I have been concerned mainly to find the actual distance between the centers of two objects in the sky. What I currently can see the distance between the body and the observer in stellarium. It changes when one changes location of the observer on the home planet.
Please can somebody help me ?
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This is a very complex problem and depends on many things that are beyond the scope of stellarium.
Distances to the solar system objects are calculated on data that is contained in the ssystem.ini file. The near objects such as the moon are calculated from the centre of the object corrected for the observers site. With all other solar system objects this accuracy is irrelevant as it insignificant to the precision of the calculation.
The distances between two solar system objects in the sky can be calculated by "flying" to one of them and looking at the other. This distance can be taken as the centre to centre as they are moving relative to each other at speeds that can only give approximate answers.
For deep sky items that we know the distance to will need to be calculated by you using the angular distance shown with the distance plugin and the distance of each from earth.
For more information check out the precision and accuracy in the user manual in the wiki.