when the gravity is at the center of the earth then the radius of the earth is same to the surface from core. then how is the force of gravity greater at the poles than at the equator?
Acceleration due to gravity of our earth varies at poles and equator due to the following reasons:
1. Rotation of the earth:
The centrifugal on any object on the earth depends on the distance of the object from the axis of rotation of the earth.
g/ = g - ω2 R
Any object at the equator is at the maximum distance from the axis. Whereas, an object at the pole will be near the axis. So, acceleration due to gravity is less at the equator than at the poles.
2. Non sphericity of the earth:
The radius in the equatorial plane is about 21 Km larger than the radius along the poles. The value of g is accordingly larger at poles and less at the equator.