If the earth doubled in mass but sun stayed the same mass. Would earths orbit stay the same. Why?

Question

If the earth doubled in mass but sun stayed the same mass. Would earths orbit stay the same. Why?

Answer 1

I believe that the earth's orbit would become elliptical moving further away from the sun from the point the mass doubled.

Answer 2

Doubling the Earth's mass would still make its mass insignificant compared to the Sun - so the orbit would not change significantly.

Technically two bodies orbit each other around the center of mass. For the earth-sun system, the center of mass is inside the sun, and it would still be inside the sun if the earth's mass doubled.

Essentially you can think of it as the gravitational force between the sun and the earth providing the centripetal force. so mv^/r = GMm/r^2

where M is the sun's mas, and m is the earth's mass.

the m's cancel - so the speed and radius of the orbit remain the same.

Answer 3

The orbit of the earth is nothing to do with the Earth's mass, but is determined only by the Sun's mass and the speed of the earth. An orbiting object needs a force of mv^2/r to pull it into a circular, and the sun's gravity is given by GMm/r^2. The m represents the mass of the earth, and the two cancel out so that the mass of the earth is irrelevant.