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A spaceship of mass 270 kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 280 m/s and at an angle of φ0 = 51°, at a distance 11000 km from the center of the planet as shown in the figure.

Part (a)  Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of mr0v0φ0, and unit vectors ij, and k

Part (b)  If the spaceship whips around the planet to the other side so that the angle is φ = 31° and is moving at 85 m/s, how far, in kilometers, from the planet is it? 

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