关键词: 广义相对论, Brans-Dicke 引力理论, 微扰法, 行星进动, 星光偏折

Abstract: As two important alternative theories of gravitation，general relativity and Brans-Dicke's theory，

play important roles in our understanding the formation and evolution of celestial bodies and cosmology. In this

paper，we study the planet precession and light deflection in general relativity and Brans-Dicke's theory. Firstly，

we derive the general orbital equation for a free particle moving in the static，spherically symmetric spacetime by a

spherical star. Then，we write down the corresponding equations，which are nonlinear ordinary differential equations

　　of motion for the planet and light ray by using the spherically symmetric solutions to these vacuum field equations in

　　these two theories. Finally，the approximation solutions to the equations of motion can be obtained by the

　　perturbation method，which yield the angles corresponding to the planet precession and light deflection. These

　　results presented in this paper will help us to check and distinguish these two theories of gravity using high -

　　precision experimental observation.

Key words: general relativity, Brans-Dicke's theory of gravitation, perturbation method, planet precession, light deflection