Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 24, Problem 27Q
To determine
The mass of the central black hole using Newton’s form of Kepler’s third law.
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Observations indicate that each galaxy contains a supermassive black hole at its center. These black holes can be hundreds of
thousands to billions of times more massive than the Sun. Astronomers estimate the size of such black holes using
multiple methods.
One method, using the orbits of stars around the black hole, is an application of Kepler's third law. The mass of the black hole
can be found by using the given equation, where a is the semi-major axis in astronomical units, P is the period in years, and k is
a constant with a value of 1 Mo X year²/ AU³.
a³
M = k-
p²
What is the mass of a supermassive black hole if a star orbits it with a semimajor axis of 959 AU and a period of 13.3 years?
mass:
Another method measures the speed of gas moving past the black hole. In the given equation, v is the velocity of the gas (in
kilometers per second), r is the distance of the gas cloud from the black hole (in kilometers), and G is Newton's gravitational
constant. In this equation, G = 1.33 ×…
An AGN hosts a central Black Hole of mass 2×1038×1038 kg. The AGN emits at 1/51/5 of the Eddington limit. Find the luminosity of the AGN. Give your answer in Watts to 3 significant figures.
How 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/s²
Chapter 24 Solutions
Universe: Stars And Galaxies
Ch. 24 - Prob. 1QCh. 24 - Prob. 2QCh. 24 - Prob. 3QCh. 24 - Prob. 4QCh. 24 - Prob. 5QCh. 24 - Prob. 6QCh. 24 - Prob. 7QCh. 24 - Prob. 8QCh. 24 - Prob. 9QCh. 24 - Prob. 10Q
Ch. 24 - Prob. 11QCh. 24 - Prob. 12QCh. 24 - Prob. 13QCh. 24 - Prob. 14QCh. 24 - Prob. 15QCh. 24 - Prob. 16QCh. 24 - Prob. 17QCh. 24 - Prob. 18QCh. 24 - Prob. 19QCh. 24 - Prob. 20QCh. 24 - Prob. 21QCh. 24 - Prob. 22QCh. 24 - Prob. 23QCh. 24 - Prob. 24QCh. 24 - Prob. 25QCh. 24 - Prob. 26QCh. 24 - Prob. 27QCh. 24 - Prob. 28QCh. 24 - Prob. 29QCh. 24 - Prob. 30QCh. 24 - Prob. 31QCh. 24 - Prob. 32Q
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- The best evidence for a black hole at the center of the Galaxy also comes from the application of Kepler’s third law. Suppose a star at a distance of 20 light-hours from the center of the Galaxy has an orbital speed of 6200 km/s. How much mass must be located inside its orbit?arrow_forwardWhat is the Schwarzschild radius (in km) of a 20 solar mass black hole?arrow_forwardThe Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot = 250 km s−1. Using Kepler’s 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.arrow_forward
- Five astronauts (A - E) are watching a star collapse to form a black hole. Which of the flight plans require that the astronaut travel faster than light? A COLLAPSING STAR THAT FORMS BLACK HOLE r=0 Singularity Time Inside of Star At B D Rs Radius of a Star Earrow_forwardUse the Schwarzchild formulaRs =2GM / c2whereRs = Radius of the star, in meters, that would cause it to become a black holeM = Mass of the star, in kilogramsG = A constant, called the gravitational constant= 6.7 x 10-11 m3 / kg . s2c = Speed of light= 3x108 meters per secondto determine to what length the radius of the Sun must be reduced for it to become a black hole. The Sun’s mass is approximately 2 x 1030 kilograms.arrow_forward(Astronomy) PSR1913+16 Problem II. Using only the Figure, what are the maximum radial velocities as found from the redshift and blueshift, respectively? Note: redshifts have positive radial velocities values in the figure, whereas blueshifts have negative radial velocity values. (Answer in km/s)arrow_forward
- The orbit of the binary pulsar PSR 1936+16, studied by Taylor and Hulse, a. is so small that the orbital period is smaller than the pulsar period. b. is growing smaller, presumably by emitting gravitational waves. c. provides evidence that it is being orbited by at least 6 planets the size of Jupiter. d. shows large changes each time an X ray burst is emitted from the system. e. contains a white dwarf and a black hole.arrow_forwardWhich of the below rotation curves best represents the orbital speeds stars in the Milky Way Galaxy would have if there were no dark matter in the galaxy? A B Distance Distance C D Distance Distance А.А В. В С. С D.D Velocity Velocity Velocity Velocityarrow_forwardA binary pulsar orbits with radial velocity 0.00004 times the speed of light. If the difference between the rest period and the minimum period over the course of the orbit is 0.001 ms, what is the rest period of the pulsar? 25 ms Trick question: this value cannot be calculated without more information 250 ms O 2.5 msarrow_forward
- 1.2 1.0 0.8 0.6 Cosmic background data from COBE 0.4 0.2 0.0 0.5 10 Wavelength A in mm c) Background (CMB) undertaken by the COBE satellite. Use this diagram to estimate the current temperature of the CMB. Based on your estimate, what would the temperature of the CMB have been at a redshift of z = 5000? The left hand diagram above shows the results from observations of the Cosmic Microwave Radiated Intensity per Unit Wavelength (16° Watts/m per mm)arrow_forward1. What would be the diameter (of the event horizon) of a black hole with the same mass as Jupiter? (2 points) answer: D BH ft m =arrow_forwardAn AGN is emitting with a luminosity of 2×1040W. The AGN's brightness varies by 10% on a time scale of 20 hours. Assuming that the size of the emitting region of the AGN is three Schwarzschild radii, choose which of the following values could give the mass of the central Black Hole, in solar masses.arrow_forward
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