My reading of the question was, is there a way to switch between perspective and parallel projection that keeps an (approximately) spherical object the same size within the view?
@dgobbi Yes, I would like to do exactly that, as shown below (fake image).
@lassoan Sorry for not being clear on my question.
@lassoan and @dgobbi Thank you both very much for the explanations and suggestions. They will help me to try to overcome this problem.