Essen, horizontal view

Internet Project Observing, Photographing and Evaluating the Transit of Venus, June 8th, 2004

Essen, equatorial view

The procedure was:

1. Measuring the positions of Mercury with respect to the center of the Sun's disc by means of an own little program.
2. Putting all positions into an Excel worksheet and calculating linear fits.
3. Taking as known the following values:
   • the geograpgical coordinates of the sites,
   • the equatorial coordinates of the Sun,
   • the sideral of Greenwich at 0.00 UT and
   • the radius of Mercury's orbit r_M/r_E.
4. Deriving the solar parallax π_S from the parallactic shift β=fρ_S of Mercury by means of the central relation

A detailed evaluation and exercises in position measurements and deriving the solar parallax can be found in our forum.

We've got very few pictures of the transit of Mercury. Most of them are not focussed well enough, deformed either by photographing the projection at an angle or during the transformation from slides to digitized pictures, have no unambiguous orientation or are unevaluable for other reasons. This fact shows us how important it is to get experience in photographing the Sun (see our related project)! Therefore, we are happy that we have been able to derive at least a rough measure for the solar parallax.

Own Results

Essen, Germany, 9.45 UT (double exposured slide, f=800mm, Δt=90s)	Keplergymnasium Pforzheim, Germany (projection with marked positions of Mercury, Δt=15min)	International Amateur Observatory, Namibia, 9.45 UT (two video pictures, afterwards added and stretched to circular pictures of the Sun)

1. Essen/Namibia

   With the following data

   • Essen: φ = 51.24°, λ = 7.0°
   • Namibia: φ = -22.34°, λ = 17.5°
   • Position of the Sun: α = 22h55m23s, δ = 16°43'
   • Radius of Mercury's orbit: r_M/r_E = 0.446
   • Sideral time of Greenwich at 0.00 UT: 14h57m43s
   we got the following value for the solar parallax: π_S=29". This is, of course, not acceptable. The main reasons may be the bad focus of the picture from Essen and the necessary stretching of the Namibia picture. But inspite of these facts, the result is surprisingly bad.

2. Pforzheim/Namibia, comparison of single positions

   With the following data

   • Pforzheim; φ = 48°54', λ = 8°43'
   • Position angle of the direction from east to west: 16.0°
   we got, by comparison of the positions at 9.45 UT, the following solar parallax: π_S=12", a better but not satisfying value.

3. Pforzheim/Namibia, comparison of interpolated positions

   By putting the positions into Excel worksheets we got the following line fits:

   • for Pforzheim:

     x	=	0.33975	+	0.00383068	*t
     y	=	0.6474	-	0.001816715	*t

   • Namibia

     x	=	0.36015	+	0.003705	*t
     y	=	0.6563	-	0,001922	*t

   By interpolating these line fits for 9.52 UT (t=112min) we finally get with π_S=7.0", a rough approach to the true value of 8.8".

Pictures of the GONG network

Some weeks ago, we were happy to get informed about the GONG network and the transit pictures taken by its solar observatories. They offer a very good opportunity to test our evaluation procedure. (Again, you can find the complete evaluation in the evaluation paper which can be downloaded from our forum.

Learmonth, Australia	Udaipur, India	Teide, Canary Islands, Spain

1. Direct comparison of single pictures

   The only directly comparable pictures are taken by the observatories of Udaipur (φ = 24.6°, λ = 73.7°) and Teide (φ =28.3°, λ = -16.5°) at 10.01 UT.

   For these pictures we found the following positions of Mercury:

   • Udaipur: x = 0.6094, y = 0.70778
   • Teide: x = 0.59385, y = 0.70397
   and, therefore, a parallactic shift of f = 0.016ρ_S from which we derived π_S=14.9", which is surprisingly bad facing the professional quality of the pictures.

2. Comparison of extrapolated positions

   Because of the large distance between Teide und Learmonth (φ = -22.2°, λ = 114.1°) we can expect the best measure of the solar parallax from the line fits of these observatories.

   • Teide:

     x	=	0.07778	+	0.004262	*t
     y	=	0.7376	-	0.0002689	*t

   • Learmonth:

     x	=	0.08539303	+	0.004226435	*t
     y	=	0.7478	-	0.000292166	*t

   In order to extrapolate the data as little as possible we chose 7.45 UT (t = -15 min) as comparison time. For this moment we get the very satisfying value: π_S=8.6",

   The combined Learmonth and Teide picture below visualizes the parallax of Mercury: It shows that Mercury, observed from Teide and Learmonth, run different paths over the Sun's face. Additionally, the extrapolated positions demonstrate the parallactic shift. Because their connection line is not perpendicular to the both paths the parallactic shift is larger than the distance between the paths.

   

   Perhaps, a little Powerpoint presentation (1.22 MB) may visualize the parallax of Mercury even more clearly:

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Prof. Dr. Udo Backhaus
last modification:  March 29th, 2015