(Ill) To escape the solar system, an interstellar

Chapter , Problem 61

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(Ill) To escape the solar system, an interstellar spacecraftmust overcome the gravitational attraction of both theEarth and Sun. Ignore the effects of other bodies in thesolar system. (a) Show that the escape velocity is v = \ / v E + (vs - Vq)2 = 16.7 km/s,where: vE is the escape velocity from the Earth (Eq. 8-19);vs = V2GMs/r8E is the escape velocity from the gravitationalfield of the Sun at the orbit of the Earth but far fromthe Earths influence (rSE is the Sun-Earth distance); and v0 isthe Earths orbital velocity about the Sun. (b) Show that theenergy required is 1.40 X 108J per kilogram of spacecraftmass. [Hint: Write the energy equation for escape from Earthwith v' as the velocity, relative to Earth, but far from Earth;then let v' + vQ be the escape velocity from the Sun.]

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