Orbital effects of Sun's mass loss and the Earth's fate
  I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it. By applying my results to the phase in which the radius of the Sun, already moved to the Red Giant Branch of the Hertzsprung-Russell Diagram, will become as large as 1.20 AU in about 1 Myr, I find that the Earth's perihelion position on the fixed line of the apsides will increase by about 0.22-0.25 AU (for \dot M/M = 2 x 10^-7 yr^-1); other researchers point towards an increase of 0.37-0.63 AU. Mercury will be destroyed already at the end of the Main Sequence, while Venus should be engulfed in the initial phase of the Red Giant Branch phase; the orbits of the outer planets will increase by 1.2-7.5 AU. Simultane- ous long-term numerical integrations of the equations of motion of all the major bodies of the solar system, with the inclusion of a mass-loss term in the dynamical force models as well, are required to check if the mutual N-body interactions may substantially change the picture analytically outlined here, especially in the Red Giant Branch phase in which Mercury and Venus may be removed from the integration. 
Lorenzo Iorio