March 26, 2017

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Calculate the tidal force experienced by Io. How does it compare to the tidal force experienced by the Moon due to the Earth? What would the Earth-Moon distance (i.e., distance between their centres) need to be in order for the Moon to experience similar tidal forces to those experienced by Io due to Jupiter?

  • astronomy - ,

    According to ,
    the force (or differential acceleration between opposite sides of a spherical body) is
    2 G r M/R^3
    where R is the distance to the body exerting the gravitational force, M is its mass, G is the universal constant of gravity, and r is the radius of the body for which the tidal force is being calculated.

    The ratio of tidal forces of Io to those of our moon is
    Force(Io)/Force(moon) = (r/r')(M/M')*(R'/R)^3
    r = Io radius
    r' = Moon radius
    M = Jupiter mass
    M' = Earth mass
    R = Io-Jupiter distance
    R' = Earth-Moon distance

    Use that formula to answer both questions. There are a lot of numbers to look up.

    For your second question, assume the tidal force ratio is 1 and solve for the R'/R value needed to make that happen.

  • astronomy - ,

    Thank you very much!

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