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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Textbook Question
Chapter 4, Problem 1EAP
Define speed, velocity, and acceleration. What are the units of acceleration? What is the acceleration of gravity?
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Newton's Law of Gravitation
2. The magnitude of the acceleration of an object under the pull of Earth's gravity is
given by Newton's Universal Law of Gravitation
МЕ
a = G
R?
where G is the universal gravitational constant, ME is the mass of Earth, and R is the
distance of the object from the center of Earth.
Let x be the distance above Earth's surface. We can rewrite the formula for the
acceleration as a function of x by noting that R = Rp + x, where Rp is the radius of
Earth. Therefore,
МЕ
a(x) = G-
(RE + x)2
d.
(a) Show that
dx
1
1
(1 – x)*
- x.
(b) Use the above fact, along with the power series of
1
to determine a power
1- x
1
series for
(1+x)²*
(c) What is the radius of convergence for the series in part (b)? (Hint: You do not
need to calculate anything. What is the radius of convergence for the power series
of
1
does not change the radius of convergence.)
-? This series has the same radius of convergence since taking a derivative
Chapter 4 Solutions
The Cosmic Perspective (9th Edition)
Ch. 4 - Prob. 1VSCCh. 4 - Use the following questions to check your...Ch. 4 - Use the following questions to check your...Ch. 4 - Use the following questions to check your...Ch. 4 - Use the following questions to check your...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 - Describe the laws of conservation of momentum, of...
Ch. 4 - Define kinetic energy, radiative energy, and...Ch. 4 - Define temperature and thermal energy. How are...Ch. 4 - Prob. 8EAPCh. 4 - 9. Summarize the universal law of gravitation both...Ch. 4 - 10. What is the difference between a bound and an...Ch. 4 - What do we need to know if we want to measure an...Ch. 4 - Explain why orbits cannot change spontaneously,...Ch. 4 - Explain how the Moon creates tides on Earth. Why...Ch. 4 - What is tidal friction? What effects does it have...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Prob. 19EAPCh. 4 - Prob. 20EAPCh. 4 - Does It Make Sense? Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Does It Make Sense?
Decide whether the statement...Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Prob. 30EAPCh. 4 - Prob. 31EAPCh. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Prob. 35EAPCh. 4 - Testing Gravity. Scientists are continually trying...Ch. 4 - Prob. 38EAPCh. 4 - Prob. 39EAPCh. 4 - Prob. 40EAPCh. 4 - Weightlessness. Astronauts are weightless when in...Ch. 4 - Units of Acceleration. If you drop a rock from a...Ch. 4 - Gravitational Potential Energy. For each of the...Ch. 4 - Prob. 44EAPCh. 4 - The Gravitational Law. How does quadrupling the...Ch. 4 - Allowable Orbits? Suppose the Sun were replaced by...Ch. 4 - Head-to-Foot Tides. You and Earth attract each...Ch. 4 - Prob. 48EAPCh. 4 - Geostationary Orbit. A satellite in geostationary...Ch. 4 - Prob. 51EAPCh. 4 - Prob. 52EAPCh. 4 - Moving Candy Bar. Table 4.1 shows that...Ch. 4 - Spontaneous Human Combustion. Suppose that all the...Ch. 4 - Fusion Power. No one has yet succeeded in creating...Ch. 4 - Understanding Newton’s Version of Kepler’s Third...Ch. 4 - Using Newton’s Version of Kepler’s Third Law....Ch. 4 - Escape Velocity. Calculate the escape velocity...Ch. 4 - Weights on Other Worlds. Calculate the...Ch. 4 - Prob. 60EAPCh. 4 - Extra Moon. Suppose Earth had a second moon,...
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