Orbital effects of Sun's mass loss and the Earth's fate

TL;DR

This paper analytically examines how the Sun's isotropic mass loss affects planetary orbits, predicting significant orbital changes during the Sun's Red Giant phase, with implications for Earth's future and planetary survival.

Contribution

It provides a classical analytical framework for orbital effects due to stellar mass loss, applied specifically to the Sun's evolution and planetary orbital shifts.

Findings

Earth's perihelion increases by about 0.22-0.25 AU.

Mercury will be destroyed at the end of the Main Sequence.

Outer planets' orbits will expand by 1.2-7.5 AU.

Abstract

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.