NACCA22

My first attempt at observing a total lunar eclipse was made in 1972 January 30 with Peter Raw the then President of the Canberra Astronomical Society. Since that time another 54 eclipses have been analysed for crater timings leading to the evaluation of the oblateness of the Earth's shadow. Many local and overseas observers have contributed during the 35 years of the project by providing me with many crater timings and images. This paper gives the history of the crater timing and lunar imaging analysis project and the current findings.

The aim of the project was to obtain data points on the umbra as the perimeter of an ellipse, computing their co-ordinates referred to the umbra centre. During the observation of 54 lunar eclipses, timings of up to six umbra contacts with the edges of lunar surface features were recorded as well as mid-contacts of craters.

The Astronomical Ephemeris¹ has always used an approximate value for the oblateness of the atmosphere of the Earth, based on a solid geoid value of 1/298.257. My computer analysis of lunar eclipse timings has enabled an observed value of umbral oblateness to be determined.

Prediction of mid-crater timing immersions and emersions of the umbra were made available to observers prior to each eclipse, to encourage recognition of named features to be practiced prior to the eclipse. Initially, an observer's report form was provided with the predictions for return of crater timings for analysis. Also requested, was that timing of three immersions should be made, that of first contact with the edge of each lunar feature, its centre and second contact with the trailing edge. Additionally, three emersions need to be timed if possible, that of third contact with the emerging edge of the feature, its centre or mid-timing and fourth contact as the feature emerged fully from the umbra. Features such as mountains and bright spots on the lunar surface could be reported as mid timings and each of the four primary contact of the umbra with the Moon should be timed.

Timings should be accurate (synchronised with GPS, VNG or WWV short wave radio time signals) to 0.1 of a second if possible. The definition of the umbra edge is difficult as there is a change from the dark umbra to the stark white of the full Moon. Effort must be made to continually judge the maximum rate of change in the density of the umbra edge for consistent crater timing observations.

Computer programs were prepared in Microsoft" Basic to carry out accurate predictions of crater timings, to find the circumstances of each lunar eclipse, to reduce crater timings to give percent umbral enlargement and the mean error of each observer's data set. Many eclipse data files were prepared for these analysis programs, including lunar and solar ephemerides for each eclipse, crater location and size as well as the statistical data necessary to find observational accuracy and acceptability for the umbral oblateness estimates. These programs are now available from my web pages in QuickBasic 4.5, compatible with Microsoft Windows XP.

Earlier work by Jean Meeus², mathematical development for the single crater timing analysis by David Herald³ and best-fit ellipse mathematics by the late Wilm Nijenhuis⁴ were included in these analysis programs.

Over the 35 years of the project, crater timing observations provided a large amount of data for the umbral enlargement to be found and for the very sensitive estimate of umbral oblateness to be made. See Table 1 for a summary of the accepted crater timings and Table 2 for a summary of the mean observed oblateness.

In 1997 September 16, images were transmitted live for my first web cast over the Internet. This was one of the first web casts made of a lunar eclipse and the response was tremendous, and included an animation of my images⁵at the clouded out Athens Observatory .

In 1998 March 13 it was found that imaging of the penumbra was possible, so from that date any penumbral lunar eclipses visible in Australia were observed in this way. Others⁶ attempted this as well, and interesting images were obtained.

Imaging of lunar eclipses presents a challenge in regard to exposure, brightness and contrast of the Moon and the umbra. An analogue video camera was used successfully to capture images to up-load for "live" web casts and to provide images for measurement of the size of the umbra. A MASS QuickImage 24 frame grabber with a Macintosh IIci computer captured the images and another program, Image Analyst used to measure the radius of a best-fit circle to the imaged umbra calibrated to the known semi-diameter of the Moon. A full image of the Moon was required to achieve this, as shown in the following image and in Figure 1.

For the 50th lunar eclipse of 2005 October 17, the output from a Panasonic digital video camera was fed to a Dell lap-top computer to produced a "live" web cast of 65 images on my web page, similar to the one shown above. In earlier work, the video camera used was an analogue unit, so a frame grabber was required to copy the images in PICT format for measurement - this is illustrated in Figure 1.

It was found that the measured umbral semi-diameter was consistently below the value expected, thought to be due to its projection onto the curved surface of the Moon and possibly, due to change in its size during the period of the eclipse. A software program was written to study this change in geometry, where the imaged umbra was compared to topocentric calculations made for each observing site. Overseas observers also provided many images for this comparative study. Table 3 lists some of the results obtained.

Umbral Enlargement : An aim of the program was to find the enlargement of the umbra from a large number of lunar eclipses based on many individual observer's crater timings. It was found that 7,885 immersion timings gave an umbral enlargement of 2.21 % with a mean error of 0.15 %. These were more consistent than the emersion timings, as each feature could be seen and timed before the beginning of the umbral immersion. Emersion timings were inherently more difficult, as the feature was not revealed before it emerged from the dark umbral shadow. However, a mean value of 2.12 % enlargement with a mean error of 0.17 % resulted from 4,243 emersion timings. It can be seen from the mean errors in Table 1, that the accuracy of each event reflects the variation in difficulty in observing the lunar features.

