In a supernova explosion, the core of a heavy star collapses and the outer layers are blown away. Before collapse, suppose the core of a given star has twice the mass of the sun and the same radius as the sun, and rotates with period 20 days. The core collapses in a few seconds to become a neutron star of radius \(20 \mathrm{~km}\).

(a) Estimate its new period of rotation.

(b) Estimate the ratio of the final rotational kinetic energy to the initial rotational kinetic energy of the core. What could account for the change?