ANALYSIS OF THE TOTAL LUNAR ECLIPSE OF

1997 September 16

There is an update of some of the observational aspects of this eclipse here.

Amended 1998 April 1, changed 2001 March 30

another Calwell Lunar Observatory page

Abstract:

Live images of the Total Lunar Eclipse of 1997 September 16 were successfully transmitted to the Internet from the Calwell Lunar Observatory. This resulted in tremendous interest from many overseas and local web browsers. Three animations have been placed onto my Home Page, one at low-resolution using the live images and cameos from Sweden during totality, another from Switzerland.

The techniques used for image capture and web-transfer, the telescope remote control and image analysis methods are presented along with some of the e-mail highlights generated by this live world wide web project.


Introduction

The very successful live capture of images of the moon during the recent total lunar eclipse of 1997 September 16 are discussed. The weather in the Canberra area was superb with about five minutes of cloud during the complete eclipse. Two CCD cameras recorded the complete eclipse on video tape from first contact to moon set. Sequential images were transmitted live to the Internet from a low resolution colour camera while another monochrome high resolution camera also recorded images. Both sets of images have been calibrated and measured to determine the geometry of the umbra.

Animations were prepared from both sets of images and these have been placed onto my Internet Home Page at

Animations

with colour images from Sweden included in one sequence to cover totality. A third animation from coloured images received from Switzerland were also included in the web page.

The live eclipse project proved to be highly successful and generated considerable amount of e-mail concerning the live images of the eclipse and the animations, while many crater timing observations were received for analysis.

Image Capture

The instrumentation used for image capture, illustrated in Figure 1 consisted of two refractor telescopes both fitted with CCD cameras. The telescopes were attached to a quartz driven equatorial mounting. One instrument was a 400 mm telephoto lens, with a 20 mm eyepiece focussed into a Sony Handycam colour CCD video camera with its time generator adjusted to UT. The other instrument was a 40 mm aperture Unitron with a 12.5 mm eyepiece focussed into a Mintron 650 line monochrome CCD surveillance camera.

Both instruments were fitted with lens hoods, UV and yellow filters to reduce full moon glare with the Unitron eyepiece also fitted with a lunar filter. The electronic shutter of the Sony Handycam was used to further reduce glare and the Unitron was masked to 50 % aperture from full moon to second contact. Neither camera was sensitive enough to record totality or stellar occultations, as it would have been difficult to remove and refit the filters while at the same time, transferring images to the Internet.

Instruments_100K

Figure 1: Instrumentation.

Telescope remote control

The relatively light weight twin telescope instrumentation was selected in place of my 150 cm Newtonian to achieve the required low magnification with a complete image of the moon in each field and to enable satisfactory remote control on both axes of the equatorial mounting.

The right ascension axis was quartz driven and easily adjusted by remote control through a cable from the observatory to the computer to maintain the image of the moon in the vignetted field of the Sony Handycam. The declination axis was also remotely controlled by a 6.3 volt DC 200:1 geared motor, but proved to be very sensitive to the inertia of the two mounted telescopes and CCD cameras. After very exact balancing, good drift correction in both directions was established. Even so, the imaged moon was temporarily lost during totality and was not re-acquired until 2 to 3 minutes after third contact. The moon was tracked to moon-set over the Brindabella Mountains with only minor interference from light cloud and from one tree on the horizon.

Web-transfer

As images were captured using my QuickImage 24 frame grabber and Macintosh IIci computer they were saved for later analysis, processed from *.PICT files to *.GIF files using Graphic Converter and "put" to my Home Page using the File Transfer Protocol (ftp) software Anarchie. Each transferred image was reviewed with my Netscape 3.0 web browser, with all ISP proxies off, browser cache set to 0 Megabytes and Auto load images set to on.

A drama occurred about 2 hours before the eclipse commenced when I discovered that my ISP security set-up prevented access to my web page for file up-loads. However, when alerted the manager quickly restore my access which allowed my very first LIVE broadcast of a lunar eclipse to the Internet to proceed.


Image Analysis Methods

Each captured CCD image was examined with Image Analyst, a commercial software package ideally suited for the calibration of the moon and measurement of the umbra. One image result is shown in Figure 2 where calibration of the moon is shown in the Measure box with the true moon's semi-diameter of 0.2789 degrees at the image time of 17h 34m 13s (UT). The measurement of the umbral semi-diameter is by a best-fit-circle placed at the maximum rate of change of brightness at the umbra edge (shown in figure 2 as a green line with its best-fit-circle in blue) using a greyscale of 50 adjusted in the Histogram box.

