THE_PENUMBRA and The_Umbra
or earthShadows


by Byron Soulsby

Isabella Plains Lunar Observatory Australia



atmosphere


The atmosphere of the Earth is studied by observing its shadow on the Moon.


Abstract

Software has been developed to compute the topocentric semi-diameter of the penumbra and umbra so that comparison can be made with eclipse images taken from any known geographic location. These images are calibrated to the semi-dimater of the Moon and the shadow of the Earth's atmosphere is measured either as penumbral or umbral semi-diameters. Measurement of images from two penumbral, two partial and two total lunar eclipses, (as well as an historical series) are compared with the computed values resulting in good agreement giving confidence in the theory, computation and measurement.


A movie showing the relative movement and angle of tilt of the Moon relative to the Earth is here. Near the Points A and C the alignment of the Sun, Earth and Moon is such that the penumbra and umbra, the shadow of the Earth is projected onto the curved surface of the Moon. By analysing images of lunar eclipses taken at these times the actual geometry of the shadow of the Earth can be accurately assessed for any observer on the Earth's surface. My original theory, programs and methods of measurement are described below.



kaguya

A very unusual view of the occulted Sun by the Earth during the penumbral lunar eclipe 20090209.


Introduction - The_Penumbra

Images of past penumbral lunar eclipses have provided interesting results, where the outer faint shadow of the Earth can be detected on the Moon's surface and then measured for its size or semi-diameter.

    A modified geometry of the topocentric penumbra has been prepared so that estimates of its size can be made and compared with measured images. A computer program, ViaX8.exe has been developed to compute the expected topocentric semi-diameter of the penumbra (Fp) from any known site. Another program ILEEP41.exe is used to generate the required data for the observer's site used by the first program.

    In 1998 and 2006, images were obtained of the penumbra which were successfully measured, but until now no comparison with the estimated semi-diameter of the penumbra has been possible.


Measurements

A calibrated and measured image of the penumbra is shown below, taken from a series of images by Bengt Ask observing in Svalov, Sweden (latitude 13o06'27.9" E, longitude 55o54'47.5" N, elevation 59m) during the 19980313 penumbral lunar eclipse. When measured with Digimizer (after calibration to the Moon's semi-diameter of 0.2458o, converted to greyscale, sharpened and then rotated left for measurement) this image gives a topocentric semi-diameter of  1.041o for the penumbra, lower than the geocentric value of 1.1949o given by Fred Espenak.

123pen123pengs

Further images by Bengt Ask for this eclipse have been measured in a similar manner to the above and then compared with the computed values of Fp. Here, the image processing was by ImageJ to highlight the penumbra which was then measured with Digimizer. Two of the images measured are shown below, the first taken at 4h10m (where Fp = 1.022o ) and the other at 4h 05m (Fp = 1.041o ):
Computed Fp

I have used my original theory and software to compute the expected topocentric penumbral semi-diameter for any location.  The pdf file here shows the computed Fp values compared with the image measurements for Bengt's observing site at Svalov, Sweden.

Bengt Ask also observed and took images of the 20010109 total lunar eclipse where a few measurements were obtained, one for the penumbra and two for the umbra. These results are shown here.


Another (slightly out-of-focus) image captured at 9h43m03s (UT) of the penumbral lunar eclipse of 20011230 at the Calwell Lunar Observatory (35o26'25.6"S, 149o05'16.6"E, 586m) is shown below on the left. The image was processed by Gamma correction under Preview and clearly reveals the penumbra at upper right as shown:


image 627627 gamma

The image was measured by Digimizer and compared with the computed topocentric penumbra as can be seen here.

The above measurements are supplemented by a further set of images by Sabahattin Bilsel, who observed the partial lunar eclipse of 20060907 from his site (37o06'09.1" N, 27o20'54.8" E, 70m) in Istanbul Turkey. One of his images is shown below where the penumbra has been measured at 1.314o, very near the geoid value of 1.3139o. 


Additional observations of this eclipse by David Herald from Kambah Australia (35o23'49.3" S, 149o03'48.8" E, 583m) were by a high quality 8mm movie to confirm my predicted early first contact time of the umbra due to its oblateness. Images from the movie were measured by Digimizer providing excellent agreement with the computed umbra (Fi). The results for 20060907 from the two observers can be seen here.

20060907


Historical Series
I have converted several historical records from images on earlier web pages, one recorded on VHS video to DVD, and others recorded on 8mm video to DVD. DVD capture software has been used for frames for measurement by Digimizer.  These can be seen at 20030516 and 20031109 from images by Willian deSouza, 19900209 from a VHS video recorded by the author in Paradise, South Australia and an 8mm movie to DVD of the 19930604 eclipse recorded by the author also at Paradise as well as the 19970916  8mm movie to DVD by the author recorded in Calwell ACT - this last eclipse was affected by intermittent cloud.

A set of digital images of the penumbral lunar eclipse of 20020526 has also been analysed with excellent agreement between the computed topocentric penumbral semi-diameter and measurements of five images as can be seen here.

