Relativistic matter wave was rewritten in terms of ultimate acceleration. If there is an ultimate acceleration β, nobody’s acceleration can exceed this limit β, in the solar system, β=2.961520e+10(m/s2). Because this ultimate acceleration is a large number, any quantum effect connecting to β will become easy to test, including quantum gravity test. In this paper, the relativistic matter wave in gravity with the ultimate acceleration establishes an approach which shows that the sunspot cycle is mainly determined by the ultimate acceleration β. As an application, the sunspot cycle is calculated out to be 10.38 years, the result agrees well with the experimental observation. Using the same approach, the radius of the Sun is calculated out to be r=7e+8 (m) with a relative error 0.72%; the radius of the Earth is calculated out to be r=6.4328e+6 (m) with a relative error 0.97%.