If G is given by 6.67 X 10-11 and the mass of the Sun is 1.98 X 1030 kg, what would be the radius of the Sun if it could be condensed into a black hole? A black hole is an object for which the escape velocity (2GM/R)½ is c the speed of light. For comparison the radius

If G is given by 6.67 X 10-11 and the mass of the Sun is 1.98 X 1030 kg, what would be the radius of the Sun if it could be condensed into a black hole? A black hole is an object for which the escape velocity (2GM/R)½ is c the speed of light. For comparison the radius

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section39.12: Gravitational Lenses And Black Holes

Problem 39.5CE

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A stellar black hole may form when a massive star dies. The star collapses down to a single point. Our Sun will not become a black hole because it does not have enough mass, so let us imagine a black hole with eight times the mass of the Sun. A single point has no radius, but a black hole has an effective radius known as the Schwarzschild radius. If an object gets inside the Schwarzschild radius, it never escapes. The Schwarzschild radius of an eight-solar-mass black hole is about 24 km. a. Find the escape speed using the Schwarzschild radius. b. Compare your answer to the speed of light and speculate on how these objects got the name black hole.
Show that the velocity of a star orbiting its galaxy in a circular oibit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.
Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force.
Using the solution from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of out Sun. Where does this increase in kinetic energy come from?
Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force.
A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)
Neutron stars are extremely dense objects formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.
The nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away from Earth. Given that the Milky Way galaxy (Fig. P1.81) is roughly a disk of diameter 1021 m and thickness 1019 m, estimate the number of neutron stars in the Milky Way to the nearest order of magnitude. Figure P1.81
Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.
A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?
. A compact neutron star has a mass of kg (about 1.4 times the mass of the Sun) but a radius of only m (approximately 6.2 mi!). If a clock on the surface of this exotic star marks the passage of 1 h of time, how much time is observed to pass on an identical clock located a very large distance from the neutron star?
Our solar system orbits the center of the Milky Way Galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.