 
Summary: ASTR 5120: Problem Set 1
1. In practice, the collisionless Boltzmann equation and FokkerPlanck equations are
useful when the system under consideration is symmetric enough to cut down the
number of degrees of freedom to something more manageable. Consider a spherically
symmetric cluster (perhaps of galaxies) that is in a steady state and in which v r
and v # vanish. By expressing the collisionless Boltzmann equation in spherical co
ordinates and taking moments (as we did to in the general case) show that the
system obeys,
d(#v 2
r )
dr
+
#
r # 2v 2
r  # v 2
# + v 2
# ## = #
d#
dr
.
