Explanation 1) Concept: We can use the concept of Newton’s law of gravitation and centripetal force . The gravitational force on the planet provides the centripetal force on the planet. We can use the expression of density and orbital speed. 2) Formulae: i) F = G M m r 2 ii) F c = m v 2 r iii) v = 2 π r T 3) Given: The uniform density of the spherical planet is ρ = 3.0 g c m 3 = 3.0 × 10 3 k g m 3 4) Calculations: a) According to Newton’s law of gravitation, the gravitational force acting on the spherical planet is F = G M m r 2 The gravitational force on the planet provides the centripetal force on the planet. Hence, the expression for centripetal force is F c = m v 2 r The gravitational force can be balanced by the centripetal force. Therefore, G M m r 2 = m v 2 r … ( 1 ) According to the expression of orbital velocity of star, v = 2 π r T v 2 = 4 π 2 r 2 T 2 Equation (1) becomes G M m r 2 = m r 4

11th Edition

ISBN: 9781119573968

Author: David Halliday

Publisher: WILEY

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

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Chapter 13, Problem 80P

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To find:

a) Show that the shortest period rotation of planet is T=3πGρ

b) Calculate the rotation period of planet.

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Chapter 13, Problem 79P

Chapter 13, Problem 81P

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Chapter 13 Solutions

Fundamentals Of Physics

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a) Show that the shortest period rotation of planet is T = 3 π G ρ b) Calculate the rotation period of planet.

Solution Summary: The author explains Newton's law of gravitation and centripetal force to calculate the rotation period of the planet.

Concept explainers

To find:

a) Show that the shortest period rotation of planet is T=3πGρ

b) Calculate the rotation period of planet.

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Chapter 13 Solutions

a) Show that the shortest period rotation of planet is T = 3 π G ρ b) Calculate the rotation period of planet.

Solution Summary: The author explains Newton's law of gravitation and centripetal force to calculate the rotation period of the planet.

Concept explainers

To find: a) Show that the shortest period rotation of planet is T=3πGρ b) Calculate the rotation period of planet.

Want to see the full answer?

Chapter 13 Solutions

To find:

a) Show that the shortest period rotation of planet is T=3πGρ

b) Calculate the rotation period of planet.