In analogy to the ultimate speed c, assume that there is an ultimate acceleration β, nobody's acceleration can exceed this limit β. By fitting observational data, it is found that the solar system has an ultimate acceleration of β=2.961520e+10(m/s/s), no rocket's acceleration can exceed this limit β. Because this ultimate acceleration is a large number, any effect connecting to β will become easy to test, including quantum gravity test. The ultimate acceleration makes a strict restriction on planet-rotation, it establishes a quantum rule for gravity, it is reported in this paper that the Sun and first four planets (Mercury, Venus, Earth, Mars) are quantized very well in accordance with the limit β. In other words, the ultimate acceleration β can derive out a generalized matter wave which causes the planetary quantization. Using the generalized matter wave and its Planck-constant-like constant, the solar system, Jupiter's satellites, Saturn's satellites, Uranus' satellites, Neptune's satellites as five different many-body systems are investigated with the Bohr orbit model. The calculation results agree well with experimental observations for these planets and satellites. This paper also discusses the possibility of applying the generalized matter wave to the Moon's orbit, tropic cyclone and virus.