The observatory logo, the first image analysed from the 1990 February 9 lunar eclipse
Video records of lunar eclipses have been measured by image
analyst techniques to determine the geometry of the umbra. A new
procedure has been developed to compute the topocentric umbral sizes
for each observing site from geocentric data. The topocentric values
are compared with the video umbral measures to determine change in
the size of the umbra during the 1996 total lunar eclipses of
September 27 and April 3-4, and the partial lunar eclipse of 1995
April 15. Update: Recently,
still images have been used for greater
accuracy in measurement.
Keywords: lunar eclipse, umbra, topocentric value
1 INTRODUCTION
Video records of lunar eclipses have been measured by image
analyst techniques for the semi-diameters of the umbra and moon to
determine the geometry of the umbra. As these images are topocentric,
a procedure has been developed to compute the expected topocentric
umbral semi-diameter for each observing site from geocentric data.
The topocentric values of umbral size have been compared with the
measurement of video images to determine change in the the umbra
during both 1996 total lunar eclipses of September 27 and April 3-4
and the partial lunar eclipse of 1995 April 15. Update: Recently, still
images of several lunar eclipses in 2007 and 2008 have been measured.
2 PROCEDURE
The total lunar eclipse of 1996 September 27 was observed at Recife, Brazil by the Universidade Federal de Pernambuco where the team lead by Jose Fernando Tepedino provided "real-time" video images of the eclipse via the Internet. The total lunar eclipse of 1996 April 3-4 was observed by two astronomers in Portugal and one in Belgium, they both used video cameras to record a series of lunar images for analysis.
Captured frames from the real time images and video records
have
been digitised and measured (Soulsby, 1995) using the commercial
software, Image Analyst Version 8.0, running on a
Macintosh
IIci computer. Update: I now
use Digimizer
as a measuring engine on a MacBook/Parallels/Windows XP.
A diagrammatic of the geometry of a typical lunar eclipse is
shown
in Figure 1, with the radius of the moon (Sc)
eclipsed by the umbra of geocentric radius
(F2) and computed
topocentric umbral
radius (Fi). A
computer program (ViaX7.exe) has been
prepared to find
the topocentric semi-diameter of the umbra by
applying the cosine rule to triangle OMC, as well as the other
parameters given in Figures 1 and 2 (also described in Soulsby,
1995). The program finds the topocentric umbral radius (Fi) for each
observer's site using the following geometry and expressions at the
time each
measured image is captured:
3 MEASUREMENT COMPARISON
The analysis of the measurements of captured frames before and after totality from the Internet images provided by the Universidade Federal de Pernambuco, in Brazil are shown in Figure 3 below. The analysis of the measurements of captured frames before and after totality from the video record by the astronomer Marques, in Portugal are shown in Figures 4 and 5.
In these figures the presumed static theoretical geocentric semi-diameter of the umbra (F2) is shown with the measured umbral radii (Ru) and the computed topocentric semi-diameter of the umbra. The topocentric values are compared with each measurement of the apparent umbral semi-diameter taken from the video frames. The computed slant angle ([Delta]') of the umbral edge to the lunar plane, also defined in Figure 2, is included for each image time in Figure 3. The departure of each measured diameter from the computed topocentric value shows the change throughout the eclipse. This is also shown as a smoothed (dashed) line in the figures as an estimate of the change in umbral size.
4 PARTIAL LUNAR ECLIPSE OF 1995 APRIL 15
Several observers in Australia provided video records of the partial lunar eclipse of 1995 April 15 (Soulsby, 1995). These are re-analysed in a similar manner using the measured image umbral radii (Ru) for comparison with the topocentric corrected values (Ft). These are compared with the assumed static geocentric theoretical value (F2) and the computed topocentric values (Fi). The results from Bennett and Sture for this eclipse are shown in Figures 6 and 7 below:
4 CHANGE IN UMBRAL SIZE
By comparing the measured semi-diameters of umbral images with the computed topocentric values, dynamic change in umbral geometry is detected. For observations of the eclipse of 1996 September 27 made in Brazil, the departures show a large spread due to the small image size and low quality, but give a general umbral increase both before and after totality.
