Posted by roach on Sunday, November 20, 2011 at 1:59am.
According to
http://en.wikipedia.org/wiki/Tidal_force ,
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
where
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.
Thank you very much!
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