Consider a spiral galaxy with a "flat" rotation curve beyond the central 2 kpc
a. Derive the general relation giving the orbital period, P, of a star (or other object) in the disc orbiting the centre of the galaxy, as a function of the radius, R (>2kpc) , from the galactic centre.
b. If stars in the flat part of the rotation curve are orbiting at 250km/s, calculate the orbital period, P in years, for a star at 8kpc from the galactic centre and a hydrogen cloud at 30kpc.