Explanation Given: r A = 607.2 × 10 6 ft r B = 966.2 × 10 6 ft v ' A , speed of spacecraft in the elliptical orbit after its speed has been decreased. Elliptical orbit between A and B, Conservation of energy, Point A: T A = 1 2 m v ' A 2 V A = − G M sat m r A M sa , mass of Saturn; calculate G M sa from the speed of Tethys in its circular orbit. v circ = G M sat r G M sat = r B v circ 2 G M sat = ( 966.2 × 10 6 ft ) ( 37.2 × 10 3 ft ) 2 = 1.337 × 10 18 ft 3 / s 2 V A = − ( 1.337 × 10 18 ft 3 / s 2 ) m ( 607.2 × 10 6 ft ) V A = − 2.202 × 10 9 m Point B: T B = 1 2 m v B 2 V B = − G M sat m r B = − ( 1 To determine (b) Speed of spacecraft when it reaches the orbit of Tethys at B.

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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Chapter 13.2, Problem 13.102P

To determine

(a)

Decrease in speed required by the spacecraft at A to achieve the desired orbit.

To determine

(b)

Speed of spacecraft when it reaches the orbit of Tethys at B.

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Chapter 13.2, Problem 13.101P

Chapter 13.2, Problem 13.103P

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Vector Mechanics for Engineers: Dynamics

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(a) Decrease in speed required by the spacecraft at A to achieve the desired orbit.

Solution Summary: The author explains the decrease in speed required by the spacecraft at A to achieve the desired orbit.