The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter S4, Problem 55EAP
Solar Mass Black Holes. Use the formula from Problem 54 to calculate the lifetime of a black hole with the mass of the Sun
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Around 2.5 centuries ago, several physicists of the time came up with the notion of a dark star. This was a star so dense, with so much gravity, that not even light could escape. The calculations used Newtonian mechanics. In class, we calculated the escape speed from the surface of the earth or the distance from the sun, and the mass of the planet or star.
Here, the process is partially reversed. Calculate the dark star radius from the mass of the star and the escape speed. Answer in kilometers.
c = 3*108 m/s
M = 2.4*1030 kg
G = 2/3 * 10-10 N*m2/kg2
Determine the surface gravity on a neutron star. Assume the star has a mass 50% bigger than the Sun, and has a radius of 10 km. Express your answer as a multiple of earth's gravitational acceleration (g), like we did in the examples in class.
Assume the event horizon is the size of the black hole (it is not: in reality, the black hole is a point source). What is the density of a black hole that has the mass of the Sun in units of kg/cm3? Please express your answer in scientific notation with the "e" format inside the text box, and keep three significant figures (for example, 5.01e3 for 5.01
× 103).
Chapter S4 Solutions
The Cosmic Perspective (9th Edition)
Ch. S4 - Prob. 1EAPCh. S4 - Prob. 2EAPCh. S4 - Prob. 3EAPCh. S4 - Prob. 4EAPCh. S4 - Prob. 5EAPCh. S4 - Prob. 6EAPCh. S4 - Prob. 7EAPCh. S4 - Prob. 8EAPCh. S4 - Prob. 9EAPCh. S4 - Prob. 10EAP
Ch. S4 - Prob. 11EAPCh. S4 - Prob. 12EAPCh. S4 - Prob. 13EAPCh. S4 - Prob. 14EAPCh. S4 - Prob. 15EAPCh. S4 - Prob. 16EAPCh. S4 - Prob. 17EAPCh. S4 - Prob. 18EAPCh. S4 - Prob. 19EAPCh. S4 - Decide whether the statement makes sense (or is...Ch. S4 - Prob. 21EAPCh. S4 - Prob. 22EAPCh. S4 - Prob. 23EAPCh. S4 - Prob. 24EAPCh. S4 - Prob. 25EAPCh. S4 - Prob. 26EAPCh. S4 - Prob. 27EAPCh. S4 - Choose the best answer to each of the following....Ch. S4 - Prob. 29EAPCh. S4 - Prob. 30EAPCh. S4 - Prob. 31EAPCh. S4 - Prob. 32EAPCh. S4 - Prob. 33EAPCh. S4 - Prob. 34EAPCh. S4 - Prob. 36EAPCh. S4 - Prob. 37EAPCh. S4 - Prob. 38EAPCh. S4 - Prob. 39EAPCh. S4 - Prob. 41EAPCh. S4 - Prob. 42EAPCh. S4 - Prob. 43EAPCh. S4 - Prob. 44EAPCh. S4 - Prob. 45EAPCh. S4 - Prob. 46EAPCh. S4 - Prob. 47EAPCh. S4 - Prob. 48EAPCh. S4 - Prob. 52EAPCh. S4 - Large-Scale Gravity. Suppose Earth and the Sun...Ch. S4 - Prob. 54EAPCh. S4 - Solar Mass Black Holes. Use the formula from...Ch. S4 - Long-Lived Black Holes. Some scientists speculate...Ch. S4 - Prob. 57EAPCh. S4 - Prob. 58EAPCh. S4 - Prob. 59EAPCh. S4 - Prob. 60EAP
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- A stellar black hole may form when a massive star dies. The mass of the star collapses down to a single point. Imagine an astronaut orbiting a black hole having eight times the mass of the Sun. Assume the orbit is circular. a. Find the speed of the astronaut if his orbital radius is r = 1 AU. b. Find his speed if his orbital radius is r = 11.8 km. c. CHECK and THINK: Compare your answers to the speed of light in a vacuum. What would the astronauts orbital speed be if his orbital radius were smaller than 11.8 km?arrow_forwardWhat is the Schwarzschild radius of a blank hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.arrow_forwardOnce again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.arrow_forward
- Explain what the mass-to-light ratio is and why it is smaller in spiral galaxies with regions of star formation than in elliptical galaxies.arrow_forwardWhat is Lorentz law? Give definition, background, uses and examples of it.arrow_forwardThe Andromeda Galaxy, M31, is the closest large spiral Galaxy to our Milky Way. When we lookat its chemical spectrum, we see that it's hydrogen alpha emission line has an observed wavelength of 655nm. a. Calculate z, being careful with the sign b. How fast is it moving in km/s c. Is it redshifted or blueshifted? Is it moving toward or away from us?arrow_forward
- How can black holes lead to parallel universes? And how do black holes lead to parallel universes?arrow_forwardThe first picture is some background information need help answering the first question about the escape velocity from the andromeda Galaxyarrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be?_________yr (b) If its period is 6.0x107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies._________ Solar Massesarrow_forward
- Define Unification, and why scientists are striving for the unification of all forces? ilac dacariba in sandardmodal and a ha.arrow_forwardThe radius Rh of a black hole is the radius of a mathematicalsphere, called the event horizon, that is centered on the blackhole. Information from events inside the event horizon cannotreach the outside world. According to Einstein’s general theory ofrelativity, Rh = 2GM/c2, where M is the mass of the black hole andc is the speed of light.Suppose that you wish to study a black hole near it, at a radialdistance of 50Rh. However, you do not want the difference in gravitationalacceleration between your feet and your head to exceed10 m/s2 when you are feet down (or head down) toward the blackhole. (a) As a multiple of our Sun’s mass MS, approximately what isthe limit to the mass of the black hole you can tolerate at the givenradial distance? (You need to estimate your height.) (b) Is the limitan upper limit (you can tolerate smaller masses) or a lower limit(you can tolerate larger masses)?arrow_forwardHow do black holes form, and what are the implications of their existence on our understanding of gravity and the structure of the universe?arrow_forward
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