(a) Explanation Given information: The radius of circular orbit ( r A ) is 1,400 mi. The radius of smaller orbit ( r B ) is 1,300 mi. The reducing speed [ ( Δ v ) A ] is − 86 ft/s . The mass of moon ( M ) is 5.03 × 10 21 lb ⋅ s 2 /ft . Calculation: Write the general equation of velocity in circular orbits ( v ). v = G M r (1) Find the speed of the vehicle [ ( v A ) 1 ] at A in circular orbit using Equation (1). ( v A ) 1 = G M r A Substitute 34.4 × 10 − 9 ft 4 /lb ⋅ s 4 for G , 5.03 × 10 21 lb ⋅ s 2 /ft for M , and 1,400 mi for r A . ( v A ) 1 = 34.4 × 10 − 9 × 5.03 × 10 21 ( 1 , 400 mi × 5 , 280 ft 1 mi ) = 4.8382 × 10 3 ft/s Find the speed of the vehicle [ ( v B ) 2 ] at B in circular orbit using Equation (1). ( v B ) 2 = G M r B Substitute 34.4 × 10 − 9 ft 4 /lb ⋅ s 4 for G , 5.03 × 10 21 lb ⋅ s 2 /ft for M , and 1,300 mi for r A . ( v B ) 2 = 34.4 × 10 − 9 × 5.03 × 10 21 ( 1 , 300 mi × 5 , 280 ft 1 mi ) = 5 (b) To determine Find the amount by which its speed should be reduced as vehicle approaches B to insert it into the smaller circular orbit.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 12.2, Problem 12.89P

(a)

To determine

Find the speed of the vehicle as it approaches B on the elliptic path.

(b)

To determine

Find the amount by which its speed should be reduced as vehicle approaches B to insert it into the smaller circular orbit.

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Chapter 12.2, Problem 12.88P

Chapter 12.2, Problem 12.90P

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Find the speed of the vehicle as it approaches B on the elliptic path.

Solution Summary: The author calculates the general equation of velocity in circular orbits using Equation (1).

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Find the speed of the vehicle as it approaches B on the elliptic path.

Find the amount by which its speed should be reduced as vehicle approaches B to insert it into the smaller circular orbit.

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Chapter 12 Solutions