In analogy with the ultimate speed c, 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 large, any effect related to β will become easy to test, including quantum gravity tests. In this paper, an approach is put forward to connect the ultimate acceleration with quantum theory, and is applied to sunspot, earth's tropic cyclones, and earth's geomagnetic field problems. The sunspot cycle is calculated to be 10.93 years due to the ultimate acceleration. A simulation was carried out, clearly showing the inner structure of a cyclone, which is consistent with the famous DIANA cyclone on 12 September 1984 in situ observation measured by an aircraft. The sunspot structure is also investigated, which has a similarity to that of a tropic cyclone. The ultimate acceleration provides a mechanism to explain geomagnetic field, the earth's geomagnetic field is calculated to be 0.6Gauss at the north pole.