A discussion regarding the duration of motion in a non-uniform gravitational field

Assume that an object is thrown vertically from a planet's surface with a low velocity. Using basic kinematics theory, it is easy to calculate the duration of the motion. In this type of problem, the acceleration due to gravity is considered to be uniform, because the motion is taking place near the planet's surface. By contrast, if we assume that an object is launched vertically from a planet's surface at its escape velocity, how much time does it take for the object to cover a specific distance? In addition, is it possible to find a simplified way to calculate the duration of the motion or to derive the equations of motion in a non-uniform gravitational field? In this paper, we provide a simplified analysis that can be used to answer these questions. (paper)