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:
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.

(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:
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:
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
Plot the results with 187Re/188Os along the horizontal axis and 187Os/188Os along the vertical axis.
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.