Consider a star orbiting around the center of its galaxy at a radius R with a velocity vc, so that the orbital angular frequency is w = vc/R.(a) Assume the galaxy is well described by an isothermal sphere model, which yields a at rotation curve: v(R) = vc. In this case, the gravitational potential is (R) = v^2c ln(R) + a constant. What is the epicycle frequency of small radial oscillations? How does it compare to w in this case? Hint: The equation for K uses the effective potential, which includes a term for specific angular momentum; that quantity is straightforward to calculate for the circular orbit assumed here.
Consider a star orbiting around the center of its galaxy at a radius R with a velocity vc, so thatthe orbital angular frequency is w = vc/R.(a) Assume the galaxy is well described by an…
