The Essential Cosmic Perspective (8th Edition)
8th Edition
ISBN: 9780134446431
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 4, Problem 11EAP
Under what conditions can we use Newton’s version of Kepler’s third law to calculate an object’s mass, and what quantities must we measure in order to complete the calculation?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Help me to solve this problem step by step and give answer as a 3 significant figures
Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is
GmM
F=
where G is the gravitational constant and r is the distance between the bodies.
(a) Find dF/dr.
dF
dr
=
What is the meaning of dF/dr?
O dF/dr represents the amount of force per distance.
O dF/dr represents the rate of change of the mass with respect to the distance between the bodies.
O dF/dr represents the rate of change of the distance between the bodies with respect to the force.
O dF/dr represents the rate of change of the mass with respect to the force.
O dF/dr represents the rate of change of the force with respect to the distance between the bodies.
What does the minus sign indicate?
O The minus sign indicates that the force between the bodies is decreasing.
O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases.
O The minus sign indicates that as the distance between the bodies increases, the…
The mean distance of Mars from the Sun is 1.52 times that of Earth from the Sun. From Kepler’s law of periods, calculate the number of years required for Mars to make one revolution around the Sun; compare your answer with the value given in Appendix C.
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The Scope and Scale of Physics Find the order of magnitude of the following physical quantities. (a) The mass of Earth’s atmosphere: 5.11018kg : (b) The mass of the Moon’s atmosphere: 25,000kg ; (c) The mass of Earth’s hydrosphere: 1.41021kg : (d) The mass of Earth: 5.971024kg : (e) The mass of the Moon: 7.341022kg : (f) The Earth-Moon distance (semimajor axis): 3.84108m : (g) The mean Earth-Sun distance: 1.51011m : (h) The equatorial radius of Earth: 6.38106m : (i) The mass of an electron: 9.111031kg : (j) The mass of a proton: 1.671027kg : (k) The mass of the Sun: 1.991030kg .arrow_forwardConsider Kepler's equation regarding planetary orbits, given as M = E e sin(E), π where M is the mean anomaly, E is the eccentric anomaly, and e measures eccentricity. Find the eccentric anomaly E when 7 and the eccentricity of the orbit e = 0.37. Use Newton's method with initial approximation Xo = 2 to find x2, rounded to the nearest thousandth. the mean anomaly M = Provide your answer below: Xx₂≈arrow_forwardNewton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GmM/r2 where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. What is the meaning of dF/dr? dF/dr represents the rate of change of the force with respect to the distance between the bodies. dF/dr represents the rate of change of the mass with respect to the distance between the bodies. dF/dr represents the rate of change of the distance between the bodies with respect to the force. dF/dr represents the rate of change of the mass with respect to the force. dF/dr represents the amount of force per distance. What does the minus sign indicate? The minus sign indicates that the force between the bodies is decreasing. The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases. The minus sign indicates that as the distance between the bodies decreases, the…arrow_forward
- "As the legend tells, Isaac Newton discovered the law of universal gravitation after an apple fell on his head. What happened with this great apple after it bounced off Newton's head?" People who visited a certain website were asked this question. Of 257 people who answered this question during the last month, 30% replied that Newton ate the apple. Calculate the margin of error for this result. Round the percentage to one decimal place. Do not round intermediate steps. QUESTION: If 30% of 257 people replied that Newton ate the apple, the margin of error is?arrow_forwardThe weight of an object is the product of its mass, mmm, and the acceleration of gravity, ggg (where g=9.8 m/s2g=9.8 m/s2). If an object’s mass is m=10. kgm=10. kg, what is its weight? Express the weight with the appropriate units.arrow_forwardA small moon with a mass of 100 kg orbits a very dense asteroid with a mass of 1 million kg. The time for one complete orbit is 100 days. The small moon’s orbit radius is 500 metres. a) Assuming that the orbit is perfectly circular, what is the speed of the small moon as it orbits the asteroid? State your result in scientific notation and in units of metres per second (m/s). b) Are the small moon’s speed and velocity constant as it orbits the asteroid? Why or why not in both cases? c) Calculate the centripetal force on the small moon as it orbits the asteroid (in newtons). d) Calculate the gravitational force between the small moon and the asteroid (in newtons).e) Compare your results of part c) and part d).arrow_forward
- Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]arrow_forwardA rocket is designed to be launched to space with an acceleration defined by the equation given below where "y" is the altitude of the rocket in the time of flight and "R" is the radius of the earth equal to 6,400 kilometers. The rocket was launched at a velocity equal to 8,900 m/s. What is the maximum altitude reached by the rocket? Express your answer in unit of meter.arrow_forwardNewton's law of universal gravitation is represented by Мт F = G- r2 where Fis the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s². What are the SI units of the proportionality constant G?arrow_forward
- Mars has a mass of 6.39 × 1023 kg and radius 3.39 x 106 m. What is the magnitude of the gravitational acceleration g on Mars' surface, in m/s2? Use G = 6.67 x 10-11 N-m2/kg?. Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.arrow_forwardYou have been assigned to a team charged with developing a plan to explore a new planetary body called Planet Z. The acceleration due to gravity of Planet Z is 3.2 meters per second squared [m/s2]. A container of unknown volume is filled with cooking oil, with a specific gravity = 0.93, on Planet Z where the liquid in the container weighs 2 pound-force [lbf]. What is the volume of cooking oil in the container in units of liters [L]?arrow_forwardEstimate the number of steps you would have to take to walk a distance equal to the circumference of the Earth. (We estimate that the length of a step for an average person is about 18 inches, or roughly 0.5 m. The radius of the Earth is 6.38 x 106 m.) 105 steps 108 steps 1011 steps 1015 steps O 1020 stepsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Components of a Vector (Part 1) | Unit Vectors | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=fwMUELxZ0Pw;License: Standard YouTube License, CC-BY
02 - Learn Unit Conversions, Metric System & Scientific Notation in Chemistry & Physics; Author: Math and Science;https://www.youtube.com/watch?v=W_SMypXo7tc;License: Standard Youtube License