General Astronomy, 29:61
Fall, 2004
Seventh Homework Set...October 19, 2004.
Due October 27, 2004

Show calculations and give reasons for your answers. Note: Two of the problems (# 2 and #3 ) are ``big person'' questions, and have twice the points of the others .

(1) What is the thermal speed (taken as the root-mean-square or rms speed of the molecules) of carbon dioxide molecules in the atmosphere of Venus?

(2) ...10pts A planet has a mass of $10^{24}$ kg and a radius of 2000 km. The surface temperature is 300K. (a) Calculate the escape speed from the surface. (b) Calculate the thermal speed of a carbon dioxide molecule. (c) Would the planet be able to retain a carbon dioxide atmosphere over a period of time equal to the age of the solar system? Justify your answer.

(3) ...10 pts The radioisotope Strontium 90 ($_{38}Sr^{90}$) has a half life of 28.8 years to a beta-decay reaction,

$$_{38}Sr^{90} \rightarrow _{39}Y^{90} + e + \nu$$ (1)

You obtain a sample which has 0.2 micrograms (1 microgram = $10^{-6}$ grams) of $_{38}Sr^{90}$. (a) How many nuclei of $_{38}Sr^{90}$ are in the sample? (b) What is the number of decays per second you would measure with a Geiger counter, or other apparatus? Hint: Here is a good opportunity to employ your differential calculus in a science problem.

(4) This problem explores the formation of craters on the surface of an object like the Moon, and how we use it to date surfaces. Let's assume for the sake of this problem that the rate of objects impacting and forming craters has been constant since the formation of the solar system. The assumed rate is 20 impacts per $10^6$ km$^2$ per Gyr. Remember that 1 Gyr $=10^9$ years. How many craters would there be on a $10^6$ km$^2$ area that had formed 4.2 billion years ago? How many craters would there be on an identical area that had formed 3.2 billion years ago? Describe how the results of this problem compare with the case for the Moon.

(5) Look at Figure 9-20g from the textbook, which presents data on craters on four of the moons of Jupiter. Based solely on the data given in this figure, what would you say about the geological histories of Callisto and Europa? Based on this figure, what would you expect for the appearance of these objects?

(6) The mean density of the Earth is 5520 kg/m$^3$. The typical density of a rock is about 3000 kg/m$^3$. Given these numbers, make a rough estimate of the size of the metal core of the Earth. Assume that it has the density of iron, which is 7874 kg/m$^3$.