5) A neutron star is a burnt out star in which gravitational forcestake over. The gravity condenses all the matter to such an extentthat all protons and electrons fuse together, creating neutrons.Thus, the star consists of one giant nucleus containing onlyneutrons. The neutron star at the center of the Crab Nebula has amass of approximately 1.4 times that of our sun, and a diameter ofonly 12.2 miles. It also spins at a rate of 4.81radians/second.
a) How long does it take for this neutron star to complete onerotation?
b) If you were standing on the surface of this star, at itsequator, how fast would you be going? Give your answer in bothmiles/hour, and also as a ratio compared to how fast youârerotating through space if you stand on the surface of the Earth atthe equator.
c) What is the density of the matter in this star? (Give youranswer in both kilograms per cubic centimeter and pounds per squareinch.)
d) The escape velocity of the Earth is about 25,000 miles/hour. Ifa rocket was launched with this velocity from the surface of thisneutron star, how far would it get from the surface?
e) What is the escape velocity for this star? (Calculate it fromfirst principles. Donât just use the formula. Give your answer inmiles/hour.)
f) At what height would a satellite around this star have to be, inorder to be in a geosynchronous orbit with it?
g) How fast would a satellite in geosynchronous orbit about thisstar be traveling? (Give your answer in miles/hour.)
5) A neutron star is a burnt out star in which gravitational forcestake over. The gravity condenses all the matter to such an extentthat all protons and electrons fuse together, creating neutrons.Thus, the star consists of one giant nucleus containing onlyneutrons. The neutron star at the center of the Crab Nebula has amass of approximately 1.4 times that of our sun, and a diameter ofonly 12.2 miles. It also spins at a rate of 4.81radians/second.
a) How long does it take for this neutron star to complete onerotation?
b) If you were standing on the surface of this star, at itsequator, how fast would you be going? Give your answer in bothmiles/hour, and also as a ratio compared to how fast youârerotating through space if you stand on the surface of the Earth atthe equator.
c) What is the density of the matter in this star? (Give youranswer in both kilograms per cubic centimeter and pounds per squareinch.)
d) The escape velocity of the Earth is about 25,000 miles/hour. Ifa rocket was launched with this velocity from the surface of thisneutron star, how far would it get from the surface?
e) What is the escape velocity for this star? (Calculate it fromfirst principles. Donât just use the formula. Give your answer inmiles/hour.)
f) At what height would a satellite around this star have to be, inorder to be in a geosynchronous orbit with it?
g) How fast would a satellite in geosynchronous orbit about thisstar be traveling? (Give your answer in miles/hour.)
