Directions: Solve these five problems, showing your work. Clearly indicate your answer for each
question, making sure that the units are correct.
1. Asteroid (4) Sylvia has a semimajor axis a of 3.48 AU and a diameter of 250km. Using
Kepler’s law, find its orbital period around the Sun, in years. [1 point]
2. Saturn’s moon Kiviuq was discovered by a Canadian-led team in 2000. It has a semimajor axis
of 11,300,000 km. What is its orbital period around Saturn, in Earth days? You will need to use
the gravitational constant, G = 6.67 x 10-11 m3
kg-1 s-2, and the mass of Saturn, 5.68 x 1026 kg
[2 points]
3. Earth and Jupiter are about 4 AU apart at their closest approach. How long does it take for a
radio signal from Earth to reach Jupiter when the two planets are closest? [1 point]
4. The Keck Telescope has a mirror diameter of 10 m and observes in visible wavelengths (λ =
600 nm = 6×10-7 m). What is its resolving power? How large a diameter would a microwave
telescope that observes at λ = 1 millimeter need to be in order to have the same resolving
power? [3 points]
5. Draw a picture that explains why we don’t see a solar eclipse every time there is a new moon
[3 points]
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