# Gravitational Mechanics!

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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