A spinning neutron star of mass M=1.4 solar masses, constant density, and radius R=10 km has a period P=1s. The neutron star is accepting mass from a binary companion through an accretion disk, at a rate of dM/dt=10^-9 solar masses per year. Assume the accreted matter is in a circular Keplerian orbit around the neutron star until just before it hits the surface, and once it does then all of the matter's angular momentum is transferred onto the neutron star. Derive a differential equation for dP/dt, the rate at which the neutron-star period decreases.
A spinning neutron star of mass M=1.4 solar masses, constant density, and radius R=10 km has a period P=1s. The neutron star is accepting mass from a binary companion through an accretion disk, at a rate of dM/dt=10^-9 solar masses per year. Assume the accreted matter is in a circular Keplerian orbit around the neutron star until just before it hits the surface, and once it does then all of the matter's
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