alexandre Amorim, an astronomer with large observational experience, had a very creative idea before the eclipse: the observer would download, to his cell phone, a color scale Alex called Danjonmeter. During totality, he would hold up his phone in order to position the color scale next to the Moon in order to compare the color of the Moon with those on the scale. He would then assign a value of L according to the prevailing color he saw.

Helio`s 3-Band Danjonmetry

Helio C. Vital proposes another simple procedure to estimate the Danjon Number. His idea is to split the disc of the Moon in three parts or bands and assign a value of L to each of them. The approximate percentage of each part relatively to the whole disc must also be estimated. Note that they must add up to 100%. Then a simple weighed sum will yield a good figure for the Danjon Number. As an example, by inspecting some photographs of totality posted on SpaceWeather, he could create a mean mental image of the Moon at mid-totality. It was structured as follows: there was a yellowish bright band to the Southeast covering some 25% of the disc and he assigned L=3 to it. Next to it, he could see a central reddish band spreading across roughly 45% of the disc and he gave L=2 to it. Finally, to the Northeast he could notice a dark band spanning about 30% of the disc and he estimated it had L=1. Then his Danjon Estimate for the entire disc of the Moon would be: L= 0.25 x 3 + 0.45 x 2 + 0.30 x 1 = 1.95 (bull`s eye, see Table 1).

Estimates of the Danjon Number

Estimates of the Danjon Number (L) gathered from 10 Brazilian observers are listed in Table 1. Two of them* were calculated for mid-eclipse from parabolic fitting to series of estimates.


Observers who would have made Danjon estimates but reported negative observations due to cloudy skies were: Alexandre Amorim  (and several members of NEOA-JBS in Santa Catarina), Antonio Padilla Filho, Márcio Mendes and Helio C. Vital.

In our project of observation for the 2015 September 27-28 total lunar eclipse we had predicted a Danjon Number of L=2.2±0.4 (1σ) at mid-eclipse, already accounting for a probable darkening effect due to lingering stratospheric aerosols from eruptions of Calbuco (VEI=4) on April 22-23, 2015.

Indirect Estimates of the Visual Magnitude of the Moon at Mid-Eclipse

Unfortunately, due to bad weather, direct estimates of the visual magnitude of the Moon using the perfected version of the reversed binoculars method were not made. However, we can use our correlation that relates the Moon`s visual magnitude to Danjon Number. Thus, entering our mean estimate for the Danjon Number:

m = 4.2 – 3 L + (L/2)2 =  4.2 – 3 (1.93) + (1.93/2)2 = -0.7±0.6

Determining the Magnitude of the Totally Eclipsed Moon from Photos

Analyses of several wide angles photos of the eclipse, contributed by Cristóvão Jacques (CEAMIG/REA), led us to conclude that the Moon was shining approximately 2 magnitudes brighter than Alpha Piscis Austrini (m=1.17), after properly accounting for the different color of the star. The estimated magnitude of the Moon based on the photos was m = -1.1±0.5.

A mean of both estimates yields a final figure with a smaller associated error:

m= -0.9±0.4

Such value is also consistent with a finding made by Willian Souza that he could not see the Moon at mid-totality through his reversed binoculars, known to dim the image by 4.8 magnitudes. Willian knew that his magnitude limit was around 4.0±0.5. So he concluded that the Moon could not be brighter than -1.3. 

How Dark Was Earth`s Atmosphere?

The observed magnitude agreed very well with our predictions (-1.2±0.8) accounting for the most likely darkening effects due to Calbuco aerosols that we had forecast to cause +1.3 magnitude drop. An aerosol-free condition for the stratosphere would have produced a moderately bright eclipse as the Moon would be shining at m=-2.5 at mid-totality. The dimming of 1.6 mag found would also typically correspond to the darkening effect due to an eruption of Volcanic Explosivity Index equal to 4, that would peak some 5-7 months later, such as the one that happened to Calbuco on April 22-23  (five months prior to the eclipse). Then we had a moderately dark, not a very dark one, as many observers claimed. The explanation for that false impression could possibly be the fact that many of those observers over the last decade could watch bright eclipses only. And they were brighter because they were not significantly darkened by volcanic dust, besides having low umbral magnitudes.

