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The reason why there is a difference between free-fall acceleration is a centrifugal force.
I attached a diagram that shows how this force aligns with the force of gravity.
From the diagram we can see that:
Where g' is the free-fall acceleration when there is no centrifugal force, r is the radius of the planet, and w is angular frequency of planet's rotation.
is the latitude.
We can calculate g' and wr^2 from the given conditions in the problem.
Our final equation is:
Colatitude is:
The answer is:
I attached a diagram that shows how this force aligns with the force of gravity.
From the diagram we can see that:
Where g' is the free-fall acceleration when there is no centrifugal force, r is the radius of the planet, and w is angular frequency of planet's rotation.
We can calculate g' and wr^2 from the given conditions in the problem.
Our final equation is:
Colatitude is:
The answer is: