The Essential Cosmic Perspective (8th Edition)
8th Edition
ISBN: 9780134446431
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 33EAP
According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass? (a) Earth would be quickly sucked into the black hole. (b) Earth would slowly spiral into the black hole. (c) Earth’s orbit would not change.
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Check out a sample textbook solutionStudents have asked these similar questions
An African elephant is walking along when a mini-black hole suddenly appears
directly above him. The mass of the black hole is so great that its gravity is able
to lift the elephant from the Earth. How close must the mini-black hole be to the
elephant's center of mass in order to just overcome the downward pull of Earth's
gravity? (Treat the mass of the elephant as if it's concentrated at the elephant's
center.
Mass of Earth ME = 6.97 x 1024 kg
Mass of mini-black hole MBH = 4.17 x 1012 kg
Radius of Earth RE = 6.40 x 106 meters
Mass of elephant (not needed)
mini black hole •
You may have an image of Sir Isaac Newton sitting under a tree and after being hit on the head by an apple he suddenly "discovered" the Law of Universal Gravitation. In fact, the theory was a result of years’ worth of research, which in turn was based on centuries of accumulated knowledge. He is credited with determining that the following relationship is universal. The gravitational attraction between two objects varies jointly with their masses (m1 and m2) and inversely with the square of the distance (d) between them. By what percent does the force of gravitational attraction change if one mass is increased by 20%, the other mass decreased by 20%, and the separation is reduced by 25%?
The active gravitational mass (m^) of a particle is an attribute that enables it to
establish a gravitational field in space, whereas the passive gravitational mass (m") is
an attribute that enables the particle to respond to this field.
(a) Write Newton's law of universal gravitation in terms of the relevant active and
passive gravitational masses.
(b) Show that the third law of motion makes it unnecessary to distinguish between
active and passive gravitational mass.
Chapter 4 Solutions
The Essential Cosmic Perspective (8th Edition)
Ch. 4 - Prob. 1VSCCh. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Check your understanding of some of the many types...Ch. 4 - Define speed, velocity, and acceleration. What are...Ch. 4 - Define momentum and force. What do we mean when we...Ch. 4 - What is free-fall, and why does it make you...Ch. 4 - Prob. 4EAPCh. 4 - Prob. 5EAP
Ch. 4 - Define kinetic energy, radiative energy, and...Ch. 4 - Define and distinguish temperature and thermal...Ch. 4 - Prob. 8EAPCh. 4 - Summarize the universal law of gravitation both in...Ch. 4 - What is the difference between a bound and an...Ch. 4 - Under what conditions can we use Newton’s version...Ch. 4 - Explain why orbits cannot change spontaneously,...Ch. 4 - Explain how the Moon creates tides on Earth. Why...Ch. 4 - How do the tides vary with the phase of the Moon?...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - Decide whether the statement makes sense (or is...Ch. 4 - A car is accelerating when it is (a) traveling on...Ch. 4 - Compared to their values on Earth, on another...Ch. 4 - Which person is weightless? (a) a child in the air...Ch. 4 - Consider the statement “There’s no gravity in...Ch. 4 - To make a rocket turn left, you need to (a) fire...Ch. 4 - Compared to its angular momentum when it is...Ch. 4 - Prob. 31EAPCh. 4 - If Earth were twice as far from the Sun, the force...Ch. 4 - According to the law of universal gravitation,...Ch. 4 - If the Moon were closer to Earth, high tides would...Ch. 4 - Testing Gravity. Scientists are constantly trying...Ch. 4 - How Does the Table Know? Thinking deeply about...Ch. 4 - 37. Your Ultimate Energy Source. Roles: Scribe...Ch. 4 - Weightlessness. Astronauts are weightless when in...Ch. 4 - Einstein’s Famous Formula. a. What is the meaning...Ch. 4 - The Gravitational Law. a. How does quadrupling the...Ch. 4 - Prob. 41EAPCh. 4 - Head to Foot Tides. You and Earth attract each...Ch. 4 - Prob. 43EAPCh. 4 - Prob. 44EAPCh. 4 - Prob. 45EAPCh. 4 - Prob. 46EAPCh. 4 - Prob. 47EAPCh. 4 - Prob. 48EAPCh. 4 - Space Station. Visit a NASA site with pictures...Ch. 4 - Prob. 50EAPCh. 4 - Prob. 51EAP
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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_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_forwardSince 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?arrow_forward
- It was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero or positive total energy is in an unbounded orbit. Why zero or positive total energy is in an unbounded orbit. Why is this true? What choice for gravitational potential energy was made such that this is true?arrow_forwardYou drill a hole right through the center of a spherical planet of radius R and mass M, and drop an object into it. How long does the object take to reach the opposite surface. Express your answer only in terms of M, R and the universal gravitational constant G.arrow_forwardAs a star ages, it is believed to undergo a variety of changes. One of the last phases of a star's life is to gravitationally collapse into a black hole. If suppose our Sun would end up a Black hole, what will happen to the orbit of the planets of the solar system? (Assuming that the planets are not affected by the evolving stages of the Sun prior to becoming a black hole and noting that for calculation of gravitational force of attraction, the distance being considered is from center to center of the two bodies). Justify your answer.arrow_forward
- The law of universal gravitation says that there is a force between two objects in the universe. Can there ever be a physical instance when the two objects will never have an influence on each other? Hint: look at the equation that relates force, mass, distance, and the gravitational constant G: Gxm, xma F = O No, no matter how far apart they are, there will always be some tiny force acting between the two. O No, Since the distance between two objects can never be zero. All listed answers here are correct. O No, they will always influence each other. You cannot divide by zero.arrow_forwardLet G denote the universal gravitational constant and let M and m denote masses a distance r apart. (a) According to Newton’s Law of Universal Gravitation, M and m attract each other with a force of magnitude _____ . (b) If r is the radius vector from M to m, then the force of attraction that mass M exerts on mass m is ______ .arrow_forward(a) At what position in its elliptical orbit is the speed of a planet a maximum? when it is closest to the sun when it is farthest from the sun when it is midway between its farthest and closest distances to the sun everywhere in its orbit, the speed is constant (b) At what position is the speed a minimum? when it is closest to the sun when it is farthest from the sun when it is midway between its farthest and closest distances to the sun everywhere in its orbit, the speed is constantarrow_forward
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