Homework Assignment 6

Fall 2008

Prof. M. F. A'Hearn

Due: Mon, 24 Nov.

Problems NOT in textbook

- The average density of Mercury is 5.43[g-cm
^{-3}] and its radius is 2440[km]. Suppose the equation of state for the mantle is given by ρ[g-cm^{-3}]=3.50+1.296*10^{-6}*P [bar], a result crudely consistent with some rocks. Suppose that the equation of state for the core is given by ρ[g-cm^{-3}]=7.83+3.6*10^{-6}*P[bar], a reasonable approximation for a mostly iron core. Note: these are**NOT**the best equations to use, but they are easy to program and illustrative of the process.- Solve the differential equations for the interior in dimensionless
form, varying the core radius, x
_{c}, until the boundary conditions are satisfied at the surface and at the center. - Plot the pressure, density, and fractional mass as functions of x.
- What is the radius of the core, both as x
_{c}and as r_{c}, and how does this compare with models for Earth? - What are the central pressure and density in physical units?

- Solve the differential equations for the interior in dimensionless
form, varying the core radius, x

Problems in textbook

- chapter 5, problem 5.6
- chapter 5, problem 5.14
- chapter 5, problem 5.15
- chapter 5, problem 5.18
- chapter 12, problem 12.19
- chapter 6, problem 6.15
- chapter 6, problem 6.21