Consider a star orbited by two planets. Assume the star to have mass twice that of the Sun. Let planet 1 orbit with semi-major axis 10 AU, and eccentricity 0.6. Planet 2 orbits with semi-major axis 4 AU, and eccentricity 0. Assume the angular momentum vectors of the two planets to point in the same direction. Both planets have a mass of 1 Earth-mass. Let's assume these planets have a collision. a. At which point in its orbit must planet 1 be, at the time of collision? b. Assume the two planets stick together in the collision forming a planet with a mass of two earth-masses. What is the angular momentum and orbital energy (kinetic + potential) of the resulting planet? c. What are the semi-major axis and eccentricity of the orbit of the resulting planet?

Consider a star orbited by two planets. Assume the star to have mass twice that of the Sun. Let planet 1 orbit with semi-major axis 10 AU, and eccentricity 0.6. Planet 2 orbits with semi-major axis 4 AU, and eccentricity 0. Assume the angular momentum vectors of the two planets to point in the same direction. Both planets have a mass of 1 Earth-mass. Let's assume these planets have a collision. a. At which point in its orbit must planet 1 be, at the time of collision? b. Assume the two planets stick together in the collision forming a planet with a mass of two earth-masses. What is the angular momentum and orbital energy (kinetic + potential) of the resulting planet? c. What are the semi-major axis and eccentricity of the orbit of the resulting planet?

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