Several participants failed in taking double exposed pictures as proposed on the photographing page but took brilliant single photos. In order to capacitate them to measure and to evaluate the positions of Venus on their pictures we propose here a procedure and concretize it with a picture taken in Hawaii at 00:05:30 UT by T. Häusler.
The basic idea is to find the unknown orientation of the picture with the help of two prominent sun spots. By comparing it with the orientation of the same sun spots on a picture made by NASA's Solar Dynamics Observatory it becomes possible to determine the orientation of the picture with respect to the celestial equator.
By superposing some SDO pictures it becomes obvious that the orientation of the prominent sun spots remained constant during the transit. The line from the lower left edge of the prominent triangle to its top (in this order!) includes an angle of βSDO=62.7° with the lower edge of the picture.
|Superposition of 6 SDO pictures (No. 774, 854, 925, 996, 1072 and 1292)
|The 00:05:25UT SDO picture (No. 857) and ...
|... its evaluation with evaltransitpicts with the known angle of orientation αSDO
On the SDO images the rotation axis of the Sun is vertically oriented. Because this axis on transit day included an angle of 76.7° with the equator the orientation of the SDO images is αSDO=13.3°. Therefore, the angle between the equator and the line connecting the two sun spots is β=βSDO-αSDO=49.4°.
This angle must be the same for all observers on Earth. Therefore, the rotation angle αObs of a picture can be determined by measuring the angle βObs and calculating the difference to the correct angle β:
With this knowledge the position of Venus on a single exposed picture can be determined in the following steps:
|00:05:30 UT picture from Hawaii, ...
|... vertically flipped and ...
|... vertically stretched to a circular Sun
|Measurement of the orientation
of the Hawaii picture and ...
|... determination of Venus' position
All the positions of Venus determined in this way may be filled into the worksheet tableofvenuspositions which will calculate a line fit to all positions. With the ".txt" version of this sheet the program comptransitpos will visualize the measurements graphically. The following picture shows the evaluation of the Hawaii images:
If no pictures are available taken by other participants of this project at the same time the distance to the Sun may be determined by comparing the own picture with that SDO image which has been taken at the same time - at least approximately. For this comparison two critical points have to be taken into account:
Therefore, for the time of interest the geocentric coordinates (α, δ, r) must be known and the algorithm of determining the solar parallaxe has to be generalized. The worksheet geocentric coordinates contains the original NASA position data and the derivation of the spacecraft's spherical coordinates. For comparing Earth made and SDO images had to be generalized. The program comptransitpos and the worksheet comp2Venuspositions.xls have been updated so that they treat positions on SDO images correctly.
For this Hawaii picture and the corresponding SDO image the results are:
πSun=8.69" ⇒ 1AE=23744RE=151440000km
|last update: 15.09.2012