All available mid-eclipse times of the eclipsing binary Z Draconis are analysed , and three sets of cyclic variations with periods of 20.1 , 29.96 and 59.88 yr are found .
The low-amplitude variations with the period of 20.1 yr may be attributed to the unavoidable and slight imperfection in the double-Keplerian model , which gives the periods of 29.96 and 59.88 yr. Interestingly , the Z Draconis system is close to a 2:1 mean-motion resonance , or 6:3:2 mean-motion resonance if the period of 20.1 yr is true .
We also find that the best solutions tend to give the minimum eccentricities .
Based on Kepler ’ s third law , the outermost companion has the minimum mass of \sim 0.77 M _ { \bigodot } , whereas the middle companion is an M dwarf star with a mass of \sim 0.40 M _ { \bigodot } , suggesting that Z Draconis is a general N-body system .