Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 7, Problem 44PQ
To determine
The final effect of the orbit of the planet around its star when the planet is converted into a black hole.
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The Schwarzschild radius, RS, of a black hole depends on its mass m, the speed of light c,and the gravitational constant G (with units m3/(kg s2)).Find a dimensionally correct expression for RS in terms of these quantities.Assuming that you found a dimensionally correct expression, can you be sure that this expression is, in fact, the correct expression for calculating the Schwarzschild radius? Explainyour answer.
Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 × 108^8 m/sm/s, making all escape impossible.
What is the radius of the event horizon for a black hole with a mass 7.5 times the mass of the sun? This distance is called the Schwarzschild radius.
Why are gravitational waves hard to detect and is there a way to simplify the process? How?
Chapter 7 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 7.1 - What important experimental skills can we learn...Ch. 7.2 - Three possible planetary orbits are shown in...Ch. 7.2 - Prob. 7.3CECh. 7.2 - Prob. 7.4CECh. 7.2 - Todays employees are rewarded for thinking outside...Ch. 7 - We use the terms sunset and sunrise. In what way...Ch. 7 - Prob. 2PQCh. 7 - For many years, astronomer Percival Lowell...Ch. 7 - Prob. 4PQCh. 7 - Prob. 5PQ
Ch. 7 - Io and Europa are two of Jupiters many moons. The...Ch. 7 - Model the Moons orbit around the Earth as an...Ch. 7 - Prob. 8PQCh. 7 - Prob. 9PQCh. 7 - Prob. 10PQCh. 7 - Prob. 11PQCh. 7 - Prob. 12PQCh. 7 - A massive black hole is believed to exist at the...Ch. 7 - Since 1995, hundreds of extrasolar planets have...Ch. 7 - When Sedna was discovered in 2003, it was the most...Ch. 7 - Prob. 16PQCh. 7 - The mass of the Earth is approximately 5.98 1024...Ch. 7 - Prob. 18PQCh. 7 - Prob. 19PQCh. 7 - A black hole is an object with mass, but no...Ch. 7 - Prob. 21PQCh. 7 - Prob. 22PQCh. 7 - The Lunar Reconnaissance Orbiter (LRO), with mass...Ch. 7 - A Suppose a planet with mass m is orbiting star...Ch. 7 - Prob. 25PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Saturns ring system forms a relatively thin,...Ch. 7 - Prob. 28PQCh. 7 - Find the magnitude of the Suns gravitational force...Ch. 7 - Prob. 30PQCh. 7 - Prob. 31PQCh. 7 - Prob. 32PQCh. 7 - Prob. 33PQCh. 7 - Prob. 34PQCh. 7 - Prob. 35PQCh. 7 - In your own words, describe the difference between...Ch. 7 - The Sun has a mass of approximately 1.99 1030 kg....Ch. 7 - Prob. 38PQCh. 7 - Prob. 39PQCh. 7 - Prob. 40PQCh. 7 - Three billiard balls, the two-ball, the four-ball,...Ch. 7 - Prob. 42PQCh. 7 - Prob. 43PQCh. 7 - Prob. 44PQCh. 7 - Figure P7.45 shows a picture of American astronaut...Ch. 7 - Prob. 46PQCh. 7 - Prob. 47PQCh. 7 - Prob. 48PQCh. 7 - Prob. 49PQCh. 7 - Prob. 50PQCh. 7 - The International Space Station (ISS) experiences...Ch. 7 - Prob. 52PQCh. 7 - Two black holes (the remains of exploded stars),...Ch. 7 - Prob. 54PQCh. 7 - Prob. 55PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 57PQCh. 7 - Consider the Earth and the Moon as a two-particle...Ch. 7 - Prob. 59PQCh. 7 - You are a planetary scientist studying the...Ch. 7 - Prob. 61PQCh. 7 - Prob. 62PQCh. 7 - Planetary orbits are often approximated as uniform...Ch. 7 - Prob. 64PQCh. 7 - Prob. 65PQCh. 7 - Prob. 66PQCh. 7 - Prob. 67PQCh. 7 - Prob. 68PQCh. 7 - Prob. 69PQCh. 7 - Prob. 70PQ
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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_forwardLook up G, c, and the mass of the Sun in Appendix E and calculate the radius of a black hole that has the same mass as the Sun. (Note that this is only a theoretical calculation. The Sun does not have enough mass to become a black hole.)arrow_forwardAs 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_forward
- A student becomes so excited by the whole idea of black holes that he decides to jump into one. It has a mass 10 times the mass of our Sun. What is the trip like for him? What is it like for the rest of the class, watching from afar?arrow_forwardWhat would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars collapsed into a black hole? Compare this to our distance from the center, about 13,000 light years.arrow_forwardNothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 ×× 1088 m/sm/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 7.5 times the mass of the sun? This distance is called the Schwarzschild radius.?arrow_forward
- Part A: Determine the mass of the massive object at the center of the Milky Way galaxy. Give your answer in kilograms. M=___kg Part B: Give your answer in solar masses (one solar mass is the mass of the sun). M=___ms Part C: Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what must the Schwarzschild radius of this black hole be? Rs=___marrow_forward9) The speed of light is 3 × 108m/s. The Sun has a mass of 2 × 1030kg.a). If all of the Sun’s mass were concentrated at a single point, at what distance would the orbital velocity of an object be the speed of light? The universal gravitational constant is G=6.67×10−11[m3/(s2 · kg)] (Schwarzchild radius). b). Suppose the Sun were to actually collapse into such a black hole meaning that its radius shrinks to the size in part (a), and the mass remains the same. How would the orbit of the Earth change (if at all?) In other words, would the orbital radius or velocity change, and if so, by how much? Explain.c). The sun rotates once every 24 days and has a radius of 6.96×108m. What would the rotational period of the sun be if it collapsed to a radius equal to the radius in part (a)?arrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. a) What should the orbital period of that star be in years? b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? 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.arrow_forward
- How can we “observe” a black hole if neither matter nor radiation can escape from it?arrow_forwardAn astronaut is flying at a distance of 317kms from the center of a blackhole of mass 2E32 kg. From the point of view of the astronaut the flight lasts for 18.6 seconds. How long did it last from the point of view of an observer on Earth? Express your answer in seconds and keep 3 significant digits.arrow_forwardThe presence of Dark Matter was theorized due to the curve of the data that the motion of the stars around the central core of our neighboring galaxy (Andromeda) has been approximately flat rather than decreasing at large distances. Which fundamental concept in this chapter helped us in understanding this phenomena? a.) Orbital speed b.) Escape speed c.) Law of equal areas d.) Law of elliptical orbits What happens to the magnitude of the force between two objects with the same mass if we double the distance between them? a.) The magnitude of the force will be doubled. b.) The magnitude of the force will be quadrupled. c.) The magnitude of the force will be halved. d.) The magnitude of the force will be 1/9 of its inital magnitude.e. Earrow_forward
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