In this work, we present the new expressions of global effective kinetic, gravitational potential and total energies, obtained in the planet-sun interaction systems, as those given in Equations (4, 5, 6), and enhanced by a new global effective kinetic mass of the planet, as that given in Eq. (1). Some concluding remarks are given as follows. At the low speed v (<< c), c being the light speed, given in the non-relativistic case, they . At v=c, given in the relativistic case, the kinetic energy is found to be equal to: , , and, in particular, for p=2, to: , in good agreement with that proposed by Einstein in 1905 [1], m being the rest mass of the planet, as those shown in Tables 2-10, for various planet-sun interaction systems.