(a) Explanation The distance from the center of the Earth to location B is calculated from Pythagorean Theorem is, r B = r A B 2 + r origin 2 (I) Here, r B is the distance from the center of the Earth to location B, r A B is the distance of the elliptical path from the location A to the location B, and r origin is the distance from the origin of the path to center of the Earth. Write the expression for kinetic energy of the satellite at the point A. K A = 1 2 m v A 2 (II) Here, K A is the kinetic energy of the satellite at the point A, m is the mass of the satellite and v A is the speed of the satellite at the position A. Write the expression for gravitational potential energy of the satellite at point A. U A = − G M E m r A (III) Here, U A is the gravitational potential energy of the satellite at point A, G is the gravitational constant, M E is the mass of the Earth, and r A is the distance from the center of the Earth to location A. Write the expression for kinetic energy of the satellite at the point B. K B = 1 2 m v B 2 (IV) Here, K B is the kinetic energy of the satellite at the point B and v B is the speed of the satellite at the position B. Write the expression for gravitational potential energy of the satellite. U B = − G M E m r B (V) Here, U B is the gravitational potential energy of the satellite at point B and r B is the distance from the center of the Earth to location B. Conclusion: According to the law of conservation of energy, total energy of the satellite at the point A is equal to the point at B. E A = E B K A + U A = K B + U B Substitute the equation (II), (III), (IV) and (V) in the above equation (b) To determine The speed of the satellite at the apogee C.

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Central Force

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Chapter 8, Problem 99GP

(a)

To determine

The speed of the satellite at the point B.

(b)

To determine

The speed of the satellite at the apogee C.

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Chapter 8, Problem 98GP

Chapter 8, Problem 100GP

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Physics for Scientists and Engineers with Modern Physics

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The speed of the satellite at the point B.

Solution Summary: The author calculates the distance from the center of the Earth to location B based on the Pythagorean Theorem.

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The speed of the satellite at the point B.

The speed of the satellite at the apogee C.

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Chapter 8 Solutions