(a) Explanation Given information: The altitude of point B ( h B ) from the surface of the planet is 280 mi. The eccentricity ( ε ) of the trajectory is 1.031. The radius of the Jupiter ( R ) is 44,423 mi. The mass of the Jupiter ( M J ) is 1.30 × 10 26 slug . The velocity ( v B ) of the probe at B forms an angle with the direction of OA is 82.9 ° The radius ( r A ) of the point A is 44,000 mi. Calculation: Find the radius ( r B ) of the point B from the center of the Jupiter using the equation: r B = R + h B Substitute 44,423 mi for R and 280 mi for h B . r B = 44 , 423 + 280 = 44 , 703 mi The angle of hyperbolic trajectory ( θ A ) at A is 0 ° . Write the equation of motion satellite and the planet at A of elliptical trajectory. 1 r A = G M j h 2 ( 1 + ε cos θ A ) Here, h is the angular momentum per unit mass and ε is the eccentricity of trajectory. Substitute 0 ° for θ A . 1 r A = G M j h 2 ( 1 + ε cos 0 ° ) h 2 G M j = r A ( 1 + ε ) (1) Write the equation of motion satellite and the planet at B of elliptical trajectory (b) To determine Find the speed ( v B ) of the probe at B .

Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977206

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

Publisher: McGraw-Hill Education

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Chapter 12.3, Problem 12.117P

(a)

To determine

Find the angle AOB.

(b)

To determine

Find the speed (vB) of the probe at B.

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Chapter 12.3, Problem 12.116P

Chapter 12.3, Problem 12.118P

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Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics

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Find the angle AOB .

Solution Summary: The author calculates the angle AOB using the equation of motion satellite and the planet at A of elliptical trajectory.