Problem set 2 for ASTR 221: Stars and Planets

Due 5pm Thursday Sept 23

Individual questions (hand in one solution each):

(1) (from Carroll and Ostlie) (a) Assuming the Sun interacts only with Jupiter, calculate the total orbital angular momentum of the Sun-Jupiter system.
(b) Estimate the contribution that the Sun makes to the total orbital angular momentum of the Sun-Jupiter system. For simplicity, assume that the Sun's orbital eccentricity is 0. Hint: first find the distance from the center of the Sun to the center of mass.

(2) (also from C&O) Verify that Kepler's third law in the form of Eq 2.37 in Carroll and Ostlie applies to the four moons that Galileo discovered orbiting Jupiter -- Io, Europa, Ganymede and Callisto.
(a) Plot log10(P) vs log10(a)
(b) From the graph, show that the slope of the best-fit straight line through the data is 3/2.
(c) Calculate the mass of Jupiter from the value of the Y-intercept.

(3)(a) Assume that a spherical dust grain located 1AU from the Sun has a radius of 0.1 micron and a density of 3 g/cm**3. In the absence of gravity, estimate the acceleration of that grain due to radiation pressure. Assume that the solar radiation is completely absorbed.
(b) What is the gravitational acceleration on the grain?

(4) Comet 1943I, which last passed through perihelion on Feb 27, 1991, has an orbital period of 512 years and an orbital eccentricity of 0.999914 (!). This is one of a class of so-called sun-grazing comets.
(a) What is the comet's semi-major axis?
(b) Determine its perihelion and aphelion distances from the Sun.
(c) What is the most likely source of this object, the Oort Cloud or the Kuiper belt?
Carroll and Ostlie (on reserve in the library) p 29, 30 may be useful here.

Group homework question (hand in one per group). Each group should hand in a description of what each person in the group did; you should agree on the approach and the general answer, but can allocate sub-tasks to each other.

(G1) Using the informative web page of David Jewitt at http://www2.ess.ucla.edu/~jewitt/kb.html write 1-2 page of words, with plots extra, about Pluto and Kuiper Belt objects, addressing the following questions:

• What is a Plutino and how does Pluto differ from the others? Do you think we should call Pluto a planet, a dwarf planet or a Kuiper belt object? Give your reasons.
• Plot up the distribution of inclination, perihelion and aphelion distance of the known Plutinos (dont just grab the plots from the web page, make them yourselves) and summarize what you see in a few sentences
  

  Hints for perfect plots:

  • label your axes
  • use plot limits that are sensible, dont just let your plotting package have its head
• How do the properties of Plutinos differ from other Kuiper Belt objects?
• Summarize the theories about how Plutinos and other Kuiper Belt objects got into, and stay in, their current orbits.