Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 3, Problem 24E
Use a history book, an encyclopedia, or the internet to find out what else was happening in England during Newton’s lifetime and discuss what trends of the time might have contributed to his accomplishments and the rapid acceptance of his work.
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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
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…
Newton showed that the periods and distances in Kepler’s third law depend on the masses of the objects. What would be the period of revolution of the Earth (still at 1 AU from the Sun) if the Sun had twice its present mass? What would be the period of revolution of the Earth (still at 1 AU from the Sun) if the Earth had twice its present mass? Give your answers in years.
Chapter 3 Solutions
Astronomy
Ch. 3 - State Kepler’s three laws in your own words.Ch. 3 - Why did Kepler need Tycho Brahe’s data to...Ch. 3 - Which has more mass: an armful of feathers or an...Ch. 3 - Explain how Kepler was able to find a relationship...Ch. 3 - Write out Newton’s three laws of motion in terms...Ch. 3 - Which major planet has the largest . . . A....Ch. 3 - Why do we say that Neptune was the first planet to...Ch. 3 - Why was Brahe reluctant to provide Kepler with all...Ch. 3 - According to Kepler’s second law, where in a...Ch. 3 - The gas pedal, the brakes, and the steering wheel...
Ch. 3 - Explain how a rocket can propel itself using...Ch. 3 - A certain material has a mass of 565 g while...Ch. 3 - To calculate the momentum of an object, which...Ch. 3 - To calculate the angular momentum of an object,...Ch. 3 - What was the great insight Newton had regarding...Ch. 3 - Which of these properties of an object best...Ch. 3 - Pluto’s orbit is more eccentric than any of the...Ch. 3 - Why is Tycho Brahe often called “the greatest...Ch. 3 - Is it possible to escape the force of gravity by...Ch. 3 - What is the momentum of an object whose velocity...Ch. 3 - Evil space aliens drop you and your fellow...Ch. 3 - A body moves in a perfectly circular path at...Ch. 3 - As friction with our atmosphere causes a satellite...Ch. 3 - Use a history book, an encyclopedia, or the...Ch. 3 - Two asteroids begin to gravitationally attract one...Ch. 3 - How does the mass of an astronaut change when she...Ch. 3 - If there is gravity where the International Space...Ch. 3 - Compare the density, weight, mass, and volume of a...Ch. 3 - If identical spacecraft were orbiting Mars and...Ch. 3 - By what factor would a person’s weight be...Ch. 3 - Suppose astronomers find an earthlike planet that...Ch. 3 - What is the semimajor axis of a circle of diameter...Ch. 3 - If 24 g of material fills a cube 2 cm on a side,...Ch. 3 - If 128 g of material is in the shape of a brick 2...Ch. 3 - If the major axis of an ellipse is 16 cm, what is...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - In 1996, astronomers discovered an icy object...
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