## ASTR 688P: Planetary Science Homework Assignment 6 Fall 2008

Prof. M. F. A'Hearn
Due: Mon, 24 Nov.

Problems NOT in textbook

1. 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.
1. Solve the differential equations for the interior in dimensionless form, varying the core radius, xc, until the boundary conditions are satisfied at the surface and at the center.
2. Plot the pressure, density, and fractional mass as functions of x.
3. What is the radius of the core, both as xc and as rc, and how does this compare with models for Earth?
4. What are the central pressure and density in physical units?

Problems in textbook

1. chapter 5, problem 5.6
2. chapter 5, problem 5.14
3. chapter 5, problem 5.15
4. chapter 5, problem 5.18
5. chapter 12, problem 12.19
6. chapter 6, problem 6.15
7. chapter 6, problem 6.21