Posted by roach on Sunday, November 20, 2011 at 1:59am.
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 - drwls, Sunday, November 20, 2011 at 2:44am
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 - roach, Sunday, November 20, 2011 at 2:03pm
Thank you very much!
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