Why is the gravitational field strength halfway up Mount Everest the same as at sea level at the equator?I'm trying to understand Newton's Laws and...

The key to answering this question is to understand that
the earth is not a perfect sphere but rather an oblate spheroid. That means that its
diameter is relatively larger around the equator than the diameter measured from pole to
pole. The difference in diameters is about 25 miles, whereas Mt. Everest is about 6
miles high.

Now the universal law of gravitation does state
that the force is proportional to the mass and inversely proportional to the square of
the distance between two objects.

However, because the
earth is deformed, the distance from the center of the earth to Mt. Everest is about the
same as the distance from the center of the earth to the surface of the sea at the
equator.  Therefore, the gravitational field strength is the same at both
points.