The Influence Of The Space Curvature On The Radial Motion Of Mercury’s Orbit

The precession detection of Mercury’s elliptical orbit is the most important one in the verifications of the general relativity.Mercury is the closest planet to the sun.It is the fastest moving planet in the solar system.It orbits the sun in an elliptical orbit.The average distance from the sun is about57.9km;the orbital period is 0.24 Earth years.At aphelion the Mercury is _ar?69.8?10~8km from the sun,and at perihelion it is at a distance of_pr?46.0?10~8km.And its orbital eccentricity is much larger than the Earth’s eccentricity.In the case of deducting the effects of precession and other planetary perturbations,the anomalous Mercury perihelion precession from Newton’s gravitational theory is a long-standing puzzle with a precession of about 43 arc seconds per century.In 1916,Einstein proposed such a precession as evidence of his test of general relativity and the result is quite coincident with the observed value.Mercury orbits contain both radial and angular variables.The gravitational attraction between Mercury and the Sun will cause the Mercury’s orbital position to change,and the radial position of Mercury will also change.However,this change has received little attention.With the advancement of astronomical ranging technology,today’s accuracy has reached the order of kilometers,and this change should be calculated.This paper mainly studies the influence of the radial motion of Mercury’s elliptical orbit,and finds that the long-axis of Mercury is shortened just in the order of kilometers.This thesis mainly composed of three parts.In the first part,we introduce the orbits of the planets in Newtonian mechanics and finds that there is an unexplained perihelion precession;but it can perfectly explain the precession effect in the general relativity.In the second part,we firstly give the general relationship between the coordinate distance and the intrinsic distance in the Schwarzschild metric.Then the coordinates of the perihelion and aphelion of the Mercury orbit are calculated respectively.By calculating the intrinsic distance corresponding to the two coordinate values,the length is given.It was found that the sun was slightly biased toward to the center of the ellipse and the length of the major-axis was slightly shortened.In the third part,due to the advancement of high-precision measurement technology,it is possible to test the high-order correction of the precession of the Mercury elliptical orbit at the perihelion.We calculated this high-order correction under two coordinates.The calculation results of this study show that the major-axis contraction of Mercury’s elliptical orbit is1.3km,and the calculated value is within the measurement accuracy range of the current astronomical distance measurement technology,and it is hoped that it will be tested in the near future.