Problem set 3 for ASTR 221: Stars and Planets
Due Friday October 3 at 5pm.
Note that Kutner has problems, questions and computer problems at the
end of each chapter: make sure you do the one I assign. Also, please
make an effort to write neatly so Ashley and I can read your solutions and give
you the credit you deserve.
Hints for perfect plots:
(1)(a) Using the table of solar system abundances in class notes, make
an estimate of the relative abundances of the following molecules in
the solar nebula:
(2) Kutner question Q26.14 (Hint: Consider the velocities of the
infalling meteors and the orbital and rotational motions of the Earth.)
(3,4) Kutner problems P26.2, P26.6
(5) Kutner Computer problem C23.1
(6) In this problem, you will calculate the age of a meteorite using actual
data on the abundances of rhenium and osmium, which are related via
the beta decay:
H2, H2O, NH3,
CH4, MgSiO3, FeS
(b)For each compound, look
up the condensation temperature in class notes
(c) using the temperature structure of the solar nebula from notes, decide which compounds would have been important in the formation of the early solar system
and, if so, whether they would have been part of the formation of the giant or terrestrial planets or both.
187Re --> 187Os, with a half life of 4.16x1010 years
(a) What is the decay constant for this reaction?
(b) The following table summarizes measurements taken of Re and Os isotope
ratios to the stable isotope 188Os, for different minerals
samples within the meteorite:
Plot the results with 187Re/188Os along the horizontal
axis and 187Os/188Os along the vertical axis.
187Re/188Os
187Os/188Os
0.664
0.148
0.669
0.148
0.604
0.143
0.484
0.133
0.512
0.136
0.537
0.138
0.414
0.128
0.369
0.124
The vertical axis is showing the isotope ratio of osmium
(daughter isotope/stable isotope), while the horizontal axis is
showing the amount of the paren element rhenium, normalized by
the amount of the stable isotope of osmium.
(c) Chemical reactions (determined by the atomic number, not the
atomic weight) determine the different amounts of rhenium and osmium
through the meteorite. Is the isotope ratio of the two osmium isotopes
determined by chemical reactions? If not, what affects this isotope
ratio?
(d) Draw a straight line that goes as closely as possible through
all the points (use a line fitting routine in your plotting package if
you prefer) and work out the y-intercept (for 187Re/188Os =0).
The value of the y-intercept is equivalent to the observed
values of the two elements at the formation time of the meteorite.
Measure the age, giving an error bar.