Kepler’s Laws and Elliptical Orbits of Planets

1. Define Kepler’s first law of planetary motion. (1 point) 2. Define Kepler’s second law of planetary motion. (1 point) 3. Define Kepler’s third law of planetary motion. (1 point) 4. Draw an ellipse and label it completely. Your diagram should include a, b, f, d, 2d, the axes, and the shape of the ellipse with labels to describe what these things are. (5 points) 5. You have been assigned to the USS Enterprise as a science officer in the astrophysics department. Mazel tov! Your captain, James Tiberius Kirk, has received orders from Starfleet headquarters to explore a quadrant of previously unexplored space. He sends the Enterprise to an unknown planetary system and sends a mission directive to the astrophysics department to analyze the system. a) It is determined that the system you are supposed to analyze has a star that has a mass that is approximately 1 ???. The planet in question, Ceti Alpha V, has an orbital period of 3.7 ??????????. What is the semi-major axis in ???? of Ceti Alpha V’s orbit? (2 points) b) The Enterprise is currently positioned on one side of the orbit. You have calculated the semi-major axis of Ceti Alpha V’s orbit on said side. The captain wants to send the Enterprise to the other end of the orbit of the planet (from vertex to vertex along the major axis ignoring the fact that Ceti Alpha V would be in the way). What is the distance between vertex to vertex? (2 point) c) In that same system, the planet Ceti Alpha VI has been observed to have a semimajor axis of 8.1 ????. What is the orbital period of Ceti Alpha VI? (2 points) d) It turns out that another science officer in your department found that the focal distance of Ceti Alpha VI’s orbit is 6.6 ????. What is the eccentricity of Ceti Alpha VI’s orbit? (2 points) e) EXTRA CREDIT: Who is waiting for Commander Pavel Chekov and Captain Clark Terrell on the surface of Ceti Alpha V? (1 point) 6. The Enterprise is now on a course for a new planetary system called Janus. Captain Kirk wants you to determine the mass of Janus IV which is a planet that is part of the planetary system. You found that the star Janus has a mass of 1.925 ???, the orbital period of Janus IV is 3.25 ??????????, and the semi-major axis of Janus IV’s orbit is 2.74 ????. What is the mass of Janus IV? 1 ???? = 1.496×1011 ?? (4 points)