I have to solve a problem regarding the minimum velocity required to escape from the solar system while taking into account the gravitational force of the earth as well as the sun. What I am supposed to do is calculate the velocity of an object after escaping from earth. Then I am supposed to go to a sun fixed frame and calculate the minimum velocity for escape from the sun. The answer that I am striving for is the following: v^2= v(escape from earth)^2 +v1^2 v1=v(escape from sun) - v(orbit) I am not sure how these equations above are derived. I can calculate the escape velocity for the sun and earth, but I am not sure how to relate these two separate frame.