The planetary synodic index(K)was created(Liu F G & Wang J,2013),based on it,the quasi-22 yr sidereal period of the Sun's motion round the mass center of solar system was given.It's the average of 23.77208 years calculated by weight function of quality and 19.8585 years according to the image of the planetary synodic index.Since every planetary cycle is the sidereal period,so we also obtained the sidereal period of 23.36886 years by taking the derivatives of the function K~2.The results of two methods are almost the same. That offers a new perspective to confirm the difference of synodic period between the sidereal period of the Sun's trajectory and the path of planetary system mass center,the internal connection between the two is which coordinates you use.So on the basis of the two cases that whether the sun's mass center moves,we take their average which is 22.33 years as the sidereal period of orbital motion of Sun, and we find that the result agrees well with the 22.20 years magnetic cycle.This shows that by revising the feature image of Sun's orbital motion,it is possible for us to predict solar activity and climate change with the corresponding time scale.