The quasi 200 a and 2400 a climate change periodic had been generally considered as a response periodic to the solar activity, but the mechanism is still not clear. Based on the coordinate system of the Sun's mass center, it is observed that the planets synodic index (K) has 20 a, 179~ 180 a and quasi 2400 a periodic. The most essential periodic of the solar orbital motion is calculated to be quasi 22.20 a using a correction efficient(q= 1.11518) under the coordinate of the mass center of the solar system. According to K index, we characterize the distance variation of the Sun relative to the mass center of the solar system,whose extremal values are significantly correlated with the extremal values of the sunspot magnetic polarity MI(r_(KMI) = 0.952). Previous reports show that the variations of tree-ring width and the ~(14)C content of tree-ring and coral have quasi bi-centurial and Hallstatt periodic which are well in agreement with the 179 ~200 a and 2300 ~2600 a periodic of K index after correction by q factor (q = 1.11518). The larger K extremum indicates the higher potential energy of the Sun,and the smaller K extremum indicates the lower potential energy of the Sun. Therefore, the energy released by the Sun into interplanetary space is relatively reduced,and the interference of galaxy cosmic rays from the Sun is also reduced. This would increase the deposition of galactic cosmic rays and energy particles entering the atmosphere, and thus, increase the 14C content in the atmosphere. The consistence between the ~(14)C content change periodic and the K index periodic suggests that there is a positive correlation between climate change periodic and the K index periodic,which is of great importance to investigate the response mechanism of climate change to the solar activity.