

Astronomy 23/223 Homework:
In class we discussed the formation of the solar system and planets, and the use of radiometric dating techniques to measure dates. In this problem set, we bring together these two concepts and ask the fundamental question: How old is our solar system? To answer this, we need to be able to make measurements in Earthbound laboratories using the oldest possible material floating around our Sun. This material comes from two sources: meteorites and Moon rocks. Although we’ll talk in more detail about these topics later in the course, for now we can use them to understand solar system formation processes. Of course, fundamentally the age of the solar system is the age of the universe, which present estimates suggest is about 12 billion years. What we’re interested in is the when various bodies formed in the solar system. Remember that these processes can be associated with any of the following: (a) the first condensation of solid particles from a nebular gas (b) differentiation with accretion of particles to form planetsized masses (c) postaccretion differentiation associated with impacts, melting, or metamorphism. As we study the various bodies in the solar system, we will come to know and understand these processes better. The purpose of this assignment is to determine the age of certain extraterrestrial objects. In class, we could have done an exercise to calculate the age of the igneous rocks that make up the anorthositic, or highland, areas of the Moon. To check your answers to that exercise, consult this link. Those dates came from a paper by Papanastassiou and Wasserburg (1972). We will now use the same techniques to determine the age of two types of meteorites, and then decide which ones are the oldest and, therefore, the best estimates of the age of the solar system. In making these calculations, you can use the Linear Regression Worksheet below or a computer spreadsheet. In Excel, the regression tool can be found under the Tools  Data Analysis  Regression tabs; make sure that the “Constant is Zero” box is NOT checked. Be sure to use the correct value of the decay constant for the isotopes in each case. After determining the age of Allende and the basaltic achondrites, rank the following in order by age: lunar anorthosites (from the inclass exercise  see links above), the Allende chondrite, and basaltic achondrites. Compare these ages with the three processes of solar system formation listed above, and then, in five sentences or less, describe a history of the solar nebula based on the timing of formation of each of these rock types. 
I. Allende CV3 chondrite Chondrites are a class of meteorites composed of tiny, rounded spheres containing silicate minerals (called chondrules) and a finegrained, dusty matrix between them. Relatively larger mineral crystals called inclusions are also present. The chondrules and inclusions are made up of elements such as Ca, Ti, and Al that are believed to have formed early in the solar nebula.. The meteorite Allende is large and commonly available for study (most large science museums count a sample of Allende in their collections). Thus, many geochemical studies have been performed on them A study by Gray et al. (1973) used Rb isotopes to study the coarsest grains in Allende: 
^{87}Rb/^{86}Sr  ^{87}Sr/^{86}Sr 
0.00014  0.698770 
0.00019  0.698810 
0.00075  0.698890 
0.00393  0.698990 
0.00432  0.699030 
0.00660  0.699250 
0.00776  0.699140 
0.00853  0.699330 
0.05213  0.702140 
0.00017  0.698770 
Determine the age of these inclusions (show all work)!
II. Basaltic Achondrites Basaltic achondrite meteorites lack chondrules and also crystallized from a magma. They probably formed as baslalt flows on their parent bodies. Although many of them have been broken up (brecciated) and metamorphosed (exposed to heat and pressure after crystallizing), some meteorites in this class may preserve evidence of early solar nebular formation processes. Use the following data from Papanastassiou and Wasserburg (1969) to estimate the ages of these basaltic achondrites: 
^{87}Rb/^{86}Sr  ^{87}Sr/^{86}Sr  
Juvinas  0.00644  0.699678 
Pasamonte  0.00769  0.699481 
Sioux Co.  0.00775  0.699491 
Nuevo Laredo  0.01228  0.699840 
Jonzac  0.01671  0.700062 
Stannern  0.02396  0.700475 
Moore Co.  0.00234  0.699140 
Caveat As is obvious, the data we are using here are at least 2030 years old. Our technology for making these measurements has improved greatly over this period of time, and many of these dates have been moved back in time a little, to roughly 4.56 billion years. However, the newer methods for calculating dates are more numerically complex than those used here, and therefore are intractable for use in this class. All of them are based on the same basic principles, however, that we are using here! 
USE OF THE FOLLOWING WORKSHEET IS OPTIONAL...
alternatively, you can do these calculations in an Excel spreadsheet.
Linear Regression the OldFashioned Way
(Fill in the Blanks...)
(Or
click here to print out a blank form as a pdf file)
X Data
X_{i} 
X_{i}^{2} 
Y Data
Y_{i} 
Y_{i} ^{2} 
X_{i}·Y_{i} 

Sample 1  
Sample 2  
Sample 3  
Sample 4  
Sample 5  
Sample 6  
Sample 7  
Sample 8  
Sample 9  
Sample 10  
SUM 
Please do not round answers until you determine the age. Any rounding before will throw your answers off!!
Find each of the following pieces of information. n = number of samples Now, solve the following equation, and you'll know the equations of your line.

Equation for regression line is: Y = (slope)X + intercept Therefore, Y = (______)X + _______

Now that you have the slope, you need to find the time that it takes to decay. This will be the age of the rocks. These equations should look familiar to you from class:
Knowing this information, recall that the slope of the 87Sr Vs 87Rb graph is as follows. Now use this information with the slope you calculated previously solve for the time (aka the Age of the rock). 
References: Chen, J.H., and Wasserburg, G.J. (1981) The isotopic composition of uranium and lead in Allende inclusions and emteoritic phosphates. Earth and Planetary Science Letters, 52, 115. Gray, C.M., Papanastassiou, D.A, and Wasserburg, G.J. (1973) The identification of early condensates from the solar nebula. Icarus, 20, 4330454. Manhes, G., Allègre, C.J., and Provost, A. (1984) UThPb systematics of the eucrite “Juvinas”: precise age determination and evidence for exotic lead. Geochimica et Cosmochimca Acta, 48, 22472264. Papanastassiou, DA, and Wasserburg, G.J. (1969) Initial strontium isotopic abundances and the resultion of small time differences in the formation of planetary objects. Earth and Planetary Science Letters, 5, 361376. Papanastassiou, DA, and Wasserburg, G.J. (1972) RbSr systematics of Luna 20 and Apollo 16 samples. Earth and Planetary Science Letters, 17, 5263. Tatsumoto, M., Knight, R.J., And Allègre, CJ (1973) Time differences in the formation of meteorites as determined from the ratio of lead207 to lead206. Science, 180, 12791283. Wasserburg, G.J., Tera, F., Papanastassiou, DA, and Hunecke, J.C. (1977) Isotopic and chemical investigations on Angra dos Reis. Earth and Planetary Science Letters, 35, 294316. 
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Last updated on 25 September, 2008 . 