If an object has just enough energy to escape from the earth, it will not escape from the solar system because of the attraction of the sun. Use Equation 11-19 with M_S replacing ME and the distance to the sun r_S replacing RE to calculate the speed v_eS needed to escape from the sun’s gravitational field for an object at the surface of the earth. Neglect the attraction of the earth. Compare your answer with that in Problem 56. Show that if ve is the speed needed to escape from the earth, neglecting the sun, then the speed of an object at the earth’s surface needed to escape from the solar system is given by v²_e, solar = v²e + + v²_eS 2, and calculate v_e,solar.

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2GM 2gR, 11.2 km/s R. 11-19