Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 59Q
To determine
The Schwarzschild radius of an object having mass equal to that of the planet Saturn.
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What is Schwarzschild radius?
Calculate the Schwarzschild Radius for each of the following:
1. A 3.3 X 108 solar-mass black hole in the center of a quasar
2. a 3.5 solar-mass black hole formed in a type II supernova
3. a mini-black hole with the mass of the moon
4. a black hole with the mass of you (estimate your mass to be 51.8 kg)
A particle maintains a circular orbit around a black hole of mass 10 Solar masses at a distance equal to 2 Schwarzschild radii. Calculate the orbital velocity of the particle and express the answer in units of the speed of light.
Chapter 21 Solutions
Universe
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- As an object falls into a black hole, tidal forces increase. Will these tidal forces always tear the object apart as it approaches the Schwarzschild radius? How does the mass of the black hole and size of the object affect your answer?arrow_forwardThe Schwarzschild radius RBH for an object of mass M is defined as (See image.) where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. 1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass? 2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass? 3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?arrow_forwardCalculate the Schwarzschild Radius for the following: 1. a black hole with the mass of you (estimate your mass to be 51.8 kg)arrow_forward
- As a person approaches the Schwarzschild radius fo a black hole, outside observers see all the processes of that person (their clocks, their heart rate, etc.) slowing down, and coming to a halst as they reach the Schwarzschild radius. (The person falling into the black hole sees their own processes unaffected.) But the speed of light is the same everywhere for all observers. What does this say about space as you approach the black hole?arrow_forward1. Let’s say we have a black hole with a mass 10 times that of the Sun (the Sun’s mass is 2 x 1030kg so the mass of the black hole is then 2 x1031 kg) Using the definitions for G and c what Schwarzschild radius of this black hole be? g=6.67 x 10-11 m3 kg-1 s-2 c=3 x 108 m s-1arrow_forwardHow close, r, to the center of a neutron star would a manned satellite be orbiting if it were at the location where the gravitational force from the star equaled the gravitational force of the Earth's surface? RN = neutron star radius = 1 × 104 kmM N = neutron star mass = 3 × 1030 kgG = universal gravitational constant = 6.67 × 10-11 N m2 / kg2g⊕ = Earth gravitational acceleration = 9.807 m/s²arrow_forward
- To what radius would the Sun have to be contracted for its escape speed to equal the speed of light? (Black holes have escape speeds greater than the speed of light; hence we see no light from them.)arrow_forwardAssume that the laws of Newtonian mechanics and Newtonian gravity still hold for a neutron star, what approximately is the escape velocity at the surface of a 1.4 solar mass neutron with a radius of 10 km? A. 2×108 m/s B. 108 m/s C. 1.5 ×108 m/s D. 2.5 ×108 m/sarrow_forwardDo binary stars (double-star systems that orbit about a common center of mass) radiate gravitational waves? Why or why not?arrow_forward
- TRUE OR FALSE A Black Hole’s singularity has zero radius yet can accommodate infinite mass.arrow_forwardBlack hole candidates are conspicuous by their continuous or flickering emission of a. infrared light. b. ultraviolet light. c. gamma rays. d. X rays. e. all of the above.arrow_forwardTrue or false The escape speed from a black hole would be greater than the speed of light. If the impact time of a collision is increased, the force of impact will decrease. A size of a Kelvin degree (oK) is larger than a Celsius degree (oC).arrow_forward
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