Kinematics in Randers-Finsler geometry and secular increase of the astronomical unit

Kinematics in Finsler space is investigated. It is showed that the result based on the kinematics with a special Finsler structure is in good agreement with the reported value of secular trend in the astronomical unit, $d{\rm AU}/dt=15\pm4[{\rm m/century}]$. The space deformation parameter $\lambda$ in this special structure is very small with scale of $10^{-6}$ and should be a constant. This fact is consistent with the reported value of an anomalous secular eccentricity variation of the Moon's orbit.