Results of the Photographing Project

The parallax of Venus has become visible and the distance to the Sun has been determined!

On this page we have described very early evaluations of the first uploaded pictures and elucidate once more the evaluation procedure with an example. Now we summerize the up to date results of the photography project and offer example images which allow to visualize the parallax effect and to determine very good own measures of the distance to the Sun.

Final results

In the weeks after the transit several images have been uploaded or submitted to U. Backhaus. The corresponding worksheets with Venus positions have been uploaded via our data exchange page. By evaluating these lists of position measurements with the program comptransitpos you can, for instance, get the following visualisations:

Arnsdorf positionsCanberra positionsSDO positions

Similar results can be derived with the tables of the Usedom, Tromsø, Hawaii and Rügen position data which have been uploaded via the data exchange page.

Comparison of the extrapolated contact times with those calculated by the USNO transit computer will show that the measured positions produce quite good line fits; most of the times differ from the calculated values by some seconds only!

Comparisons between these positon data within the same program yield the following results:

Comparisons
Arnsdorf-SDO Canberra-SDO Arnsdorf-Canberra

The following table summerizes the values of the solar parallax which can be determined by evaluating the uploaded lists of Venus position data.

Results for the solar parallax
 ArnsdorfCanberraHawaiiRügenTromsøUsedomSDO
Arnsdorf-9.59.6-(15.1)-9.2
Canberra -(5.9)8.99.49.58.8
Hawaii  -8.48.79.39.5
Rügen   --9.48.4
Tromsø    -9.48.8
Usedom     -8.7

It is difficult to estimate the errors of these measures. Therefore, they are given without variance. Perhaps, they will be rated later.

Additionally, it is possible to compare single pictures which have been simultaneously taken at distant sites by using the worksheet comp2Venuspositions. In this way you can get very excellent results for the Astronomical Unit by comparing pictures made by our participants especially with those of the SDO spacecraft. This success is due to the long baseline between the "observers" and the corresponding large parallax effect.

In many cases, however, even the comparison between Earth made images is quite satisfying. In the case of bad parallax results possible reasons may be

Composition of (nearly) simultaneously taken images

The following images from Canberra, Australia (S. Bolton), Tromsø, Norway (J. Trebs), Usedom, Germany (A. Hänel) and Arnsdorf, Germany (E. Merker) may be regarded as a challenge

One can get clippings of the original images by clicking on the thumbnails. In the case of the Usedom 3:00 UT image it will be necessary to stretch the picture. Therefore, the result will not be as satisfying as in the other cases.

original 1original 2combinationresulting solar parallax
1. Usedom 3:00:01 UT
2. Canberra 3:00:11 UT
πS=10.4"
1. Usedom 4:29:30 UT
2. Canberra 4:29:32 UT
πS=8.9"
1. Usedom 4:40:10 UT
2. Canberra 4:40:07 UT
πS=9.0"
Tromsø 3:12:15 UT
Canberra 3:12:16 UT
πS=8.9"
Arnsdorf 4:21:49 UT
SDO 4:21:48 UT
πS=9.2"
Rügen 3:59:18 UT
Hawaii 4:01:56 UT
πS=8.4"

Due to the reasons stated above not all combinations of project images will lead to so excellent results.

Example: Comparison of images taken at 4:00 UT from Arnsdorf, Germany, (E. Merker), Canberra, Australia, (S. Bolton) and from space (SDO)

As an example we will demonstrate the evaluation of (nearly) simultaneously taken transit photos with three 4:00 UT images:
Arnsdorf, 4:00:30 UTCanberra 4:00:02 UTSDO 03:59:59 UT

The evaluation is done in four steps:

  1. Eventally, the Arnsdorf image should slightly be stretched vertically in order to make the Sun circular.
  2. The orientation of the images is measured with an actualized version of the program evaltransitpicts. The images should be displayed as large as posiible (Factor of size reduction=1). Two circles must cover the two prominent sun spots:

    Results:
    SDO β=62.7°, α=13.3°
    Arnsdorf β=85.4° ⇒ α=36.0°
    Canberra β=76.2° ⇒ α=26.8°
    The angle α of the SDO image is known.
  3. Determination of Venus' position using evaltransitpicts and displaying the images so that the whole Sun is visible on the screen:
    x'y'
    SDO0.8681360.327877
    Arnsdorf0.7513620.389124
    Canberra0.7745420.424383
  4. Calculation of the solar parallax using comp2Venuspositions:
     πSun 1 AU
    Arnsdorf/SDO 8.74" 150480000 km
    Canberra/SDO 8.65" 152210000 km
    Arnsdorf/Canberra 8.53" 154270000 km

  5. Graphical visualization

    The parallax of Venus can be made visible by the following steps:

    1. Size reduction of the images so that the pixel radius of the Sun is the same in all pictures.
    2. Rotation of the pictures by -α
    3. Determination of the center of the Sun with evaltransitpicts.
    4. Translation of the pictures so that the Sun has the same center in all of them.
    5. Superposition of the images
    Steps a, b, d and e can be done with ImageJ, for instance.

    Results:

    Arnsdorf-SDOCanberra-SDO
    Arnsdorf-Canberra ...... and the corresponding daylight side of the Earth

First evaluations

Only Andreas Hänel partly followed our suggestions to take "twice exposured pictures". The worksheet in our database contains a preliminary evaluation of some of his pictures. The following picture (produced with comptransitpos) visualizes the result.


Positions of Venus, measured on images taken by A. Hänel in Usedom, Germany

For the uploaded single exposure pictures the orientation is not given. However, because at transit time there are some prominent sunspots on the sun's surface it may be possible to find the orientation by comparing the pictures with professional images taken at nearly the same time. We use for this idea the images taken by NASA's Solar Dynamics Observatory. Pictures of which we saw first as Astronomy Picture of The Day. NASA published related videos and the complete full size images, too.

Because this observatory circuits on a geosynchronous orbit its distance to the Earth's center is quite large and therefore it generates a large parallaxe effect. In order to compare project photos with SDO photos exact timing and position data must be known. We will describe the detailed procedure later. For today, the interested reader may use the worksheet containing time and position data. A slightly adapted version of comp2Venuspositions.xls can be found in our stuff page.

In this way we first found the orientation of the images taken bei T. Häusler in Hawaii and could then measure the positions of Venus on them.


Positions of Venus, measured on images taken by T. Häusler in Hawaii

Finally, it was possible to combine pictures of A. Hänel and T. Häusler with those of SDO - with (for the first attempt) quite satisfying results!

Observer combined picture resulting solar parallaxe
A. Hänelπ=8.60"
T. Häuslerπ=8.73"


Editors: Udo Backhaus
 last update: 07.12.2012
Stephan Breil