Explanation Given: Period of Europa, T = 3.55 Earth days Period of Ganymede, T = 7.16 Earth days Period of Callisto, T =16.7 Earth days The mass of the Jupiter, M J =1 .9×10 27 kg . Formula Used: The centrifugal force is equal to gravitational force. M ( 2 π T ) 2 R = G M J M R 2 R = ( G M J M R 2 ) 1 3 Where, M -mass of moon R -the distance between the moon and Jupiter. T -period of the moon. Calculation: R = ( 6.673 × 10 - 11 × 1.9 × 10 27 4 π 2 ) 1 3 T 2 3 R = 1.475 × 10 5 T 2 3 For IO, period is: T I O =1 .77 days = ( 1.77 × 24 × 60 × 60 ) s Substitute the value and solve: R I O =1 .475×10 5 ( 1 .77×24×60×60 ) 2 3 m = 421 .8×10 3 km For Europa: T E U = 3

Physics: Principles and Applications -- Pearson e Text Instant Access (Pearson+)

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ISBN: 9780137679065

Author: Douglas Giancoli

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