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Gravitation: Spacecraft launch speed to escape from the solar system altogether

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 effect of 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 on the figure. The figure shows the sun, and at its right on a circular orbit there is the earth and California is at the left of the earth. The direction of speed is counter clockwise, such that the velocity at point "California" is vertical, (upwards on the drawing).

The rotation and orbitals motions of the earth are in the same direction. The launch facilities in Florida is 28.5° noth of the equator.

c) The European Space Agency (ESA) uses launch facilities in 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 sytem if launched from French Guiana?

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With good explanations, formulas and a graph, the problems are explained and answered.