The total lunar eclipse of 19670424 was observed by David Herald from Box Hill, Victoria. This event has been analysed as a check on my software after the generation of new data for the Moon and for the Sun. Initially it was computed for Soulsby at Elizabeth, South Australia and then for Box Hill to see if the topocentric output differed. The results can be seen here.

These records have added weight to the evidence that measurement of lunar eclipse images can validate my topocentric theory for umbral and penumbral predicted geometry.

Comments

It is interesting to note the comparison in the data sets produced for each eclipse. Due to the curvature of the Moon, it is logical to expect the projected shadow from the Earth to be initially zero at first penumbral contact (P1) increasing rapidly to near the Geoid value given in the classical ephemeris. Similarly, the Moon's curvature causes the penumbra size to drop from a steady value to zero at the final penumbral contact (P4) at the end of the eclipse. It is important that the topocentric penumbra size is computed only while its edge is on the Moon's surface. This is allowed for in the software.

Conclusions

The measured penumbra taken from the sets of high quality images provided especially by Bengt Ask and Sabahattin Bilsel, have enabled conclusive proof of my topocentric penumbra theory and computation. For the first time these measurements have provided data points for the increase in the penumbra size correlating closely to that computed.
It has also been shown that the observed penumbra increases in size from zero at first contact rising rapidly towards the expected ephemeris value and then falling towards zero as the penumbra edge leaves the surface of the Moon.


Introduction - The_Umbra

The measurement of 31 images of the umbra for the total lunar eclipse of 20080221 provided by Bernard Durand observing in France, has enabled a comparison to be made with the computed topocentric umbral semi-diameter for his site.

Good agreement between the data sets was obtained and it has been conclusively shown that the umbra increases in size from primary contact to a value near the geocentric umbral semi-diameter.


Measurements
The image below illustrates a typical measurement of one image where the umbral semi-diameter (Fi) has been measured with a calibrated image of the eclipsed Moon (red circle) with the best fit circle set to coincide with the edge of the umbra. The value of Fi was 0.646 o. The software used for measurement is Digimizer.




Computed Fi

I have developed an original theory and software to compute the expected topocentric umbral semi-diameter for any location. Bernard provided his observing site co-ordinates at  "Le Sauze du Lac", France (44o28'39"N, 6o18'48"E,1050m) and the pdf file here shows the computed Fi values for 20080221 compared with the image measurements. These images are supplemented by a further set provided by Jay Pasachoff (42o42.7'N, 73o12.1'W, 215m) and these result can be seen here.


Bernard also provided a further set of images for the total lunar eclipse of 20080816 observed from "La Roche des Arnauds" (44o33'43"N, 5o59'32"E, 1169m), which have been similarly analysed along with my images of this eclipse observed from Isabella Plains (35o25'52.2"S, 149o05'16.6"E, 586m) and those images by Gerhard Dangl from Nonndorf, Austria (48.79oN, 15.24oE, 542m). The charts have been prepared for the actual location of each of the three observers, and good comparison has been found for all measured values. The overall results are shown here.

It is possible to measure the inner and outer umbra where the transition from dark to light in an ImageJ contour trace across the umbra edge is pronounced, as shown below for one of my images 1065:

                                                   Inner umbra
Contour of 1065
          Outer umbra
 

Comments

It is interesting to note the comparison of computed and measured values in the two data sets. Due to the curvature of the Moon, it is logical to expect the projected shadow from the Earth to be initially zero at first primary contact (1C) and then increasing rapidly to a value very near the Geoid value given in the classical ephemeris (for the eclipse of 20080221 the Geoid value is 0.6983o at 1C to 0.6969 o at 4C and for 20080816 around 0.6901o). It can also be seen that the Moon's curvature causes the umbra size to drop to zero at totality, rise from zero at third contact to the maximum and again decrease toward zero at fourth contact at the end of the eclipse.


Conclusions

The measured umbra taken from two sets of high quality images provided by Bernard Durand has enabled conclusive proof of my topocentric umbra theory and computation. For the first time measurements of eclipse images have provided data points for the increase in the umbra size correlating closely to that computed.

It has been conclusively shown that the observed umbra increases in size from zero at first contact rising rapidly to the expected ephemeris value and falls towards zero when the umbra edge is not traversing the surface of the Moon.



I believe this is the first time the characteristics of the penumbra and umbra have been adequately examined.


Acknowledgments

I am indebted to David Herald, Bengt Ask and Sabahattin Bilsel for the excellent images provided of the 19980313, and the 20010109 and 20060907 eclipses and for their interest early in this project.

I am also very thankful to Willian DeSouza, Gerhard Dangl and Bernard Durand for their many excellent images of past and more recent lunar eclipses, and for their vital interest in this project.



References

The web pages for the Soulsby series of lunar eclipses.

My geometry for the computer program for the determination of the topocentric penumbral size.

A summary of observers and images measured can be seen here.

A BookSmart has been prepared, the earthShadows book proof (first 15 pages only) can be seen here.
 


Produced by the Isabella Plains Lunar Observatory Australia, 20090308.