It is important that the region of interest (ROI) is correctly set to achieve optimum fit of the limb (the red box in figure 2) and the umbra (the yellow box). Configuration of the ROI measurement parameters are also required for optimum fit to the moon and umbral images.

Analyst_43K

Figure 2: Image Analyst calibration of the moon and best-fit-circle measurement of the umbra

Umbral change

Measurements of umbral semi-diameter during the lunar eclipse are compared with the computed topocentric umbral geometry at the location of each observatory. The umbral semi-diameter best-fit measurements obtained from each of the Calwell Lunar Observatory Mintron CCD images are shown in Figure 3.

Figure 3: Computed topocentric umbra, angle of incidence and Image Analyst data plot of umbral radius measurements and change

A good result for the mean change in umbral size was obtained by comparing the measured images from the Calwell Lunar Observatory high resolution Mintron CCD images with the computed topocentric umbral geometry as shown in Figure 3.

However, the measured images for both the Calwell low resolution Sony CCD images and the Switzerland sites gave a less satisfactory result for the umbral change during the early phase of the eclipse as each was affected by an unusual mathematical discontinuity in the computed topocentric umbral semi-diameter just after the commencement of the eclipse.

The high resolution Mintron CCD images of Figure 3 were analysed at 3 minute intervals with a break at totality. The computed topocentric umbra gave a typical smooth result, while the departure of each measured image was a little scattered, it produced a mean increase in umbral geometry of 0.2 degrees (from 0.15 to 0.35 degrees) over the complete lunar eclipse.


A video received from Poland in March this year has also been analysed, a typical image analysis for umbral semi-diameter is given in Figure 3A. Other images were analysed after totality at 5 minute intervals and the mean change in umbral geometry from the Topocentric values is shown in Figures 3B and 3C below.

Figure 3A: Image Analyst showing umbral radius measurement of a Warsaw image from a video by Marek Zawilski received in March 1998

The computed topocentric umbra (Fi) gave a reasonably smooth result, while the departure of each measured image (Fi-Ru) was a little scattered, a consistent mean increase in umbral geometry of 0.6 to 0.7 degrees was seen over the last part of this eclipse. These values of umbral change are similar to that found from the Calwell images, that is a general increase, but the numerical values are nearly double that found from the Southern hemisphere data.

Figures 3B and 3C: Measurements from the Lodz and Warsaw images


Crater timing analysis

To date, seventeen observers have reported crater timings made during the eclipse. These have been analysed to give the % umbral enlargement and for those that meet the statistical criteria, the oblateness of the umbra.

Plot2_30K

Figure 4: A typical oblateness result from Bethanga observations

The detailed results for the other observers are shown in the up-dated Table 1 for umbral enlargement and Table 2 for the best-fit-ellipse umbral oblateness estimates.


 

ANALYSIS OF LUNAR ECLIPSE OBSERVATIONS

by Byron W. Soulsby, CALWELL LUNAR OBSERVATORY, AUSTRALIA

Statistical acceptance used is 0 < %E < 4

CRATER TIMING REDUCTIONS FOR 1997 SEPTEMBER 16

 

IMMERSIONS on the left and EMERSIONS on the right

 

OBSERVER

 

NUMBER

MEAN %E

MEAN ERROR

NUMBER

MEAN %E

MEAN ERROR








ANDERSON, PETER

34

1.8319

0.1176




PRICE, ROBERT & ELIZABETH

67

2.0619

0.1027




CASTANO, JOSE GOMEZ




31

1.7744

0.1411

GARCIA, ALBERTO SICILIA




3

0.9291

0.1395

BARONI, SANDRO




18

1.8991

0.0771

BUECHNER, REINHOLD




15

1.7630

0.0921

BULLING, ANDREAS

7

2.5602

0.2739

18

2.0223

0.1006

RAPAVA, DANIELA

25

2.2184

0.0667

29

2.0350

0.0838

KEREKESOVA, KATARINA

19

2.0217

0.1211

11

2.2461

0.1190

HANUS, ROMAN

14

2.1396

0.0923

16

1.9686

0.1210

AMBROZ, JAROSLAV

11

1.5989

0.2032

19

1.9327

0.1497

PAPISTA, ADRIAN

7

2.0161

0.3339




DZAFIC, OLIVER

6

2.2242

0.2355

4

2.7730

0.3261

HILL, JOHN




9

2.3690

0.1241

CLARK, MAURICE L

124

2.2457

0.0736

26

2.0472

0.2066

RIGBY, PAUL

14

2.3492

0.2076

13

1.5756

0.3409

OVERALL MEAN %E FOR 328 IMMERSIONS IS 2.1298 +/- 0.1100 %

 

