Explanation Given information: Sun mass: M s u n = 332.8 × 10 3 M e a r t h Venus relative position: θ v = ? Venus radius of orbit, r v = 67.2 × 10 6 m i = 354.816 × 10 9 f t Earth radius of orbit, r E = 93 × 10 6 m i Earth radius, R E A R T H = 3960 m i = 20.908 × 10 6 f t Let elliptical transfer orbit periodic time be τ T R To travel from earth to Venus, the time taken by the probe is t P R O B E = 1 2 τ T R Applying Kepler’s 3 r d law, τ 2 T R τ 2 E A R T H = a 3 T R a 3 E A R T H Here, a T R = 1 2 ( 93 × 10 6 + 67.2 × 10 6 ) = 80.1 × 10 6 m i Since, a E A R T H ≈ r E τ T R = ( a T R r E ) 3 / 2 τ E A R T H ∴ t P R O B E = 1 2 ( a T R r E ) 3 / 2 τ E A R T H We know, τ E A R T H = 365.25 ∴ t P R O B E = 1 2 ( a T R r E ) 3 / 2 × 365

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 12, Problem 12.132RP

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The Venus relative position with respect to earth.

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