Influence of Sudden Change of Solar Mass in the PN Stage on the Orbit of Earth-Like Planet

Abstract

Assuming that the terminated mass is confined within the range 0.4551-0.5813M when the sun is going to evolve into a white dwarf, the velocity of the sun projecting the shell in the PN stage is much greater than the revolving velocity of the earth-like planet, therefore, we think that the solar mass change is instantaneous.Key words. Sun-orbit-dwarf. Enveloping model on solar projection in the PN stageThe total solar mass is (M c + M env ), where M c is the mass of core, and M env is the projecting mass of the enveloping layer. The shells hit the companion stars according to their own speed. Based on the study of Villaver & Stanghellini (2005), we assume that the initial velocity of the projecting material of the solar enveloping layer v env0 = 2 × 10 4 km s −1 , and the velocity of the enveloping layer decays according to the exponential formwhere r is the position of the planet, and r J is the distance of Jupiter. Orbital eccentricity of the planetWhen v env is big enough, the physical radius of the collision cross section is approximately equal to R, therefore, the planets accept the matter M env πR 2 /4πr 2 0 coming from the solar shell. These matter hits the planets at a velocity v env , and produce a radial momentum of the planet with a radius R.The radial velocity obtained by the planets is v r = M env R 2 4r 2 0 v env e − r r J .