Week 2 Lecture 2
Solutions at the bottom.

1)  In-video quiz at timepoint 04:58.

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola."
- Wikipedia, orbital eccentricity, http://en.wikipedia.org/wiki/Orbital_eccentricity

2)  In-video quiz at timepoint 05:58

Oops! Ronen said he would "exaggerate the ellipticity" of the orbit. He meant eccentricity.

3)  In-video quiz at timepoint 13:25.

Consider the Earth, with a semimajor axis a=1AU (astronomical unit) and a period of P=1 year. If a new dwarf planet was discovered with a semimajor axis of 200 AU, how long would it take the new dwarf planet to complete one sidereal trip around the Sun, in years? Round your answer to two significant digits.

[Open-ended]

4)  In-video quiz at timepoint 14:55.

Consider Venus in the Ptolemaic model of the Solar System. Which of the following would best describe what an observer should expect to see?

a) No phases of Venus. Venus always remains close to the same size.
b) Some phases of Venus but not all. Venus always remains close to the same size.
c) Full range of phases for Venus. Venus noticeably changes size.
d) No phases of Venus. Venus noticeably changes size.

Solutions:

3) (2700,2900)
Although we don't know the value of K, we can take a ratio of the periods and semimajor axes in order to solve this problem. P2 = K⋅a3, so writing this for both planets gives (Pdwarf / PEarth)2 = K⋅a3dwarf / K⋅a3Earth = (adwarf / aEarth)3. Plugging in 1 year for PEarth, 1 AU for aEarth, and 200 AU for adwarf allows you to solve for Pdwarf in years. This comes out to 2,828 years, but rounded to two significant digits this would be 2,800 years.

4) b) Some phases of Venus but not all. Venus always remains close to the same size.