1. The problem statement, all variables and given/known data Calculate the relative change in the distance of the Earth from the Sun, if the mass of the Sun is 15% lower than today weight of the Sun. Suppose that the Earth moves and will move along a circular path and will maintain its angular momentum. 2. Relevant equations Equality of gravitational and centrifugal forces. 3. The attempt at a solution For mass of the Sun today: Valid for Earth: The centrifugal force = gravitational force m_e*(v)^2/r=κ*m_e*m_s/(r)^2 (v)^2=κ*m_s/r For mass of the Sun when is 15% lower than today weight of the Sun: Valid for Earth: The centrifugal force = gravitational force Mass and velocity of the Earth does not change because it does not change angular momentum. m_e*(v)^2/r_1=κ*0,85m_s*m_e*/(r_1)^2 (v)^2=κ*0,85m_s/r_1 Equal squares of velocities: κ*m_s/r=κ*0,85m_s/r_1 1/r=0,85/r_1 When is r=1 AU, then r_1=0,85AU Why? I think it's stupid. Why the Earth is closer to the Sun, when the Sun is lighter? I think must be the Earth from the Sun farther, because the gravitational effects diminish. Why my ideas don't coincide with the results? How would you counted it? Thanks very much.