OVERALL MEAN %E FOR 212 EMERSIONS IS 1.9476 +/- 0.1420 %

 

VALUES OF F & FM ARE 298.26, 221.181

DATE: 12-03-1997 AT TIME 11:29:34

 


OBLATENESS ESTIMATES FOR 1997 September 16

Statistical range is 0 to 4 %

Table 2: Crater Timing reductions - Umbral oblateness.

 

OBSERVER Location

TYPE

 

O or T

No

Ecc

Re

Rp

Fo

SD

SK'










ANDERSON, PETER The Gap, Queensland, Australia









IM

O

34

0.1206

0.7626

0.7571

137.0288

0.0694

1.6141

IM

T

34

0.0792

0.7443

0.7420

318.1485

0.0443

0.6952

PRICE, ROBERT & ELIZABETH Bethanga, Victoria, Australia









IM

O

67

0.1748

0.7733

0.7614

64.9347

0.0940

3.4062

IM

T

67

0.0916

0.7456

0.7425

237.7645

0.0476

0.9303

BULLING, ANDREAS Munich Germany









IM

O

7

0.1182

0.7617

0.7563

142.6841

0 89

1.5501

IM

T

7

0.0874

0.7451

0.7423

261.1243

0.0621

0.8470

EM

O

18

0.1612

0.7681

0.7580

76.4383

0.0414

2.8936

EM

T

18

0.0794

0.7447

0.7423

316.7152

0.0198

0.6984

RAPAVA, DANIELA Observatory Rimavska Sobota, Slavokia, Europe









IM

O

25

0.0625

0.7574

0.7559

-

0 38

0.4319

IM

T

25

0.0864

0.7448

0.7420

267.6563

0.0537

0.8264

EM

O

29

0.1036

0.7610

0.7569

185.9242

0 50

1.1896

EM

T

29

0.0743

0.7443

0.7422

361.4879

0.0168

0.6119

KEREKESOVA, KATARINA Observatory Rimavska Sobota, Slavokia, Europe







IM

O

19

0.0838

0.7567

0.7540

284.3632

0 59

0.7778

IM

T

19

0.0849

0.7447

0.7420

277.1448

0.0520

0.7981

EM

O

11

0.1375

0.7665

0.7592

105.3316

0.0288

2.0999

EM

T

11

0.0738

0.7443

0.7422

366.4977

0.0150

0.6035

HANUS, ROMAN Observatory Rimavska Sobota, Slavokia, Europe









IM

O

14

0.1100

0.7636

0.7590

164.7509

0.0743

1.3425

IM

T

14

0.0789

0.7441

0.7418

320.4432

0.0512

0.6902

EM

O

16

0.2474

0.7829

0.7585

32.1797

0.0584

6.8733

EM

T

16

0.0827

0.7449

0.7424

291.9637

0.0189

0.7576

AMBROZ, JAROSLAV Observatory Rimavska Sobota, Slavokia, Europe









IM

O

11

0.2335

0.7622

0.7411

36.1658

0 59

6.1158

IM

T

11

0.0936

0.7455

0.7423

227.7056

0.0592

0.9713

EM

O

19

0.1037

0.7609

0.7568

185.3158

0.0260

1.1935

EM

T

19

0.0671

0.7439

0.7422

443.6515

0.0169

0.4985

CLARK, MAURICE L, Western Australia.


