The weight of a star is usually balanced by two forces: the gravitational force,

Question

The weight of a star is usually balanced by two forces: the gravitational force, acting inward, and the force created by nuclear reaction, acting outward. Over a long period of time, the force due to nuclear reactions gets weaker, causing the gravitational collapse of the star and crushing atoms out of existence. Under such extreme conditions, protons and electrons are squeezed to form neutrons, giving birth to a neutron star. Neutron stars are massively heavy - a teaspoon of the substance of a neutron star would weigh 100 million metric tons on the Earth.

a) Consider a neutron star whose mass is twice the mass of the Sun and whose radius is 12.1 km. (The mass of the Sun is 1.99

Explanation / Answer

a) v = 2 pi r/T = 2*pi*12.1E3/3.01= 2.53E4 m/s

b) g = G M/R^2 = 6.67E-11*2*1.99E30/12.1E3^2= 1.81E12 m/s^2

C) W neutron/W earth = g neutron/gearth = 1.81E12/9.81= 1.845E11

d) G M m/r^2 = m v^2/r

G M/r = v^2

v = 2 pi r/T = 2 pi r f

G M/r = ( 2 pi r f)^2

6.67E-11*2*1.99E30/(24.2E3) = (2*pi*24.2E3*f)^2

f=689 Hz = 689 rev/s

so 41340 rev/min

e) geostationary is when T = T of star = 3.01 s

6.67E-11*2*1.99E30/(r) = (2*pi*r/3.01)^2

r= 3.93E6 m

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