For the next part, let's first solve a general problem. Suppose you have a planet or star of radius and surface gravity . Then the escape velocity on the surface of that object is . (We answered that question in class.). Now suppose you are already at a distance from the center of that object. Then the escape velocity is only .
Let's apply this to our actual world. Suppose you are launching a space craft from a point in Earth's orbit. Ignoring earth's gravity the minimum speed required to cause your craft to leave the solar system is kilometers per second.
You can earn partial credit on this problem.