# Gravity Effectively Isn't Constant

Consider a spherical planet with radius $$R$$, that is rotating with angular velocity $$\omega$$ about it's axis. The lattitude $$x$$ of a point $$P$$ that is a height of $$h$$ away from the equator, is denoted as $$x = \frac{h}{R}$$. Suppose that the acceleration due to gravity at the North pole is $$g$$, then what is the effective acceleration ar point $$P$$ in terms of the latitude $$x$$?

• $$T \cos x$$ is the Centrifugal force along the tangent for rotation.
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