About five billion years from now, our Sun will move into the last phases of its life. It will expand to a red giant and then push its outer layers into the interstellar medium via a slow stellar wind, producing a planetary nebula. Suppose that at the end of this process the Sun is left with half its initial mass (in the form of a white dwarf star). Assume that the Earth has a circular orbit and that this orbit is held constant until we arrive at the end of the above process. What kind of orbit will the Earth have at this point? Will it remain in the solar system? We are looking for the theoretical physics and equations in this problem if this was to happen.