Abstract: Starting from Lagrangian，Runge -Lenz vector and differential equation，respectively，the Kepler’s three laws are derived from the law of gravity and Kepler' s equation and the orbital period are obtained by integration.The eccentricity and period of revolution of the earth are calculated by employing the data of perihelionand aphelion speed from two references and large inconformity is found between the calculated results and the observed values.The cause is analyzed and the corrected velocities are given resulting in self-consistency.

Key words: Kepler's laws, law of universal gravitation, eccentricity, perihelion velocity, aphelion velocity