IM

O

124

0.0503

0.7576

0.7566

-

0.0092

0.2799

IM

T

124

0.0946

0.7458

0.7424

222.8462

0.0559

0.9925

EM

O

26

0.2108

0.7769

0.7594

44.5066

0.0616

4.9696

EM

T

26

0.0966

0.7460

0.7425

213.6985

0.0277

1.0350

 

VALUE OF FM (RECIPROCAL) = 221.18

DATE OF RUN 12-03-1997 AT TIME 11:31:34

Nomenclature:

No = number of crater timings (IM = immersions, EM = emersions)

O or T = Observed or Theoretical analysis

Ecc = eccentricity of elliptical umbra

Re = equatorial semi-diameter of umbra in degrees

Rp = polar semi-diameter of umbra in degrees

Fo = observed reciprocal oblatness from best-fit-ellipse

SD = standard deviation of data

SK' = ratio of Fo to geoid oblateness (1/298.3)

FM (RECIPROCAL) = Value of umbral oblateness from geometric considerations ( see Meeus)


Table 1 shows an expected umbral enlargement of very near 2 % and Table 2 the range of observed reciprocal umbral oblateness from those observers whom met the statistical creteria for their crater timings. For a complete list of individual crater timing reductions for all observers see: Individual crater timing reductions

e-mail Highlights

A recent report received from my Internet Service Provider (ISP) included some startling figures concerning access to the Home Page during the week of the eclipse. A staggering 55,000 or more "hits" on the page were recorded on eclipse day as shown in the following graph.

My ISP has also provided ongoing statistics for access to my Home Page on a daily basis, see: Home Page stats.

And here are just a few of the hundreds of e-mail queries and reports received, starting with the most recent on 1997 October 3 from Egypt.


From Cairo Egypt:

Thanks for your recent info about the eclipse time in Cairo. We had a wonderful view sitting on the roof of our building, 13 stories up. A number of the neighbourhood kids also joined us and I passed your info on to some of the teachers in my school. None of these people knew about it beforehand as there's not a lot of information about such things in the local press. The time was exactly right, though an hour later (20.08) due to Egyptian summer time being 3 hours ahead of GMT, but I knew that. Summer time here runs from the last Thursday night in April to the last Thursday night in September, generally - nothing is sure in Egypt. (A few years ago, Ramadan was in May, so we changed to summer time as normal, then winter time again for Ramadan, so people could eat at an earlier time in the evening, then we changed back to summer time when Ramadan ended. It was very confusing.) We spent about 2 hours watching the eclipse then the kids had to go in for they had school next day, but we kept looking out till it finished.Thanks again for giving us the chance to see such a beautiful sight.

Eva Abdin


From Germany:

Subject: Your eclipse transmission was great!

Dear colleague,

When the Lunar Eclipse of last week started, the moon had not risen here in Germany, but many people had already arrived at Bonn Observatory in anticipation. So I printed out a current picture of the progressing penumbral phase from your feed and brought it down to the crowd. Immediately some news photographers got hold of me and the picture - how that looked in the paper (Bonner Rundschau) the other day, see

http://www.astro.uni-bonn.de/~dfischer/MOFIDAFI.GIF

Regards, Daniel

Bonner_31K


From Brazil:

Congratulations on your live eclipse coverage. We watched many of your images of the eclipse. Yours was the only WWW site which showed so many pictures of the event. I had notified many colleagues of your transmission so that I think many of them also monitored your WWW pages. I read it was a bright eclipse as expected.

Greetings from Brazil.

Helio C. Vital (vitalhc@centroin.com.br).


From the BAA United Kingdom:

I'm afraid that the BAA observations of the eclipse on the 16th are likely to be held up for a while. Alan Wells gets the Lunar Section Circular duplicated at the college where he teaches, and the last issue seems to have been held up in the rush at the beginning of the academic year. I volunteered to collect the eclipse data, but my article asking that the data should be sent to me, which should have been sent out at the beginning of September, is still stuck in the log-jam. So I suppose that any observations will be sent to Alan. I'm sure you will get some results eventually, but it may take a bit of time. Judging by the weather forecast maps, most of the South of England was fairly clear but a bit hazy. The North may have been less good. I saw most of the emersion (from Sussex), but the low Eastern elevation meant that I had to migrate to the front garden with 20x80 binoculars to avoid houses. There were some clouds blowing across the Moon that messed up some of my timings. I'm sorry about the delay.

Best wishes, John Hill.


