Homework 3: Finding exoplanets

This homework must be submitted on paper; you may write out your work on paper, or type it into some word processor and then print it. Either way, staple together all pages and write your name legibly at the top of each page.

This assignment focuses on exoplanets: how do we find them? A good place to gain some basic information is this presentation:

In particular, read the sections on "Watch for a tiny eclipse" and "Detect tiny shifts in wavelength."

  1. Suppose that alien astronomers, in some nearby stellar system, are studying the Sun. They wonder if any planets might be orbiting it. They attempt to use the "transit" technique to detect planets as they pass in front of the Sun and block some of its light.
    1. What fraction of the Sun's light would Jupiter block if it passed directly in front of the Sun from their point of view?
    2. How long would the little dip in the Sun's apparent brightness last due to Jupiter's transit?

  2. The aliens make some measurements that suggest that there might be a transit ... but they aren't sure. Therefore, they attempt to use the radial velocity technique: they measure the radial velocity of the Sun over and over, looking for small, periodic variations which would indicate that the Sun is orbiting its center of mass with a planet. Again, we'll consider Jupiter as a possible target.
    1. What is the orbital velocity of Jupiter as it orbits the Sun?
    2. What is the orbital velocity of the Sun around its center of mass with Jupiter?
    3. The alien astronomers focus on an absorption line in the spectrum of the Sun at a rest wavelength of 500 nm. By how much does this wavelength change due to the Sun's varying radial velocity?
    4. How long must the aliens keep watching to see one complete period of this variation?

Bonus! The aliens could be in any location in space around the Sun. What is the probability that they happen to lie in just the right region to see transits by Jupiter?