Essen, horizontal view
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Internet Project
Observing, Photographing and Evaluating the
Transit of Venus, June 8th, 2004
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Essen, equatorial view
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Project 6: The Transit of Mercury on May 7th, 2003
The distance to the Sun has been determined!
We have determined the solar parallax by evaluating pictures taken by
participants of our project and pictures taken by the GONG network.
The procedure was:
- Measuring the positions of Mercury with respect to the center of the
Sun's disc by means of an own little program.
- Putting all positions into an Excel
worksheet and calculating linear fits.
- 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 rM/rE.
- Deriving the solar parallax πS from the parallactic shift
β=fρS 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
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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)
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- 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: rM/rE = 0.446
- Sideral time of Greenwich at 0.00 UT: 14h57m43s
we got the following value for the solar parallax:
πS=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.
- 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:
πS=12",
a better but not satisfying value.
- 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
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y | = | 0.6474 | - | 0.001816715 | *t
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- Namibia
x | = | 0.36015 | + | 0.003705 | *t
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y | = | 0.6563 | - | 0,001922 | *t
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By interpolating these line fits for 9.52 UT (t=112min) we finally get with
πS=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.
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Learmonth, Australia
| Udaipur, India
| Teide, Canary Islands, Spain
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- 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 = 0.016ρS
from which we derived
πS=14.9",
which is surprisingly bad facing the professional quality of the pictures.
- 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
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y | = | 0.7376 | - | 0.0002689 | *t
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- Learmonth:
x | = | 0.08539303 | + | 0.004226435 | *t
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y | = | 0.7478 | - | 0.000292166 | *t
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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:
πS=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:
back to the main page
Prof. Dr. Udo Backhaus
last modification: March 29th, 2015