Homework 2
Due: 14 October 2015, by end of the work day
8. page 295, 6.6, Problem 14
9. page 323, 6.10, Problem 15
10. page 527, 10.9, Problem 1
11. page 528, 10.9, Problem 2
12. page 528, 10.9, Problem 10
13. In a spherical, nonrotating star, hydrostatic equilibrium is given by
where P is the pressure, ρ is the density, and φ is
the gravitational potential. Show that at any given point, normals to
surfaces of constant P and constant φ
are parallel. Suppose the mass rotates uniformly about the z-axis with
frequency Ω o so that the new equilibrium equation is
∇ P + ρ ∇ φ - εs
ρ Ωo2s = 0,
where εs is the unit vector in the radial direction (in
cylindrical coordinates) and s is the radial coordinate in cylindrical
coordinates.
Show that at any given point, normals to
surfaces of constant P and constant φeff
are parallel. Here, φeff is an effective potential. Find
the form for φeff.