The weight of a star is generally balanced by two forces: the gravitational force, acting inward and the force made by nuclear reaction, acting outward. Over a long period of time, the force due to the nuclear reactions gets weaker, causing the gravitational collapse of the star and crushing atoms out of existence. Beneath such extreme conditions, protons and electrons are squeezed to form neutrons, giving birth to the neutron star. Neutron stars are very heavy - a teaspoon of the substance of a neutron star would weigh 100 million metric tons on the Earth.
i) Let, consider a neutron star whose mass is two times the mass of the Sun and whose radius is 10.1 km. When it rotates with a period of 2.51 s, determine the speed of a point on the Equator of this star?
ii) Determine the value of g at the surface of the star?
iii) When a satellite is to circle 10.1 km above the surface of such a neutron star, determine how many revolutions per minute will it make?
iv) Evaluate the radius of the geostationary orbit for the neutron star?