(a) Explanation Given information: The radius of the earth ( R ) is 3,960 mi. The altitude of orbit of satellite from the surface of the earth ( r 1 ) is 22,240 mi. The altitude of orbit A from the surface of the earth ( r 2 ) is 185 mi. The increasing speed ( Δ v B ) of the satellite is 4,810 ft/s. Calculation: Find the radius of the orbit A ( r A ) using the equation: r A = R + r 2 Substitute 3,960 mi for R and 185 mi for r 2 . r A = 3 , 960 + 185 = 4 , 145 mi × 5 , 280 ft 1 mi = 21.8856 × 10 6 ft Find the radius of the satellite orbit B ( r B ) using the equation: r B = R + r 1 Substitute 3,960 mi for R and 22,240 mi for r 1 . r B = 3 , 960 + 22 , 240 = 26 , 200 mi × 5 , 280 ft 1 mi = 138.336 × 10 6 ft Find the product of the constant of gravitation G and the mass M of the earth [ ( G M ) earth ] using the equation: G M = g R 2 Here, g is the acceleration due to gravity and R is the radius of the earth. Substitute 32.2 ft/s 2 for g and 3 , 960 mi for R . G M = ( 32.2 ) ( 3 , 960 mi × 5 , 280 ft 1 mi ) 2 = 14.077 × 10 15 ft 3 /s 2 Find the speed on the circular orbit through A using the equation: ( v A ) circ = G M r A Substitute 14 (b) To determine Find the increase in speed resulting from the first firing at A .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Chapter 12.2, Problem 12.88P

(a)

To determine

Find the speed of the satellite as it approaches B on the elliptic transfer orbit.

(b)

To determine

Find the increase in speed resulting from the first firing at A.

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Chapter 12.2, Problem 12.87P

Chapter 12.2, Problem 12.89P

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Find the speed of the satellite as it approaches B on the elliptic transfer orbit.

Solution Summary: The author calculates the speed of the satellite as it approaches B on the elliptic transfer orbit.

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Find the speed of the satellite as it approaches B on the elliptic transfer orbit.

Find the increase in speed resulting from the first firing at A.

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Chapter 12 Solutions