From Australia:

Yes, clear sky great viewing. This was the first total lunar eclipse I've seen. I was expecting the moon to be almost invisible since it was in the earths shadow. I noticed it was reddish and was thinking this was due to light being refracted through the earths atmosphere and reaching the moons surface. This would make sense since the suns light is also red seen at sunrise or set, due to the long path through the atmosphere. Please let me know if this is wrong. Thanks.

Grant Salmon


From Singapore:

If you care to know the eclipse was all right here considering I was watching with my naked eyes and there was haze (caused by forest fires in Indonesia) but visibility was so-so - couldn't see a single star I watched till the moon entered umbra (about 2:30 am my time) that's all. cos I have to sleep) thanx anyway

----------------A.s.T.r.a.L.----------------

Familiarity breeds contempt - and children

--------------------------------------------

http://www.geocities.com/TelevisionCity/5438


From the USA:

At jump.to we've had a spurt of requests from Brazil (.br) for your site... any reason? Anything we should know about?

Hamish. At work


From Sweden:

I just thought that you might want to know about my new page with almost 20 pictures of the lunar eclipse that I managed to take between the clouds! Best regards from the other side of the world!

Bengt Ask, bengt@df.lth.se


From South Africa:

Thanks for your QUICK response. After 5 days of rain (unseasonable of course! - should only start in Oct/Nov here) the skies last night were clear crisp (as always just after rain!) Eclipse was brilliant - last one visible from Southern Africa this century I believe? Can you confirm this? Most people here appear not too interested in these things here. Visited http://planets.gsfc.nasa.gov/eclipse/eclipse.html and learnt that the total solar eclipse on Dec 4 2002 will be visible over Botswana/Zimbabwe. You have any more detail on this? cheers

Erik Bartsch ebartsch@abacus.global.bw


From Perth WA:

Thanks for helping us to view the Lunar Eclipse. The co-ordinates and times helped us immensely. We observed the event till about 3:30 am on the coast about 50 km north of Perth CUB. The night was clear with minimal city light pollution. That was my first Lunar Eclipse and I was impressed with the red glow of the moon. Again thank you for your time and help.

Graham Baggett


From Taiwan:

It was magnificent! I only had my naked eye to view it with, but it was such a clear night there was no problem seeing it. Thank you for computing the time for me, I hadn't paid attention to the newspapers' talk about the eclipse and suddenly it was coming and I didn't know what time to start looking. The internet can be helpful! I also watched it on your live viewer...so I got it from the "down under" perspective as well. Thanks again for your help.

Nancy Leet


From China:

I just wanted to express our appreciation for your information and that of our 6 year old who had a great time looking. Here in Beijing, we are not really set up to take measurements but you might want to check with the Beijing observatory since the seeing was about as good as it gets here. A front came out of Mongolia the night before with moderate winds and blew all of the smoke and dust out of the air, dropped the humidity and the temperature and generally made things bright and clear. If you didn't know, this eclipse occurred on the night of the Chinese mid-autumn festival where people eat moon-cakes and fruit and watch the moon. Best Regards

Charles Krabek.


From Athens National Observatory:

Congratulations for your fantastic live coverage of the lunar eclipse. Bad weather conditions did not allow us in Athens to see this phenomenon directly. Thanks to your web page, many enthusiasts that visited our Institute during the last night were impressed by the indirect live imaging of the eclipse. During the eclipse I downloaded 19 of your images (I am not sure if these is the final number) starting from the one at 17:00 and ending at 19:50. I would like to ask for your permission to include in our Institute's web page (www.astro.noa.gr) an animation, prepared from these images, of course with a copyright (suggested by you) and a link to your page. Waiting to hear news from you. (The animations were prepared here and sent, they are now on the Institute's Home Page).

Best regards, Dr Ioannis Bellas.


From Astronet:

I just visited your great site. Too bad I didn't know before so I could have linked to it from ASTRONET. Anyway, I'll add a link to your site later on this evening.

http://www.xs4all.nl/~carlkop/astroeng.html

Cheers, Carl Koppeschaar


From Pretoria South Africa:

Would you be so kind to direct me to a site where I can view the movement of the moon through the shadow of the earth on a schematic basis. We are a few friends from Pretoria in South Africa, with no astronomical knowledge, trying to understand the route of the moon through the shadow of the earth, based on our observations. Thanking you.

Avril Malan.


From Portland, Oregon USA:

Thanks for your info about the Sept 97 lunar eclipse.

