THE_UMBRA

 

by Byron Soulsby

 

Isabella Plains Lunar Observatory Australia



atmosphere


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

 

Abstract

 

The measurement of 31 images of the total lunar eclipse of 2008 February 21 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 two 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 and the Excel chart below shows the computed Fi values in purple for his site compared with the image measurements in blue.

 

 

 




Comments

 


It is interesting to note the shape of the above curve through 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 at zero at first primary contact (1C) and then increasing rapidly to a value very near the Geoid value given in the classical ephemeris (for this eclipse the Geoid value is 0.6983o at 1C to 0.6969 o at 4C). Similarly, the curvature causes the umbra size to drop to zero at totality, rise from zero at third contact to the maximum and again decrease to zero at fourth contact at the end of the eclipse.

 

Conclusions

 

The measured umbra taken from a set of high quality images provided by Bernard Durand has enabled conclusive proof of my topocentric umbra theory and computation. For the first time these measurements 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.

 

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

 

Acknowledgments

 

I am indebted to Bernard Durand for the many excellent images provided and for his interest in this project.

 

References

 

The web pages for the Soulsby series of lunar eclipses.

 

My theory and computer programs for the determination of the topocentric umbral size.

 

 

Produced by the Isabella Plains Lunar Observatory Australia, 2008 May 9.