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B3NR4Y
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Homework Statement
On a certain planet, which is perfectly spherically symmetric, the free-fall acceleration has magnitude g = g0 at the North Pole and g = λ g0 at the equator (lambda is between zero and 1). Find g as a function of theta, the colatitude angle.
Homework Equations
[tex] \vec{g} = \vec{g_0} + (\Omega \times R_E ) \times \Omega [/tex]
The Attempt at a Solution
The colatitude angle at the North Pole is 0 degrees, and at the equator it is 90 degrees.
I subtracted the vector g0 from both sides, to only have to deal with the magnitude of the cross product term. The magnitude of that term is Ω2 RE sin2 θ, which is equal to zero for theta equals 0, and for theta = 90 it equals lambda minus one. I'm not sure where to go from here to get what the book gives.