The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height zo): p(r) = Po, r< Ro 0, r > Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobs (r) = VGT P0žo Ro 5/2 1+e-4r/Ro Draw the expected and observed rotational velocity into the plot below:

The most mass of our Milky Way is contained in an inner region close to the core with radius Ro- Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height zo): p(r) = Po, r< Ro 0, r > Ro (a) Derive an expression for the mass M(r) enclosed within the radius r. (b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r. (c) Astronomical observations indicate that the rotational velocity follows a different behaviour: Vobs (r) = VGT P0žo Ro 5/2 1+e-4r/Ro Draw the expected and observed rotational velocity into the plot below: