Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.