Explanation Given information: h 1 = 225 m i ϕ B = 60 o h 2 = 40 m i Formula used: G M = g R 2 T = 1 2 m v 2 V = − G M m r L = m v r Calculation: As we have, r A = 3960 m i + 225 m i = 4185 m i r A = 4185 m i × 5280 f t / m i = 22097 × 10 3 f t And, r B = 3960 m i × 40 m i = 4000 m i ⇒ r B = 4000 × 5280 = 21120 × 10 3 f t ⇒ R = 3960 m i = 20909 × 10 3 f t We know that: G M = g R 2 Put the values in the above equation; ⇒ G M = ( 32.2 f t / s 2 ) ( 20909 × 10 3 f t ) 2 ⇒ G M = 14.077 × 10 15 f t 3 / s 2 According to conservation of energy; ⇒ T A = 1 2 m v A 2 ⇒ V A = − G M m r A Put the values in the above equation; ⇒ − 14.077 × 10 15 m 22097 × 10 3 ⇒ − 637.1 × 10 6 m ⇒ T B = 1 2 m v B 2 ⇒ V B = − G M m r B ⇒ − 14 To determine (b) The sped at point B at given condition.

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 13.110P

To determine

(a)

The speed of the vehicle as it leaves its circular orbit at A at given condition.

To determine

(b)

The sped at point B at given condition.

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Chapter 13.2, Problem 13.109P

Chapter 13.2, Problem 13.111P

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A communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the rotation of the earth,which is approximately 24 hours. Determine the satellite’s altitude h above the earth’s surface and its orbital speed.

A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17 440 km and 13 950 km, respectively. Knowing that the speed of the satellite at point C is 4.78 km/s, determine (a) the speed at point A, the perigee, (b) the speed at point B,the apogee.

A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17,440 km and 13,950 km, respectively. Knowing that the speed of the satellite at Point C is 4.78 km/s, determine (a) the speed at Point A, the perigee, (b) the speed at Point B, the apogee. 606 km R = 6370 km 13 950 km B, A 17 440 km 17 440 km

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Vector Mechanics for Engineers: Dynamics

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(a) The speed of the vehicle as it leaves its circular orbit at A at given condition.

Solution Summary: The author calculates the speed of the vehicle as it leaves its circular orbit at A at given condition.