Gravitational Mechanics!

Classical Mechanics Level 3

Consider a hypothetical planet of mass \(M\) and radius \(R\), in deep space such that there's no interaction of any other celestial body on any objects nearby it. Now imagine , an object of mass \(m\) taken up to the height of \(2R\) from the planet's center and then released. Find the time taken by it to hit the surface. If the time taken can be expressed as: \[ \dfrac{R^{\frac{a}{b}}(\pi^{c} +d )}{e\sqrt{GM}} \] where \(a,b,c,d,e\) are positive integers, find the value of \(a+b+c+d+e\)

\(\text{Details And Assumptions}\)
\(1.)\) Assume the planet has no atmosphere
\(2.)\) The Object is not given any initial energy, except the potential energy it gains


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