The reference book gave a way of estimating the accuracy of the results. What I found is that the formulas can give me the answer within 1000km.

This means that a 6 segment display will be enough (between ~54Mkm and ~400Mkm)

If I go from center of earth to center of mars, the calculations will save a step and it will simplify the information that is needed to just be the current time/date.