posted by roach on .
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?
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.
Thank you very much!