Second post-Newtonian approximation of Einstein-aether theory

In this paper, second post-Newtonian approximation of Einstein-aether theory is obtained by Chandrasekhar's approach. Five parametrized post-Newtonian parameters in first post-Newtonian approximation are presented after a time transformation and they are identical with previous works, in which gamma = 1, beta = 1, and two preferred-frame parameters remain. Meanwhile, in second post-Newtonian approximation, a parameter, which represents third order nonlinearity for gravity, is zero-the same as in general relativity. For an application for future deep space laser ranging missions, we reduce the metric coefficients for light propagation in a case of N point masses as a simplified model of the Solar System. The resulting light deflection angle in second post-Newtonian approximation poses another constraint on the Einstein-aether theory.