4. The kings of planet A (mass 4M, radius 2R) and planet B (mass M, radius...

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4. The kings of planet A (mass 4M, radius 2R) and planet B (mass M, radius 3R) want to meet for negotiations. The planets are a distance 10R from one another, center to center. For absolute fairness, the kings (who possess no physics knowledge) decide that the meeting place P is to be exactly halfway between the planets. A space capsule of mass m is launched from Planet A P VL 4M, 2R 10R Planet B M3R 5R 53 point X on the surface of planet A by means of a giant cannon, which gives it a launch speed VL. It travels directly along the line that connects the centers of both planets. Ignore the orbital motion of the planets. a) Derive an expression for the speed V with which the capsule arrives at the meeting place P, in terms of relevant system parameters. b) Derive an expression for the net force (magnitude and direction) experienced by the capsule when it is at point P. c) At what distance from planet A is the net gravitational force zero? 4. The kings of planet A (mass 4M, radius 2R) and planet B (mass M, radius 3R) want to meet for negotiations. The planets are a distance 10R from one another, center to center. For absolute fairness, the kings (who possess no physics knowledge) decide that the meeting place P is to be exactly halfway between the planets. A space capsule of mass m is launched from Planet A P VL 4M, 2R 10R Planet B M3R 5R 53 point X on the surface of planet A by means of a giant cannon, which gives it a launch speed VL. It travels directly along the line that connects the centers of both planets. Ignore the orbital motion of the planets. a) Derive an expression for the speed V with which the capsule arrives at the meeting place P, in terms of relevant system parameters. b) Derive an expression for the net force (magnitude and direction) experienced by the capsule when it is at point P. c) At what distance from planet A is the net gravitational force zero?