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14 The Dynamical Equations of Cosmology
14.3 Consider a star orbiting near the edge of a galaxy in a circular orbit, with
the mass of the galaxy concentrated in the central bulge. What is the relation
between the orbital velocity and radius of the orbit?
14.5 Now suppose that the galaxy is dominated by dark matter distributed spherically symmetrically as in Fig. 14.1 with density ρ(r ). What is the relation
between the orbital velocity and radius of the orbit? In the special case that the
velocity is constant show that the density distribution is proportional to 1/r
2 .
What is the total mass of the dark matter in the galaxy? Is this a problem?
14.6 Look up a reference on the work of Zwicky, then work out the way that the
random motion in a cluster of galaxies (velocity dispersion) can determine
their mass (Zwicky 1933; Wiki DM).
14 The Dynamical Equations of Cosmology
14.3 Consider a star orbiting near the edge of a galaxy in a circular orbit, with
the mass of the galaxy concentrated in the central bulge. What is the relation
between the orbital velocity and radius of the orbit?
14.5 Now suppose that the galaxy is dominated by dark matter distributed spherically symmetrically as in Fig. 14.1 with density ρ(r ). What is the relation
between the orbital velocity and radius of the orbit? In the special case that the
velocity is constant show that the density distribution is proportional to 1/r
2 .
What is the total mass of the dark matter in the galaxy? Is this a problem?
14.6 Look up a reference on the work of Zwicky, then work out the way that the
random motion in a cluster of galaxies (velocity dispersion) can determine
their mass (Zwicky 1933; Wiki DM).