Gravitational Mechanics!

Consider a hypothetical planet of mass $$M$$ and radius $$R$$ in deep space such that there is no interaction of any other celestial body on any object 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: $\large t = \frac{R^{\frac{a}{b}}(\pi^{c} +d )}{e\sqrt{GM}}$ where $$a$$, $$b$$, $$c$$, $$d$$, and $$e$$ are positive integers, find the value of $$a+b+c+d+e$$.

Details And Assumptions

• Assume the planet has no atmosphere.
• The object is not given any initial energy, except the potential energy it gains.
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