The actual value of umbral enlargement (%E) varied for each eclipse, but overall the values are within a narrow range particularly for experienced observers. The table summarises mean values for all observers only, but where some observers timed a large number of features for each eclipse, they achieved a very low error of the mean.

Umbral Oblateness : From the large number of crater timings (a total of 12,128 timings are presented in Table 1 in the range of 0<%E<4) it was possible to obtain a meaningful sample of these accurate timings for the very sensitive estimate of umbral oblateness.

The values were found to vary quite widely and are presented in Table 2, however the mean value of reciprocal oblateness for 4,356 immersion timings was 1/153 with a mean standard deviation of 0.05 and for 1,562 emersions it was 1/103 with a mean standard deviation of 0.05.

The height of the upper atmosphere of the Earth can be found from these oblateness values, using R_pas the polar semi-diameter of the Earth, R_e as the equatorial semi-diameter of the Earth and F_i as the observed reciprocal umbral oblateness. With values of the Earth's radii taken from the BAA Handbook⁷ 2001, the following was found:

Difference in the semi-diameter of the outer atmosphere from immersions, with %E = 2.21 and F_i = 102, is:

= R_e(1 + %E/100) - R_p(1 + %E((1 - 1/F_i)/100)
= R_e(1.02210) - R_p(1.02188)
= 6378.140(1.02210) - 6356.755(1.02188)
= 6519.097 - 6495.862
= 23.24 km (the difference in the geoid is 21.39 km)

where the height of the atmosphere at the equator = 140.9 km
and the height of the atmosphere at the pole = 139.1 km
hence, the difference in height is due to the oblateness of the atmosphere, which is only 1.8 km

Improved Lunar Eclipse Ephemeris : An earlier mean observed oblateness of 1/102 was incorporated into an improved lunar eclipse ephemeris⁸(ILEE) to compute the corrected time of primary contacts for lunar eclipses. The program for eclipse circumstances included these time differences for each of the primary contacts for comparison. In the last eclipse observed, that of 2005 October 17, 65 images were captured for a "live" web cast to my web pages and to verify the ILEE predictions for first and fourth primary contacts of this 1 hour long partial eclipse. The results are shown in Figure 3.

Measurements of the Umbra : while it is conceded that the variation in the measurements of the imaged umbral semi-diameter as presented in Table 3 could be questioned, the results speak for themselves, in as much that there is a consistency in the values which are all well below the expected umbral semi-diameter F₂. At first contact with the Moon the measured umbral size is lowest due to the greatest curvature of the Moon's surface. The size of the umbra slowly increases at second contact as this curvature decreases, is greatest at mid-eclipse, and decreases near third contact when the Moon begins to emerge from the umbra, and again with increasing curvature, it has a lowest value near fourth contact.

Measurements taken indicate a slow increase in umbral size to mid-eclipse followed by a similar decrease to fourth contact. A computer program was written to find the expected measured semi-diameter of the umbra throughout any lunar eclipse with allowance for topocentric effects for the site of the observer. Computed values for the eclipse of 2001 July 5 for my site, then in Calwell, Australia are shown in Figure 2 where the change in geometry of the umbra can be seen. F_i is the measured semi-diameter of the umbra, delta is the slant angle to the umbra edge and Poly. (F_i) is the sixth order best fit polynomial to F_i.

Mean values of measurements made of the size of the umbra from seven eclipses were found to be 0.42 degrees near first contact, 0.61 near second contact, 0.57 near mid-eclipse, 0.52 near third contact and 0.47 near fourth contact. These measured values should be compared with the expected mean umbral semi-diameter of 0.73 degrees as shown in Table 3.

However, mean values of measurements made of the size of the umbra from two eclipses using a new measuring engine, Digimizer were found to be near the expected values but still showing a change in umbral size similar to my earlier measurements. These latest measured values should be compared with the expected mean umbral semi-diameter as shown in Table 4.

A large number of crater timing observations have yielded observed umbral enlargement within a narrow range of 2.12 % for emersion timings to 2.21 % for immersion timings, both very near the expected value of 2 %.

A mean umbral oblateness value of 1/153 has been derived from a large number of immersion crater timings and 1/103 from emersion timings, where both values are approximately three times that of Earth's geoid value (or flattening), of 1/298.257. The values obtained were incorporated into an improved lunar eclipse ephemeris to provide more exact prediction of primary contact times of lunar eclipses. The ILEE computed primary contact times have been verified in those eclipses where due to their geometry, the effect of umbral oblateness is greatest.

A small number of images of the umbra measured, show low values and a change in the umbral geometry, suggesting that variations in the size of the umbra may occur during a lunar eclipse, however measures of two recent eclipses with Digimizer have shown that the measured umbra semi-diameter is near the expected values but exhibits a change in umbral size similar to my earlier measures.

It was found that imaging of the penumbra is possible and reasonable processed images were obtained from several penumbral eclipses.