Explanation Given: W = 6000 − l b Geosynchronous orbit: r 1 = 3960 + 200 = 4160 mi = 21.965 × 10 6 ft r 2 = 3960 + 22 , 000 = 25 , 960 mi = 21.965 × 10 6 ft Total energy E = T + V E = 1 2 m v 2 − G M m r M , mass of earth m , mass of satellite Newton’s second law, F = m a n : G M m r 2 = m v 2 r ⇒ v 2 = G M r T = 1 2 m v 2 = m G M 2 r V = − G M m r E = T + V E = 1 2 G M m r − G M m r = − G M m r G M = g R E 2 E = − g R E 2 m r = − 1 2 R E 2 W r Where, W = m g E = − g R E 2 m r = − 1 2 ( 6000 − l b ) ( 20 To determine (b) Energy required for placing the satellite in the same orbit by launching it from the surface of the earth.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Conservation of Energy

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Chapter 13.2, Problem 13.87P

To determine

(a)

Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000 mi above the surface of the earth.

To determine

(b)

Energy required for placing the satellite in the same orbit by launching it from the surface of the earth.

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Chapter 13.2, Problem 13.86P

Chapter 13.2, Problem 13.88P

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(a) Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22 , 000 mi above the surface of the earth.

Solution Summary: The author explains the additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000-mi above the surface of the earth.

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(a)

Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000 mi above the surface of the earth.

(b)

Energy required for placing the satellite in the same orbit by launching it from the surface of the earth.

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Chapter 13 Solutions

(a) Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22 , 000 mi above the surface of the earth.

Solution Summary: The author explains the additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000-mi above the surface of the earth.

Concept explainers

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(a) Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000 mi above the surface of the earth.

(b) Energy required for placing the satellite in the same orbit by launching it from the surface of the earth.

Want to see the full answer?

Chapter 13 Solutions

(a)

Additional energy required to place the satellite in a geosynchronous orbit at an altitude of 22,000 mi above the surface of the earth.

(b)

Energy required for placing the satellite in the same orbit by launching it from the surface of the earth.