Astronomy 201 

Problem Set THREE

  1. Calculate a surface density (kg m-2) profile for the solar system in the form of a simple bar graph. Your y-axis will be surface density, the x-axis will be AU.  Compute one data point (i.e., bar on your bar graph) for each planet. To do this, use the estimated nebular masses thought necessary to form each planet and a surface area for each planet corresponding to an annulus in the ecliptic plane from which it might have  collected its material when it formed (e.g., for Jupiter, you might assume an annulus with an inner distance of 4 AU and an outer distance of 6 AU).  Comment on any general features/trends of your graph and on any deviations from the general features that you think demand an explanation.
  2. Show that most of the angular momentum in the planets is associated with Jupiter? Show that most of the angular momentum in the solar system is contained in Jupiter, not the Sun. [Click here, for some hints on how to proceed.]
  3. What is the gas retention age of a meteorite containing 8.72 gm 40K and 91.28 gm 40Ar?  You should assume that the meteorite formed without any trapped gasses and that the only decay process possible for 40K is decay to 40Ar. You will need to use the half-life to find the decay constant (lambda) for the decay of 40K to 40Ar. You may find useful information on half-lives, decay rates and the mathematics of radioactive decay here. To do this problem, you need to be able to work with natural logarithms.  If you need help with this, contact me or work with a classmate. (See also p. 143-144 for information on meteorites, meteorite ages, and gas retention ages.)
  4. What is the most distant known TNO (transNeptunian object)? What are the biggest five known TNOs and what are their orbital  semi-major axes? [go to this link to find information on the known TNOs and on how to determine their sizes.  The brightest objects are presumably the biggest.  Note that smaller values of the absolute visual magnitude H indicate brighter objects than larger values of H and that brightness is equivalent to size, i.e., smaller H corresponds to larger size. Use the semi-major axis as the basis for determining "most distant.")
  5. How many TNOs have orbital periods within 1/2 of one percent that of Pluto?
  6. Estimate the lifetime for a star that is 10,000 times more luminous and 20 times more massive than the Sun. [see here for some hints]