Neutron stars are extremely dense objects that are formed fr

Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose that the mass of a certain spherical neutron star is three times the mass of the Sun and that its radius is 12.5km. Determine the greatest possible angular speed it can have for the matter at the surface of the star on its equator to be just held in orbit by the gravitational force.

Solution

From Newton\'s Law of Gravitation

G M m / r² = m v² / r

v = sqrt [G M / r]

v = sqrt ( 6.67 * 10^-11 * 3 * 1.99 * 10³⁰ / 12500 )

v = 1.78 * 10⁸ m/s

angular speed = v / r = 1.78 * 10⁸ / 12500

w = 1.42 * 10⁴ rad/s