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## Main Question or Discussion Point

Suppose an object is moving toward the Earth(with a direction perpendicular to the Earth's surface) at an initial speed

I tried solving this second order differential equation:

d

I ended up with a mess of stuff. And it seems impossible to make

**v**, starting from a distance_{0}**r**. The object also experiences gravitational acceleration. Is it possible to obtain an expression of_{0}**r**as a function of t? In other words, whats the distance from the Earth at a time t?I tried solving this second order differential equation:

d

^{2}**r**/dt^{2}= GM/**r**^{2}I ended up with a mess of stuff. And it seems impossible to make

**r**the subject of the equation.