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 a large number, any effect connecting 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, as an application, the quantum theory with the ultimate acceleration provides a useful formula to calculate the space debris distribution around the earth, this calculation results agree well with the experimental observation which are a set of measurements by incoherent scattering radar of EISCAT in the Arctic circle. 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%. The double-slit interference of space debris is also investigated for demonstrating its quantum behavior.