Gravitation

The gravitational acceleration experienced by a point particle at a height above the Earth's surface, denoted as , and at a depth below the Earth's surface, denoted as , are dependent on the Earth's radius and its uniform mass density. The Earth's gravitational acceleration inside and outside its surface can be described mathematically.The gravitational acceleration inside the Earth at depth is given by: The gravitational acceleration at a point outside the Earth at height (often confused with depth here trivialized) is calculated using: To find the ratio : Simplifying further: This reduces to: Let , so: For critical points: Factoring gives: This implies critical points at: Given that the distance cannot be negative, we dismiss . Therefore, the maximum value of the ratio occurs at: Visually, this behavior can be represented by the graph shown below:

Let us first understand all the given information.$ v_{\min } A B C A v_x v_0 v_0 2 v_{\text {min }} v_{\min } m $$ $