# Example 2: The use of the evaluation utilities of this project

In order to test the evaluation procedures, programs and worksheets developed for this project topocentric positions of Sun (αSS) and Venus (αVV) during the coming transit have been calculated by means of horizons. Additionally, the corresponding geocentric positions have calculated. From these values the relative positions of Venus on the Sun's disc (x',y') have been derived with the following equations:

x' = -(αVS)cosδSS, y' = (δVS)/ρS

where ρS is the angular radius of the Sun. In history it was crucial (and it will be essential for the success of these projects, too!) to get as many measurements as possible from sites as far as possible from each other. As the pictures on the project homepage show Alaska and Australia are the optimal locations for measuring the distance to the Sun:
• Their (linear) distance is nearly as large as the Earth's diameter and
• from both countries the entire transit will be visible.
Therefore, we have chosen Sydney (φ=33.862°S, λ=151.205° E) and Anchorage (φ=61.167°N, λ=149.983°W) as hypothetical observation sites.

### Sheets with position data and line fit

The theoretical positions have have to be copied (via "insert content" → "values" in order to keep the cells format unchanged) into colums F, G and C the Excel sheet tableofVenuspositions in the project's stuff. After having clicked the green button the linear fit will be calculated automatically and the corresponding parameters will be displayed in cells F15-I15. Attention: The line fit can be calculated only when macros have been enabled!

For further evaluations the geographical coordinates of the observation site must be filled into line 4 before saving the complete worksheet in ".xls"-format and "line" as tab-seperated text file. The results are contained in

The table with the geocentric data has been ubloades via our data exchange page.

### Combining single pairs of position data

For deriving the Astronomical Unit on the basis of two simultaneous positions following the procedure described in extenso in an additional paper and in the other example we offer two possibilities:

1. the little program calcparallax. When the (pre-adjusted) data of the Sun on transit day and the geographical positions of Sydney and Anchorage (pre-adjusted, too) are input the program repeats asking for times und rectangular coordinates of Venus. For 1.45 UT it displays:

 Parallactic displacement beta : 34.8" Linear distance of the two observes Delta : 1.60 RE Projected distance Delta*sin(w) : 1.60 RE Parallax of the Sun piS : 8.8" 1 Astronomical Unit (AU) : 23461 RE

That means: The angular distance between both observed positions is β=34.8". Because the straight line connecting Sydney and Anchorage is nearly perpendicular to the direction to the Sun the projection doesn't diminish it: The Sun "sees" the full distance. As seen from the Sun the Earth's radius covers an angle of πS=8.8". And the Astronomical Unit (that is the mean, not the actual distance between Earth and Sun) is 23461 times as large as the radius of the Earth.

That is a nearly perfect result! Because of the theoretical input data this is a proof for the used algorithm.

2. If you input the same data into the sheet "Measurements" of comp2Venuspositions it will display (nearly) the same results for the solar parallax and the Astronomical Unit. In comp2SydneyAnchorage.xls this has been done for you.

This sheet has been constructed for filling in the results which have the project partners uploaded via the data exchange page. If you download these results and open that file with a worksheet program the data can be copied into comp2Venuspositions.xls (via ) you can select arbitrary pairs of simultaeneous (Δt<=5min) measurements and look for the resulting value of the solar parallax.

### Combining series of position data

For combining complete sets of position data measured at the same sites the program comptransitpos has been developed. The text versions of the above mentioned position tables from Sydney and Anchorage serve as input files for this program. As described in the other example it first displays position data in a graphic which additionally contains some fit results, for instance the extrapolated contact times.

 Sydney Anchorage

But the main goal of this program is to derive the best possible measure for the solar parallax from the data.

Results of combining the theoretical Sydney and Anchorage data
In the case of the theoretical values evaluated here the advantage of the use of statistics doesn't become clear because all combinations of single pairs yields similar perfect results. With real measurements, however, this method causes better results and higher reliability (see the 2004 example). Therefore:

You should not expect similar exact results by analysing real data of this project! The above perfect result is due to not only the theoretical calculation of the positions but also caused by the long baseline Anchorage-Sydney and by the long time intervall of common data.

 Editors: Udo Backhaus last update: 22.04.2012 Stephan Breil