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The Motion Of Objects Thrown Away From Earth

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How can the function for distance over time be found for an object which is thrown away from Earth? Acceleration as a function of distance is

g = GM/r^2,

where GM is constant, so let c = GM, then

g = c/r^2.

Then I wondered, maybe the formula for distance can be found by solving the differential equation

r'' = c/r^2?

I have never studied differential equations, so I have no idea about it, even to whether I can really say r'' = c/r^2.

If someone can elucidate my mind, I shall be grateful.

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