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
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.

- astronomy -
**roach**, Sunday, November 20, 2011 at 2:03pm
Thank you very much!

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