Gravitational Field Of The Earth

The acceleration due to gravity at a height above the surface of the earth and at a depth below the surface can be given by the following relationships: At height , the acceleration due to gravity is: where is the radius of the earth. At depth , the acceleration due to gravity is: where is the acceleration due to gravity at the surface. Given that the gravity at the height is the same as at the depth , we can equate : Simplifying: Now solving for . Let (radius of Earth). First calculate and square it: Now substitute this value back into the equation: Thus, the depth is approximately 14 km.