A spacecraft is to be launched from the surface of the earth so that it will escape from the solar system altogether.
(a) Find the speed relative to the center of the earth with which the spacecraft must be launched. Take into consideration the gravitational effects of both the earth and the sun, and include the effects of the earth's orbital speed, but ignore air resistance.
(b) The rotation of the earth can help this spacecraft achieve escape speed. Find the speed that the spacecraft must have relative to the earth's surface if the spacecraft is launched from Florida at the point shown in Fig. 1237. The rotation and orbital motions of the earth are it the same direction. The launch facilities it Florida are 28.5° north of the equator.
(c) The European Space Agency (ESA) uses launch facilities it French Guiana (immediately north of Brazil), 5.15° north of the equator. What speed relative to the earth's surface would a spacecraft need to escape the solar system if launched from French Guiana?