set1 - Problem Set I Seasons Image of a Candidate...

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Problem Set I: Seasons; Image of a Candidate Exo-Planet due 19 Sep 2008 General comment about problem sets: things are usually simpler than you think (no trick ques- tions!). More specifically, (i) you should not need more space than what is provided below the questions (OK, assuming neat, fairly small handwriting ;-); (ii) unless explicitly stated, you should not need information other than the lectures and Carroll & Ostlie; (iii) unstated complications should be ignored; for instance, in I.1.1, do not worry about the atmosphere, and assume we’re interested in the flux received on a 1 square meter piece of ground that is perfectly horizontal, and in I.2 ignore the orientation of the orbit (of course, it does not hurt your mark to mention that you ignore such complications and thus show that you are aware of possible pitfalls). Also, a request: please start on the problem set well before the due date (due at the start of class on the above date), and preferably come to office hours if you have questions (we do answer e-mails, but only by the time of the next lecture; hence, e-mails the day before the due date will likely not be answered in time). Before you start this problem set, you may find it useful to read CO § 1.3, “Daily and seasonal changes,” § 2.3, “Kepler’s laws derived,” and § 3.2, “The magnitude scale.”
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I.1. Solar System Seasons In principle, two effects could cause seasons: a changing distance from the Sun in an eccentric orbit, and changing amount of daytime and height of the Sun in the sky if a planets rotation axis is inclined relative to its orbit. For Earth, the latter effect dominates. Here, we derive this
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