# Homework set 5

Due Dec 5, 2017

1. Derive an equation which gives the equilibrium temperature of a spherical blackbody in orbit at a distance r around a star of luminosity L. Proceed as follows:
1. Write an equation for the amount of energy striking the planet each second; we'll assume that all this energy is absorbed.
2. Write an equation for the amount of energy radiated away from the planet's surface each second. Assume that the planet rotates quickly enough that all portions of its surface are at the same temperature.
3. Set the incoming and outgoing energies equal to each other, and solve for temperature T in terms of the other quantities.
2. We will study proto-planetary disks around Sun-like stars using the JCMT, which has a diameter of D = 15 m. Our goal is to look for rings in the disk material at two specific distances: 1 AU and 20 AU from the host star.
1. What are the wavelengths at which dust at those two orbital distances will emit most strongly?
2. What is the diffraction limit of JCMT at these wavelengths?
3. How far away from Earth could a star be before features at 1 AU become indistinguishable? What about features at 20 AU?
4. Look in the Gliese catalog for Sun-like stars -- defined as stars with a spectral class starting with "G". So, "G", "G2", "G4V" would all qualify. For features at 1 AU, and then for features at 20 AU,
1. How many stars are close enough for us to see the features?
2. How many of those stars would be visible at an airmass of less than 2.0, as seen from JCMT?