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Donald,
For your students you might look at:
https://www.youtube.com/watch?v=lNJ2icc1fPk
The YouTube video neglects a small correction by assuming that N points inbob
the radial direction. This is the old question of "which way does a plumb
point" on a rotating earth point? The correct answer is to do a vector sumof
g_0 (called g_s in the video) and g_0*A (called w_e^2*R_e in the video).
Then they agree:
dropping the A^2 term in Polvani we have g(theta) = g_0*sqrt(1-
2A*cos^2(theta)) = g_0*sqrt(1-2A*sin^2(lambda)) switching to co-latitude
lambda rather than latitude theta
which is approximately g*0*(1-A*sin^2(lambda)), the same result as in the
video.