quarta-feira, 1 de abril de 2015

The April 04 2015 lunar eclipse, most likely total

Helio C. Vital
(Lunissolar Section Coordinator)

A lunar eclipse will be visible from western North America, eastern Asia, the Pacific and Oceania as the Moon will cross the northern half of Earth`s shadow on April 4, 2015. It is expected to be a very interesting event due to the fact that at 12:00 UT its umbral magnitude will probably barely exceed 1.00. It is thus within the range of current uncertainties associated with the size of Earth`s umbra (the darker inner region of Earth`s shadow). Consequently, as surprisingly as it may seem, this time it may not be utterly appropriate to simply predict that it will be a total eclipse.

It has been widely known for centuries now that in order to reproduce the observed radius of the shadow cast by our planet, an enlargement factor must be used in the lunar eclipse calculations. The most rigorous way to do so is to assume that such excess is due to the influence of Earth`s atmosphere, that would slightly increase the visible size of our planet or, more accurately, the equatorial horizontal parallax of the Moon, that is the predominant term in the models for calculation of the size of Earth`s umbra.

However, for reasons not yet fully understood, that contribution varies significantly not only from one eclipse to another, but also during the eclipses themselves, as we have concluded from the analyses of seven thousand contact timings. Furthermore, systematic and statistical observational errors only partially explain the variations. Therefore indications are that they are also due to: (1) random localized physical disturbances in the mesopause, that cause some observed mean contact times of craters to depart significantly from calculations, superimposed on (2) diurnal and semidiurnal cycles of air density fluctuations at the top of the mesosphere, that would explain fairly significant (3–7%) differences in the observed heights of the optically active atmosphere, found to be consistently higher during the entrance of craters in the umbra. A rough analogy that can be used to understand those two effects would be to consider the roughened surface of the sea, with localized waves produced by the wind, sea depth etc, adding to tidal effects, which cause the mean level of the sea to oscillate.

As example of such variations, we estimated the atmospheric contribution to the radius of the umbra as 1.258% during the eclipse on May 25, 1975 based on analyses of 583 crater and limb contact timings. Such value contrasts with 1.435% determined from the 672 timings of the July 06, 1982 eclipse. Those extreme figures differ in 14% and can be compared with our overall mean of (1.343±0.058) %. The corresponding height of that atmospheric layer can be simply determined by multiplying that value by Earth`s equatorial radius such that 0.01343 x 6378 = 85.7±3.7 km.

In our analyses, predicted and mean observed contact times have usually agreed within ±0.3% (≈±0.3 min.) with roughly 1/5 of crater timings departing more than that, up to ±0.5%. By using our program to predict umbral contacts times, we entered different values for the atmospheric enlargement (or contribution) and calculated the corresponding durations of totality as listed in Table 1:

Note how the duration of totally becomes sensitive to the height of the optically active layer of Earth`s atmosphere, a mere 5-meter causing a difference of 11.7 seconds between options 6 and 7. Option 3 refers to NASA Fred Espenak`s predictions of 4m43s for totality. By using our programs, it was possible to calculate the values for the parameters that would reproduce it. Our prediction for duration of totality is 6 minutes and 47 seconds considering the atmospheric contribution remains close to its all-time mean. 

Also for this particular event, the probability of a total eclipse can be roughly estimated based on our statistics of thirty past events. Assuming a normal distribution; recalling the mean percent value of the atmospheric Moon`s parallax as 1.343 and its sample standard deviation as 0.058; and also using the minimum threshold value for detection of totality (listed as option 6 in Table 1 as 1.2500, we find that such value is (1.343-1.250)/0.058 = 1.6 standard deviations below the mean. Then the probability of the umbra being larger than that, meaning a total eclipse, can be obtained from Gaussian Tables as 95%. In other words, we can say that the chance of this eclipse being partial is only 5% or 1 chance in 20. Strictly speaking, that is as far as we can go.

As a guide for those willing to time the advance of Earth`s umbra across the lunar disc, Table 2 lists our predictions, considering ∆T=67.8s. The calculations are based on mean values found in our statistical analyses of observed data from more than 30 lunar eclipses. Different values were used for immersions and emersions.

Analyses of both the duration of totality as well as crater and limb contacts timed during this event could be used to accurately determine the size of the umbra during the eclipse. Thus the science of lunar eclipses still thrives on them. So please send us your crater timings (lunissolar@gmail.com). During totality, sunlight passes through Earth`s atmosphere and, after being partially absorbed and scattered, a small fraction of it is refracted towards the Moon. Consequently, an observer on the lunar surface would observe a bright ring shining around Earth`s dark silhouette, corresponding to our backlit atmosphere. That initially bluish-white ring would gradually become reddish as deeper and darker layers of our atmosphere would increasingly contribute to its appearance and so would the very sensitive lunar screen, illuminated by it.

The brightness of the Moon during totality depends primarily on how deep it is inside the umbra and also on how clean our stratosphere is. During this event, the path of the Moon through the umbra will most probably be as shallow as it can be for a total eclipse. Since the outer regions of the umbra are less dark, that would contribute to make it a bright eclipse. In addition, since no major volcanic eruptions have occurred recently, the stratosphere is expected to be free of volcanic dust, its major source of pollution.

Consequently, this eclipse is expected to be roughly as bright as a total clipse can be. In terms of visual magnitude, our expectation is that at mideclipse, the Moon will be shining at m=-3.5±0.3. Since such estimates are rare and valuable, please share yours with us and good luck on your observations. 

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