1. Suppose we built a base on one of jupiter\'s small moons (a distance of 5AU f

Question

1. Suppose we built a base on one of jupiter's small moons (a distance of 5AU from the Sun). How fast would you have to launch a rocker from there to reach a moon of Saturn (10 AU away)? (assume the speed to escape the small moon can be ignored, and we're far enough away from Jupiter that we don't have to worry about escaping Jupiter's gravity either)

2. A rocket is fired from the surface of the Earth at a speed of 20,000 m/s. Ignoring atmospheric effects, how fast will the rocket be traveling when it is very far away from the Earth?

Explanation / Answer

a) 1/2 mv2 =GMm(1/r1 -1/r2 )
v2= 2*6.6738*10-11 *1.9891*1030 (1/10*150*109)
v = sqrt (176998074.4) =13304 m/s

b) change in kinetic energy = change in potential energy
  1/2 m (Vf2 -Vi2) = GMm/R -GMm/r
when r = infinite
1/2 m (Vi2 -Vf2) = GMm/R
Vi2 -Vf2 = 2*6.6738*10-11 *5.97*1024 /(6400*103 )
Vi2 -Vf2 =124508081
Vf2 = 400000000-124508081
   = 275491919
Vf =16597.9 m/s

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