At mid-eclipse, the total drop in the Moon`s brightness reached 11.8 magnitudes, corresponding to a dimming of 50 thousand times. An observer standing on the Moon`s surface would then see a bright ring surrounding Earth`s dark silhouette. That narrow mostly red ring produced by Earth`s atmosphere would be shining at m≈ -15, some 8 times brighter than the Full Moon. Moving from the extreme North of the lunar disc to its South, the observer would see that ring brighten, turning from rust red into orange as he approached the center of the disc. Finally it would brighten further, becoming mostly yellow by the time he got to the Southern part of the Moon as he also approached the border of the umbra.

How Thick Was the Shadow-Casting Layer of Earth`s Atmosphere?

That analysis requires contact timings. Fortunately, Antonio Rosa Campos and his CEAMIG/REA team had clear skies during the entire eclipse and they obtained a fine data set that included 43 selected limb and mid-crater timings. Let us then see what those numbers have in store for us, in spite of the fact that hundreds of contacts, contributed by many observers, would be the ideal data set to work with in order to get very good statistics. Table 2 lists the mid-crater and limb contact times observed by Campos and the corresponding percentage increase in Earth`s radius (or in the Moon`s parallax) due to Earth`s atmosphere.

Table 2 – Contact Times (UTC) Observed by Campos and Corresponding Increase in the Moon`s Parallax (or Earth`s Radius) due to Earth`s Atmosphere

The value found for the contribution of Earth`s atmosphere, 1.27±0.08 %, is approximately halfway between its 1.20% minimum (apparently reached last year) and its all-time average (1.35%). It is also in good agreement with our prediction, extrapolated from figures of the April 15, 2014 (1.20%) and April 4, 2015 (1.22%) eclipses. Note that our contact times for this eclipse had been calculated by using increments of 1.27% for immersions and 1.23% for emersions as informed in our Observation Project for the 2015 September 27-28 Total Lunar Eclipse. The increase of 1.27% in Earth`s radius found for this eclipse would correspond to a mesopausic height of 81±5 km and it would be produced by a thin atmospheric light ring only 47 arcseconds thick if observed from the Moon.

Photos and Videos of the Eclipse

The CEAMIG/REA observers` team (in Belo Horizonte) posted nice photos, videos and an advanced report on their Sky and Observers Pages.

Final Considerations on Lunar Eclipse Predictions

Improving predictions of lunar eclipses demands a great deal of observational data (contact timings and estimates of the Moon`s magnitude, mostly). However, visual observers of such events are now very rare in spite of the fact that the science of lunar eclipses is essentially observational. Thus in order to predict the circumstances of these events better, it is fundamental to further understand the several mechanisms that play a significant role in the complex movie of our upper atmosphere that is projected onto the sensitive lunar screen.  Up to now, the major official sources of information on lunar eclipses have failed to fully acknowledge and widely inform that the intricate dynamics of Earth`s upper atmosphere severely limits the accuracy of their predictions. Not to mention the fact that they still rely on the same model for calculation of Earth`s umbra that Danjon used more than a century ago. However as ironic as it may seem and in contrast to what most people believe, the cause of the “missing totality” of the tetrad on April 4 was not the use of an outdated model. In fact its prediction (mag.=1.0001) was closer to the observed figure (mag.=0.9996) than the one (mag=1.0020) calculated with a sophisticated model used by Sinnott-Herald and myself.  The villain that ruined most predictions on that day was Earth`s atmosphere, that had almost shrunken to its minimum size. Consequently, when the onset of totality required a minimum 1.25% increase of Earth`s radius on that day, it could only provide 1.22%.

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