Question

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?

Answer 1

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.

Answer 2

Thank you very much!