The weight of a star is usually balanced by two forces: the gravitational force,
ID: 1467807 • Letter: T
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 13.3 km. If it rotates with a period of 2.91 s, what is the speed of a point on the Equator of this star? 2.8717×104 m/s You are correct. Your receipt no. is 154-986 Help: Receipt Previous Tries
b) What is the value of g at the surface of this star? 1.5016×1012 m/s^2 You are correct. Your receipt no. is 154-794 Help: Receipt Previous Tries
c) Compare the weight of a 1.80-kg mass on the Earth with its weight on the neutron star. How many times bigger is this mass on the neutron star than on Earth? 1.5307×1011 You are correct. Your receipt no. is 154-4634 Help: Receipt Previous Tries
d) If a satellite is to circle 13.3 km above the surface of such a neutron star, how many revolutions per minute will it make? Do not enter unit. 3.5874×104 You are correct. Your receipt no. is 154-1223 Help: Receipt Previous Tries
e) What is the radius of the geostationary orbit for this neutron star?
Explanation / Answer
e) the time period of geostationary satellite = time periode of the star.
T = 2.91 s
mass of the star, M = 1.5307*Me
= 1.5307*10^11*5.98*10^24
= 9.154*10^35 kg
let r is the radius of geostationary obit for the star.
we know, Time periode, T = 2*pi*r^(3/2)/sqrt(G*M)
T^2 = 4*pi*r^3/(G*M)
r^3 = G*M*T^2/(4*pi^2)
r = (G*M*T^2/(4*pi^2))^(1/3)
= (6.67*10^-11*9.154*10^35*2.91^2/(4*pi^2))^(1/3)
= 2.357*10^8 m
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