Corey D.Hachey


From Wahroonga, NSW:

We got up to see the eclipse, but the sky was against us and filled with thick cloud! What we really wanted to see was the Orange Moon, but all the pix we have been able to find on the web are monochrome. Did you get any colour pix? Are you going to post them on the web?

Regards, Jan and Joe.


From Newcastle, NSW:

Would you be able to email me some high res images of the totality. Your broadcast did not give an indication of the colour and darkness of the totality. It was raining in Newcastle at that time, however I did see the lead up to 3:55 am. It looked great, even through the gaps in the cloud cover and rain. regards

David Hough


From the USA:

I visited your web page during the eclipse of the moon because it was not visible in the United States and I was looking for images. Glad to see you're a Macintosh user and proud of it. Up here, it's a Windows world, but I still run a Mac Performa 575. I really prefer it to any other machine that runs Windows anything. If you'd like a good astronomy program, try Starry Nights from Sienna Software in Canada. I like what they have. I'm a member and officer in the Amateur Astronomers Association of Pittsburgh (in western Pennsylvania). If you're ever up this way, stop in. I'd love to show you the Big Dipper and Polaris. Maybe someday, I'll look in the direction of Sigma Octantis! Wishing you clear and dark skies,

Pete Zapadka.


From Switzerland:

As our country has quite high mountains, it was impossible for me to see the beginning of the eclipse. So I was happy to look at your pictures. The quality is ok! The time delay is the following 19:50:12 on your picture, 22:32 local time in Switzerland. It looks like your last picture because at 22:43 it is still the same! I wish you good observations of the moon, Bye,

Alain


From Cape Town South Africa:

Good day/evening to you. my name is Justin and i am 10 years old. i live in cape town south Africa and i am watching the lunar eclipse now. Could you please explain to me how i can find out when the next full eclipse of the moon will be and how i can find this out in future. please also explain to me how the eclipse happens and if it is every year. many thanks for your reply. Regards e-mail address hamfam @icon.co.za

justin hamburgere


From Germany:

I just observed the eclipse and want to send you the crater timings now. There seem to be some systematically error in the data, because the times are _always_ /smaller/ than the predicted values. So you might not include them for calculations; I have no idea what the reason could be. I synchronised the computer clock with the USNO clock at http://tycho.usno.navy.mil/what.html Doesn't the Java applet give the real time? Or were your times Eph.T.? The observation point is in Munich, Germany. If you need exacter values, please tell me. (I have not looked after it until now.) I estimate the mean errors to be about 10-20 sec. The Danjon value should be around 2. Best wishes,

Andreas


From Texas USA:

Thanks for responding to my questions. I had several thousand dollars riding on the stock market based on your response. I know this sounds illogical, however my Chinese partner is very superstitious and bet the market would fall because of the lunar eclipse today. Thanks to your response, I bet the other way and avoided losing several thousand dollars. The Dow Jones Industrials in the United States today went up 174 points today. The fifth largest rise in history. I am thankful to you and to e-mail. I wish you the very best weather for the lunar eclipse. nafco@aol.com Houston, Texas

Larry


From Webmaster ASTRONOMY MAGAZINE:

Very CCOOOOOLLL! We're watching you and loving it - thanks! I put a link on our Hotlinks page -- keep it up - Patti Kurtz

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* Patricia A. Kurtz *

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* 21027 Crossroads Circle (414) 796-8776 ext. 311 *

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From Geneva:

Dear friend, good luck for next week ! Did you see the September 2nd eclipse ? How was your location's weather ? I was extremely lucky on Kangaroo Island. It rained all day before, and just 2 minutes before first contact the sun was still in clouds. Then it opened, I saw all the eclipse, and clouds returned after last contact. magic !Ciao ! AND

Thanks Byron,

Now I got it (via your website). Hey, this is great: after the Bermuda triangle, here's the Calwell-Geneva-SanDiego triangle ! By the way, I wonder why your moon's picture is the same way as in the northern hemisphere, not upside down ? Did you turn it around, or is it because you film through a telescope which inverses the view ? Olivier R. Staiger, High Moon 115 route du Mandement, 1242 Satigny Geneva/Switzerland homepage http://eclipse.span.ch e-mail olivier.staiger@span.ch

Olivier


References

For a full explanation of the methods used see: Lunar Eclipse Umbral Analysis


Return to lunar eclipse FINDER