You wake up one morning to find that you have been abducted by aliens. In a desperate escape attempt, you steal a small spacecraft and try to run away. Once you leave the alien saucer, you realize you are in orbit around an unknown planet with a very large moon.
Using the distances and masses of the bodies in the given diagram, calculate the speed that you need to reach in order to escape the gravitational pull of this system.
In your haste to leave the alien saucer, you forgot to refuel your little ship. Upon realizing that you do not have enough fuel to achieve the speed in part A, you decide to go into orbit around the planet (the bigger one). Assuming you are not moving in the diagram, what minimum speed is required to go into orbit of the larger body without hitting it (remember: 2a=ra+rp). Ignore any gravitational effects of the moon.
How fast will your ship be moving at the periapsis of the orbit you designed in part B?