(a) Explanation Given information: The radius of point A is r 0 The radius of point B is r 1 Calculation: Refer Equation (12.37’) in text book. The trajectory angle at minimum radius is zero ( θ A = 0 ) . Consider the minimum radius 1 r 0 = G M h 2 ( 1 + ε cos θ ) Here, G is the gravitational constant, M is the planet, h is the angular momentum per unit mass of the satellite, C is the constant, and θ A is the trajectory angle at A . Substitute 0 for θ A . 1 r 0 = G M h 2 ( 1 + ε cos 0 ) 1 r 0 = G M h 2 ( 1 + ε ) (1) The trajectory angle at maximum radius is 180 ° ( θ B = 0 ) . Consider the maximum radius. 1 r 1 = G M h 2 ( 1 + ε cos θ ) Here, θ B is the trajectory angle at B . Substitute 180 ° for θ B . 1 r 1 = G M h 2 ( 1 + ε cos 180 ° ) 1 r 1 = G M h 2 ( 1 − ε ) (2) Find the eccentricity ( ε ) of the elliptic orbit (b) To determine Find the approximate maximum distance from the sun reached by comet Hyakutake

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 12.3, Problem 12.119P

(a)

To determine

Express the eccentricity ε of the elliptic orbit.

(b)

To determine

Find the approximate maximum distance from the sun reached by comet Hyakutake

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Chapter 12.3, Problem 12.118P

Chapter 12.3, Problem 12.120P

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Vector Mechanics for Engineers: Statics and Dynamics

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Express the eccentricity ε of the elliptic orbit.

Solution Summary: The author explains the expression of eccentricity epsilon of the elliptic orbit.

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Express the eccentricity ε of the elliptic orbit.

Find the approximate maximum distance from the sun reached by comet Hyakutake

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Chapter 12 Solutions