For the eclipse of 1996 April 3-4 observed in Portugal, a decrease in umbral size was determined before totality and an increase after totality, each around 0.1 of a degree. A similar departure between the umbral measurements and topocentric umbral semi-diameters was found from the video record by Garcia, whom also observed in Portugal. There is considerable spread, but the nominal increase before totality is near that found for the other Portuguese observations.
The 1996 data suggests that change in umbral geometry occurred during both lunar eclipses, probably due to variation in transparency and/or cloud cover in the Earth's atmosphere.
Two other sets of scattered data for the partial lunar eclipse
of
1995 April 15 from the observers Bennett and Sture, Australia gave a
general decrease in umbral semi-diameter of around 0.2 of a degree.
Update:
A recent lunar eclipse of 2008
February 21
provided results for a comparison of computed topocentric umbral
size and image measurement. In this comparison it can be seen that the
image
measurements and the computed topocentric values are very close. A
comparison of the measured umbral semi-diameter and
computed
topocentric umbra size for Bernard Durand's images can be seen here.
5 CONCLUSIONS
In work reported earlier (Soulsby, 1995, 1994) the puzzling result of consistently low values of measured umbral semi-diameters taken from video records near first and fourth contact has now been resolved by considering computed topocentric values of umbral semi-diameter at the time of each image frame. Most umbral measurements, and those corrected to topocentric values by other techniques (Soulsby, 1995) are now much closer to the computed topocentric semi-diameters. The previously large difference between the measured umbral semi-diameter and the static geocentric values has been resolved.
Even though there is some large scatter for the 1995 April 15
partial lunar eclipse measurements and the corrected topocentric
values, these now compare well with the computed topocentric values.
There appears to be a measurable, but slow dynamic change in umbral semi-diameter during these three lunar eclipses, although the scatter suggests that improved image quality and accuracy in their measurement should be persued. Update: Recent measurements of the 2008 February 21 total lunar eclipse show good comparison with the computed topocentric umbral data.
6 COMMENTS
One problem with the image analysis technique is associated with the high magnification used by most observers. A preferred value (around 84 X) is that which provides a complete image of the moon during all stages of the eclipse, as this greatly assists image calibration and measurement. Most video images tend to be overexposed, due in part to both high magnification and high telescope aperture. An improvement in image contrast (by reducing the effective aperture, but not by filtering) would also assist measurement analysis of future lunar eclipses.
The video imaging and measurement technique requires improvement, but it is the only known approach where change in the upper atmosphere of the Earth can be detected during lunar eclipses. By improved refinement, it may also be possible to measure dynamic change in umbral oblateness in addition to the change in size presented here.
The exciting prospect of obtaining live video images from lunar eclipses not visible in Australia has been achieved for the first time for the 1996 September 27 total lunar eclipse, thanks to the team in Brazil. They provided me with my "first" day time lunar eclipse.
Update: The images of the
2008 February 21 eclipse provided
the best
results so far in this project, and images from
Bernard Durand and Jay Pasachoff have provided important data.
7 ACKNOWLEDGMENTS
The author would like to express his thanks to the astronomers whom have contributed to this research by providing video records. In particularly to those overseas observers who have provided video records and real-time Internet images of the moon in eclipse when such lunar eclipses are not visible in Australia.
8 REFERENCES
Update: see http://www.netspeed.com.au/minnah/2008/LE2008-1.html
Soulsby, B.W., 1995, Analysis of the 1995 April 15 partial lunar eclipse, Aust. J. Astr., (6)2: 33-52.
Soulsby, B.W., 1994, Change during lunar eclipses, Proc. 16th Natn. Aust. Conv. amat. Astrer., Canberra, pp 101-114.
Meeus, J., 1991. Astronomical Algorithms, pp 263-4. Willmann-Bell Inc. 429 pp.