Example: Evaluation of Simulated Data

On this page we explain how to evaluate measured positions of Mercury on the solar disc if one have found simultaneously taken pictures and/or measurements of a distant participant (here: Hannover, Germany, and Windhoek, Namibia). The simulated measures have been calculated by using the (Windows-) program eclipses (or its German version Finsternisse).

  1. The pictures have been taken with an azimutal mounted camera every half hour. Superimposing of the pictures yields the following results:
    HannoverWindhoek

  2. By rotating the images so that the direction east-west is horizontal, for instance by evaluating double exposed images with the (Windows-) program evaltransitpicts, by determining the angle of rotation with it and by superimposing the rotated images one will get the results like the following:
    HannoverWindhoek

  3. During the evaluation of the double exposed images the program evaltransitpicts can also display the positions of Mercury with respect to the solar disc. These positions may be filled into the Excel sheet tableofMercurypositions.xls which will yield the sheets tableofMercurypositionsHann-sim.xls and tableofMercurypositionsWindh-sim.xls

  4. Single pairs of simultaneous positions may be evaluated with the (Windows-) program calcparallaxNew. For 15:00:00 UT, for instance, you will find in the sheets:
    HannoverWindhoek
    x'-0.158821-0.160049
    y'-0.301869-0.292700
    When you fill these values together with the geographical coordinates of the cities into that program (the parameters of the sun and the 0:00 UT sideral time of Greenwich of the transit day are preset) you will get the following measure of the solar parallax: πS=9.2".

  5. If you save the sheets as tab-seperated text files these files may serve as inputs for the (Windows-) program comptransitofmercurypos which will display diagrams of the position values, calculate line fits to these and calculate improved values of the solar parallax by averaging (a) the measures of all exactly simultaneous position measurements and (b) the quarter hour values of the line fits. The latter will be possible without any simultaneous measurements!
    Simulated position measurements from Hannover Simulated position measurements from Windhoek Comparison of both series of simulated measurements
    In this way, we get to a considerably better measure of the solar parallax with an estimate of the confidence interval: πS=8.94"±0.03"

  6. If you don't find any partner to compare your photos with you may compare your position measurements with the positions calculated for the geocentre (These values can only be calculated!).
    Comparison Hannover-Geocentre Comparison Windhoek-Geocentre
    Of course, these results will be less satisfying because (a) you compare your measures with simulated values and (b) the baselength of the parallax measurement is shorter.

Editor: Udo Backhaus
  last update: 28.03.2016