Abstract:

 According to the exact solution of Binet differential equation for general relativity two-body problem in function integral form，three kinds of precise trajectory curves are obtained，two of which can be integrated to get analytic solutions. Einstein directly approximated and simplified this exact solution which is in function integral form，and obtained the high-precision calculation results of mercury precession highly consistent with the iterative approximate solution，which mutually verified the calculation accuracy of different solutions. By calculating the poles of Binet equation of general relativity，the exact formulas for calculating the aphelion and perihelion of the orbit of　the planet and the exact radius of the circular orbit are obtained. There is a difference of about 5 km with the results of Newtonian mechanics，which is mainly determined by the mass of the sun，and has little to do with planetary orbit radius. The above difference is also the maximum absolute error of the approximate solution for polar radius. The precise numerical trajectory of the general relativistic two - body problem can be obtained by using the high -precision mathematical calculating software to calculate the numerical integral.

Key words: general relativity, two-body problem, Binet equation, Mercury procession, exact solution