ASTR 688P: Planetary Science
Homework Assignment 6
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
- 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.
- Plot the pressure, density, and fractional mass as functions of x.
- What is the radius of the core, both as xc and as
rc, and how does this compare with models for Earth?
- What are the central pressure and density in physical units?
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