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Io, one of the moons of Jupiter, circles Jupiter once every 1.77 days. The radius of its orbit is 4.22 X 108 m. If this orbit is circular, what is the mass of Jupiter?

  • physics -

    m=mass of satellite, M=mass of Jupiter
    R=4.22•10^8 m, T= 1.74 days=1.74•24•3600 seconds,
    G =6.67•10^-11 N•m²/kg²,

    F= G•M•m /R²
    Centripetal acceleration
    a=v²/R =(2•π•R/T)² /R=4• π²•R/T². (1)
    Newton’s 2Law
    F=m•a = G•M•m /R².
    a= G•M /R² (2)
    Equate (1) and (2)
    4• π²•R/T² = G•M /R²
    M= 4• π²•R³/T²•G = ...

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