> As the horizontal image width (in POV units) as
> camera_distance*tan(angle/2), a sphere with a radius of 3396.2 units
> (the planet Mars) should exactly fit into the camera window when viewed
> from a distance of 9330.982812 units - but instead the planet's disc is
> still too large for the image (see attachment)!

  Did you take into account perspective? You are not using a disc, but a
sphere, and perspective will make the half of the sphere closer to the
camera be larger than the "disc" at that exact distance.

  You should try it with a true disc object instead.

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