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)
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