Homework assignment 2

Please show all your work, written as neatly as possible. Hand in your papers to me directly or place them into the plastic mail folder outside my office door, anytime up to and including the class meeting on Friday, Dec 19.

1. Carroll and Ostlie Problem 3.2:
   At what distance from a 100-watt light bulb is the radiant flux equal to the solar constant?

2. Carroll and Ostlie Problem 3.7:
   An average person has 1.4 square meters of skin at a temperture of roughly 306 K. Consider this person to be an ideal radiator standing in a room at temperature 293 K.
   1. Calculate the energy per second radiated by the person. Express your answer in erg/s and in Watts.
   2. Determine the peak wavelength of the person's blackbody radiation. In what region of the spectrum is this?
   3. A blackbody also absorbs radiation from its environment. Calculate the energy absorbed by the person, in both erg/s and in Watts.
   4. Calculate the net energy per second lost by the person due to blackbody radiation.
   5. Extra: compare this to the energy in a typical diet of 2000 calories per day.

3. Carroll and Ostlie Problem 3.8:
   Consider a model star as a perfect blackbody of surface temperature T = 28,000 K and radius 5.16 x 10^(11) cm, located a distance 180 pc from the Earth. Calculate
   1. luminosity
   2. absolute bolometric magnitude
   3. apparent bolometric magnitude
   4. distance modulus
   5. radiant flux at star's surface
   6. radiant flux at Earth's surface, and compare to the solar constant
   7. peak wavelength

4. The star of the previous problem is observed through the standard astronomical filters B and V. You can find transmission curves for these filters at
   • B filter tranmission curve
   • V filter tranmission curve
   Estimate as accurately as you can the total energy from the star which would be collected through each passband in a single second by a (perfect) telescope with a mirror diameter of 12 inches (like one in the RIT Observatory). Estimate also the number of photons collected per second by this instrument.

5. The star of the previous-previous problem is surrounded by a thin disk of dust. The disk has an inner radius of 100 AU and an outer radius of 200 AU. Radiation from the star heats the dust, which radiates away energy in the infrared. You may treat the disk as an optically thick body.
   1. Assume each dust particle is a little sphere which acts like a perfect blackbody. Derive a formula which gives the temperature of a dust particle as a function of distance r from the star.

      For simplicity, assume that all the dust has a single temperature, the temperature of a particle halfway out in the disk, at r = 150 AU.

   2. What is that temperature?
   3. How much total energy does the disk radiate each second?
   4. At what wavelength does the spectrum of the dust reach a peak?
   5. At that wavelength, which emits more radiation, the star or the disk?
   6. Make a graph which shows the spectrum of the disk+star system, running from the blue end of the visible (4000 Angstroms = 0.4 microns) to the mid-infrared (1,000,000 Angstroms = 100 microns). Use a log-log scale on your graph.

      Now, for extra credit and a gold star on your paper, repeat the calculations in steps c-f for a disk in which the temperature of the dust varies smoothly with radius, so that particles at any distance r are in thermal equilibrium.

   Copyright © Michael Richmond. This work is licensed under a Creative Commons License.