Problem Set THREE

Due Monday, February 10, 2003, at beginning of class.

Late penalty: 5 points if turned in by 5 p.m., 2/11. 10 points if turned
in by 5 p.m., 2/12. Not accepted after 5 p.m., 2/12.

Answer Key

Calculate a surface density (kg m^{2}) profile for the
solar system in the form of a simple bar graph. Your yaxis will be surface
density, the xaxis 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.

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.]

What is the gas retention age of a meteorite containing 8.72 gm
^{40}K
and 91.28 gm ^{40}Ar? You should assume that the meteorite
formed without any trapped gasses and that the only decay process possible
for ^{40}K is decay to ^{40}Ar. You will need to use the
halflife to find the decay constant (lambda) for the decay of ^{40}K
to ^{40}Ar. You may find useful information on halflives, 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. 143144 for information on meteorites, meteorite ages, and gas retention
ages.)

What is the most distant known TNO (transNeptunian object)? What are the
biggest five known TNOs and what are their orbital semimajor 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 semimajor
axis as the basis for determining "most distant.")

How many TNOs have orbital periods within 1/2 of one percent that of Pluto?

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]